Research ArticleMechanical Properties of Steels for Cold-Formed SteelStructures at Elevated Temperatures
Zhen Nie1 Yuanqi Li 12 and Yehua Wang12
1Department of Structural Engineering Tongji University Shanghai 200092 China2State Key Laboratory of Disaster Reduction in Civil Engineering Shanghai 200092 China
Correspondence should be addressed to Yuanqi Li liyqtongjieducn
Received 12 September 2019 Revised 28 April 2020 Accepted 25 May 2020 Published 1 July 2020
Academic Editor Michael Yam michaelyampolyueduhk
Copyright copy 2020 Zhen Nie et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
It is highly important to clarify the high-temperature mechanical properties in the design of cold-formed steel (CFS) structures underfire conditions due to the unique deterioration feature in material properties under fire environment and associated reduction to themechanical performance of members is paper presents the mechanical properties of widely used steels for cold-formed steelstructures at elevated temperatures e coupons were extracted from original coils of proposed full annealed steels (S350 and S420with nominal yielding strengths 280MPa and 350MPa) and proposed stress relieving annealed steels (G500 with nominal yieldingstrength 500MPa) for CFS structures with thickness of 10mm and 12mm and a total of nearly 50 tensile tests were carried out bysteady-state test method for temperatures ranging from 20 to 700degC Based on the tests material properties including the yieldstrengths ultimate strengths the elasticity modulus and the stress-strain curve were obtained Meanwhile the ductility of steels forCFS structures was discussed en the temperature-dependent retention factors of yield strengths and elasticity modulus werecompared to those provided by design codes and former researchers Finally a set of prediction equations of the mechanicalproperties for steels for CFS structures at elevated temperatures was proposed depending on existing tests data
1 Introduction
As the main components in light weight steel structuralbuildings worldwide cold-formed thin-walled steel (CFS)members are manufactured from cold-rolled thin-walledsteel sheets or strips approximately from 03mm to 30mmthickness with grades from 200 to 1000 [1ndash5]e applicablesteels for CFS structures are specified in codes [1ndash5] withdifferent elongation and nominal yield strength In thesestandards [1ndash5] elongation of 10 is a significant boundaryfor dividing the category of steel materials In the meantime450MPa is also a rough line for separating massive steelsused for CFS structures [1ndash5] Generally the steel coils formanufacturing of CFS sections are made from both hot-rolled steel sheets and cold-rolled steel sheets [1ndash5] in whichcold-rolled steel sheets may involve the annealing processAlso for cold-forming process into cross section shapesstress-hardening effect takes place leading to reduced duc-tility of the raw material Hence annealing [6] may be
involved after the cold-forming process to improve themechanical properties or to relief the residual stress Steelswith a specified minimum elongation of 10 or greater arefull annealed steels and the remaining part is the stressrelieving annealed steels (the classification approach isproposed in this paper based on the manufacturing processof steels) For instance G250 and G300 steels are widely usedin North America Australia and Europe [1ndash4] S280 with anominal yielding strength of 280MPa and S350 with anominal yielding strength of 350MPa steels suggested byChinses code [5] belong to the full annealed steels On theother hand G550 class steels including G450 G500 andG550 steels [2 5] are typical stress relieving annealed steels
At ambient temperatures besides the yield strengththere is a significant difference on ductility between the fullannealed and stress relieving annealed steels as mentionedabove ese different characteristics of those two kinds ofsteels are determined by the variety in the manufacturingprocess especially heat treatment procedures [6]
HindawiAdvances in Civil EngineeringVolume 2020 Article ID 9627357 18 pageshttpsdoiorg10115520209627357
At elevated temperatures the strain hardening in cold-rolled thin-walled steels is relieved with time accordinglythe strength reduction of this type of steel may be higherthan that of hot-rolled steels Meanwhile these steels de-velop faster heating rates for having higher thermal con-ductivity ratio and thinner thickness than hot-rolled steelsHowever current specifications [7ndash10] of steel structuralfire designs on the mechanical properties at elevatedtemperatures were based on hot-rolled steels Particularlyan integrated provision of high-temperature materialmodels for the entire cold-formed thin-walled steel familyhas not been provided in current Chinese CFS design codes[5] In recent years there is already a considerable databaseestablished by global researches on material properties offlat steel sheets for CFS structures at elevated temperatures[11ndash19] In general tested specimens range from 050mmto 250mm thick with yield strengths from 250MPa to550MPa at ambient temperature However no systematicdiscussion on classification of steels for CFS structures hasbeen conducted when exploring temperature-dependentmechanical properties From the perspective of steel gradesand the ductility at ambient temperature tested steels incurrent researches can be divided into two groups fullannealed steels [11 12 14 15 17ndash19] (with nominalyielding strength under 450MPa and elongation greaterthan 10) and stress relieving annealed steels [12ndash16] (withnominal yielding strength over 450MPa and elongationless than 10)
is paper presents a detailed experimental investigationof the material properties of two full annealed flat steel sheets(S350 and S420) and one stress relieving annealed flat steelsheet (G500) cut from original steel coils Here S350 is themost common grade in past tests [11 17 18] however fewdata exist on S420 and G500 steels at elevated temperatureen by means of comparative study discussion is con-ducted on the failure mode ductility constitutive rela-tionships and retention factors for both full annealed steelsand stress relieving annealed steels Meanwhile after ac-cumulating the existing test data so far further comparisonis made on the reduction trend of mechanical properties atelevated temperatures for two different group steels Finallya set of prediction equations of mechanical properties for theentire family of steels used in CFS structures at elevatedtemperatures is proposed
2 Manufacturing Process of Steels forCFS Structures
Cold-rolled thin-walled steels are manufactured by coldworking mild sheet steels on cold reducing roll to a thicknessranging from 03mm to 30mm Cold reducing producesdistinct deformations of the microcosmic grain texture andstructure which cause a strengthening in strength andhardness a decrease in FuFy ratio and a reduction inductility e effects of cold working are cumulative andharmful for steels that are used for structural membersus it is necessary to change and recover the grainstructure and to control the steel properties through sub-sequent heat treatment after cold rolling [6]
e process of heat treatment is carried out first byheating the material and then cooling it in the brine waterand oil e purpose of heat treatment is to soften the metalto change the grain size and structure to modify theproperties of the material and to relieve the stress setup inthe material after hot and cold working e various heattreatment processes commonly employed in engineeringpractice include annealing normalizing quenching andtempering Specifically annealing is the most commonlyused heat treatment method in manufacturing of steels forCFS structures Further based on the heating temperatureswhen annealing is carried out there are several typesannealing as follows [20 21]
Full annealing - e steel is heated to above the criticaltemperature Ac3 (eutectoid point 700degCndash750degC for lowcarbon steel) for some time and then cooled in a specific rateHere all the ferrite transforms into austenite Full annealedsteel is soft and ductile with no internal stress Partialannealing - e steel is heated to a temperature below to thecritical temperature Ac3 held at this temperature for sometime and then cooled slowly e purpose is to relive stressand lower the hardness of the steel Stress relieving annealing- e steel is heated to below the critical temperature Ac1(pearlite transforms into austenite at this temperature point500degCndash600degC for low carbon steel) held until the temper-ature is constant throughout its thickness then cooledslowly In this process the steel is stress relieved howeverrecrystallization does not occur Figure 1 illustrates thetypical annealing process of steels
Table 1 shows the chemical composition of tested metalsand Table 2 indicates the key temperatures duringmanufacturing procedures of tested steels which are ac-quired from original manufacturer It is easily find that theG500 steel experienced a significant lower annealing tem-perature than that of S350 and S420 steels us we cansafely say that S350 and S420 steels are fully annealed al-though the G500 steel is stress relieving annealed accordingto definitions of different annealing process In other wordsS350 and S420 steels are typical full annealed steels and theG500 steel is the stress relieving annealed steels Further-more after consulting CFS design standards provisions onmaterials collecting current tested steels information andexploring manufacturing process of steels commonly usedsteels for CFS steel structures are divided into two categoriesFull annealed steelsmdashsteels that experience full annealingprocess during manufacturing with nominal yieldingstrength under 450MPa and elongation greater than 10Stress relieving annealed steelsmdashsteels that experience stressrelieving annealing process during manufacturing withnominal yielding strength over 450MPa and elongation lessthan 10
Specifically stress relieving annealed steels are basicallyequivalent to G550 series steels widely used in Australianand Chinese building industry G550 series steels [2 5]including three grades (G450 with thickness greater than orequal to 15mm G500 with thickness greater than 10mmand less than 15mm and G550 with thickness less than orequal to 10mm) share similar features on mechanicalproperties at ambient temperatures [2 5] and these features
2 Advances in Civil Engineering
(high strength and low ductility) come from stress relievingannealing process [6] on production line
3 Experimental Study
31 Test Method Two major methods [11ndash19] may be usedto evaluate the mechanical behavior of construction mate-rials under high-temperature environment [11ndash19] emost common method currently used for investigating themechanical properties of steels at elevated temperatures isthe steady-state test in which the specimen is heated up to atarget temperature and held for a period of time until thetemperature is stable and uniform along the specimen thengradually subjected to a tensile load through to fractureAnother well-known method is the transient-state test inwhich the specimen applied a static load and then is heatedup slowly until failure criteria are met Most researchersemploy steady-state test technique since it is able to obtainstress-strain curves directly avoids fluctuant temperatureenvironment eliminates the influence of thermal expansionand generally saves resources According to current papersthere is no final conclusion [11 13 16] yet on which methodis more accurate for testing and predicting the mechanicalproperties of steels at elevated temperatures Also the mainfocus of this investigation is on the prediction of different
types of steels for CFS structures material properties underhigh temperatures erefore the steady-state test methodwas adopted in this test study
32 Test Specimens All coupons were cut by a wire cuttingmachine from original coils of S350 and S420 steels withnominal thickness of 10mm and G500 steels with nominalthickness of 12mm e dimension of the test specimenswas determined by ISO standard [22] as presented inFigure 2 ere were four small lugs at the edge of parallelpart for fixing extensometer system and two holes forpinning extension tension rods e metal thickness andgage width of the specimens were average of those valuesmeasured at three points within gauge lengths by using amicrometer before testinge base metal thickness and realgage width were used in the calculations of the initial crosssectional area
33 Test Devices and Procedure e experiment setup is theEDC222 Doli testing system shown in Figure 3 which is anintegrated closed loop digital control thermal and me-chanical testing system e tensile testing machine is anelectronic servo system with 100 kN capacity which wascalibrated before testing A high-temperature stove with a
Table 2 Manufacturing key temperatures of S350 S420 and G500 steels
Manufacturing key process Hot rolling (degC) Final rolling (degC) Annealing (degC)S350 1220 Room temperature 730S420 1200 Room temperature 700G500 1200 870 500
0
Tem
pera
ture
Time
Full annealing
Stress relieving annealing
Ac3
Ac1
Figure 1 Annealing process
Table 1 Chemical compositionlowast of S350 S420 and G500 steels
S350 (10mm) C () Mn () Al () S () Nb ()006 08 0045 002 0015
S420 (10mm) C () Mn () Al () S () Nb ()006 06 0045 0015 009
G500 (12mm) C () Mn () Al () S () B ()004 022 0038 0015 0002
lowastPercentage of element by mass
Advances in Civil Engineering 3
maximum temperature of 1200degC was employed in thetesting ree pairs of thermocouples binding separately onupper rod surface of specimen and lower rod in a range of150mm provided signals for accurate feedback control ofspecimen temperatures presented in Figure 4 In this way auniform temperature zone would be generated when thetemperature of three thermal couples remained stable ematerial for fixing thermocouples herein is the refractory heatinsulation ceramic fiber cloth band shown in Figure 5 A setof linear displacement gratings including high-temperatureresistance extension rods with a range of 125mm relative to50mm gauge was used to acquire the deformation of spec-imens between the gauge lengths e extensometer systemdetailed in Figure 6 created a 50mm gauge which was able tocollect more displacement data from the gauge scope beforethe coupon failed and was also calibrated before testing
Tensile coupon tests were carried out by adopting thesteady-state testmethod First the specimenwas heated up to apreselected temperature at a rate of 20degCmin Free thermalexpansion was allowed when heating up by keeping tensileload zero e temperature levels selected in this experiment
were 20degC 100degC 200degC 300degC 400degC 500degC 600degC and700degC e specimen was kept for 30sim40min at this constanttemperature until it reached the steady condition en theload was applied by controlling the displacement of theelectronic tensile grip until failure while maintaining the settemperature degreee displacement rate was set to 024mmmin which was specifically in elastic stage equivalent to astrain rate of 000007s as the minimum rate specified by ISOstandard [22] Moreover the sampling frequency was 10HzMost of the specimens were repeated twice for doublechecking Some additional experiments have been conductedfor verification (500degC for G500 steel) and supplement (350degCand 700degC for S350 and S420 steels) at several temperaturepoints Summary of tested specimens is present in Table 3
Temperature control is the most critical part in a high-temperature material test undoubtedly During tests pro-cedure real-time temperatures at three different pointsalong the specimen were detected by thermocouples andrecorded by data acquisition system Figure 7 gives a set oftypical temperature curves from three thermal couples overtime for a certain specimen at a certain temperature con-dition (take 500degC for example) At about 25min thecoupon temperature reached preselected 500degC in the grosshowever the temperature was quite uneven and unstable atthat point Until the 45min under the working of feedbackcontrol system the heat conduction and thermal convectionin the furnace were balanced dynamically Consequentlythree curves narrowed into a tiny range and the entirespecimen was clearly and steadily at the target temperatureAt that moment the coupon was ready to be elongated
4 Test Results and Discussion
In this section based on the purses of investigating thedifference between two kinds of cold-rolled thin-walledsteels on material properties at elevated temperatures theresults of tests are discussed in the way of comparison
41 Failure Mode Figures 8ndash10 present the failure modes ofthree grades of tested coupons All specimens fractured within
(a)
15 plusmn
02
15 plusmn 02
2 times ϕ8 0+0015
15 0+0
3
4 times R25 B
t22
46 (46)18 18
22
30
58
186
005 A
A
(b)
Figure 2 Test specimens and dimensions
Figure 3 Testing system (Doli control system)
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the gauge length scope expectedly which means the stress-strain curves recorded from data acquisition system were realstress-strain relationships within the gauge length Meanwhilethe carburization layer coated the specimen for all tested grades
when temperature reached 500degC illustrated by the darksurface of those coupons in Figures 8ndash10 is carburizationcoating was incompact and could be scratched using thin sheetmetal Specifically steel plates presented a blue brittle
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
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Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
At elevated temperatures the strain hardening in cold-rolled thin-walled steels is relieved with time accordinglythe strength reduction of this type of steel may be higherthan that of hot-rolled steels Meanwhile these steels de-velop faster heating rates for having higher thermal con-ductivity ratio and thinner thickness than hot-rolled steelsHowever current specifications [7ndash10] of steel structuralfire designs on the mechanical properties at elevatedtemperatures were based on hot-rolled steels Particularlyan integrated provision of high-temperature materialmodels for the entire cold-formed thin-walled steel familyhas not been provided in current Chinese CFS design codes[5] In recent years there is already a considerable databaseestablished by global researches on material properties offlat steel sheets for CFS structures at elevated temperatures[11ndash19] In general tested specimens range from 050mmto 250mm thick with yield strengths from 250MPa to550MPa at ambient temperature However no systematicdiscussion on classification of steels for CFS structures hasbeen conducted when exploring temperature-dependentmechanical properties From the perspective of steel gradesand the ductility at ambient temperature tested steels incurrent researches can be divided into two groups fullannealed steels [11 12 14 15 17ndash19] (with nominalyielding strength under 450MPa and elongation greaterthan 10) and stress relieving annealed steels [12ndash16] (withnominal yielding strength over 450MPa and elongationless than 10)
is paper presents a detailed experimental investigationof the material properties of two full annealed flat steel sheets(S350 and S420) and one stress relieving annealed flat steelsheet (G500) cut from original steel coils Here S350 is themost common grade in past tests [11 17 18] however fewdata exist on S420 and G500 steels at elevated temperatureen by means of comparative study discussion is con-ducted on the failure mode ductility constitutive rela-tionships and retention factors for both full annealed steelsand stress relieving annealed steels Meanwhile after ac-cumulating the existing test data so far further comparisonis made on the reduction trend of mechanical properties atelevated temperatures for two different group steels Finallya set of prediction equations of mechanical properties for theentire family of steels used in CFS structures at elevatedtemperatures is proposed
2 Manufacturing Process of Steels forCFS Structures
Cold-rolled thin-walled steels are manufactured by coldworking mild sheet steels on cold reducing roll to a thicknessranging from 03mm to 30mm Cold reducing producesdistinct deformations of the microcosmic grain texture andstructure which cause a strengthening in strength andhardness a decrease in FuFy ratio and a reduction inductility e effects of cold working are cumulative andharmful for steels that are used for structural membersus it is necessary to change and recover the grainstructure and to control the steel properties through sub-sequent heat treatment after cold rolling [6]
e process of heat treatment is carried out first byheating the material and then cooling it in the brine waterand oil e purpose of heat treatment is to soften the metalto change the grain size and structure to modify theproperties of the material and to relieve the stress setup inthe material after hot and cold working e various heattreatment processes commonly employed in engineeringpractice include annealing normalizing quenching andtempering Specifically annealing is the most commonlyused heat treatment method in manufacturing of steels forCFS structures Further based on the heating temperatureswhen annealing is carried out there are several typesannealing as follows [20 21]
Full annealing - e steel is heated to above the criticaltemperature Ac3 (eutectoid point 700degCndash750degC for lowcarbon steel) for some time and then cooled in a specific rateHere all the ferrite transforms into austenite Full annealedsteel is soft and ductile with no internal stress Partialannealing - e steel is heated to a temperature below to thecritical temperature Ac3 held at this temperature for sometime and then cooled slowly e purpose is to relive stressand lower the hardness of the steel Stress relieving annealing- e steel is heated to below the critical temperature Ac1(pearlite transforms into austenite at this temperature point500degCndash600degC for low carbon steel) held until the temper-ature is constant throughout its thickness then cooledslowly In this process the steel is stress relieved howeverrecrystallization does not occur Figure 1 illustrates thetypical annealing process of steels
Table 1 shows the chemical composition of tested metalsand Table 2 indicates the key temperatures duringmanufacturing procedures of tested steels which are ac-quired from original manufacturer It is easily find that theG500 steel experienced a significant lower annealing tem-perature than that of S350 and S420 steels us we cansafely say that S350 and S420 steels are fully annealed al-though the G500 steel is stress relieving annealed accordingto definitions of different annealing process In other wordsS350 and S420 steels are typical full annealed steels and theG500 steel is the stress relieving annealed steels Further-more after consulting CFS design standards provisions onmaterials collecting current tested steels information andexploring manufacturing process of steels commonly usedsteels for CFS steel structures are divided into two categoriesFull annealed steelsmdashsteels that experience full annealingprocess during manufacturing with nominal yieldingstrength under 450MPa and elongation greater than 10Stress relieving annealed steelsmdashsteels that experience stressrelieving annealing process during manufacturing withnominal yielding strength over 450MPa and elongation lessthan 10
Specifically stress relieving annealed steels are basicallyequivalent to G550 series steels widely used in Australianand Chinese building industry G550 series steels [2 5]including three grades (G450 with thickness greater than orequal to 15mm G500 with thickness greater than 10mmand less than 15mm and G550 with thickness less than orequal to 10mm) share similar features on mechanicalproperties at ambient temperatures [2 5] and these features
2 Advances in Civil Engineering
(high strength and low ductility) come from stress relievingannealing process [6] on production line
3 Experimental Study
31 Test Method Two major methods [11ndash19] may be usedto evaluate the mechanical behavior of construction mate-rials under high-temperature environment [11ndash19] emost common method currently used for investigating themechanical properties of steels at elevated temperatures isthe steady-state test in which the specimen is heated up to atarget temperature and held for a period of time until thetemperature is stable and uniform along the specimen thengradually subjected to a tensile load through to fractureAnother well-known method is the transient-state test inwhich the specimen applied a static load and then is heatedup slowly until failure criteria are met Most researchersemploy steady-state test technique since it is able to obtainstress-strain curves directly avoids fluctuant temperatureenvironment eliminates the influence of thermal expansionand generally saves resources According to current papersthere is no final conclusion [11 13 16] yet on which methodis more accurate for testing and predicting the mechanicalproperties of steels at elevated temperatures Also the mainfocus of this investigation is on the prediction of different
types of steels for CFS structures material properties underhigh temperatures erefore the steady-state test methodwas adopted in this test study
32 Test Specimens All coupons were cut by a wire cuttingmachine from original coils of S350 and S420 steels withnominal thickness of 10mm and G500 steels with nominalthickness of 12mm e dimension of the test specimenswas determined by ISO standard [22] as presented inFigure 2 ere were four small lugs at the edge of parallelpart for fixing extensometer system and two holes forpinning extension tension rods e metal thickness andgage width of the specimens were average of those valuesmeasured at three points within gauge lengths by using amicrometer before testinge base metal thickness and realgage width were used in the calculations of the initial crosssectional area
33 Test Devices and Procedure e experiment setup is theEDC222 Doli testing system shown in Figure 3 which is anintegrated closed loop digital control thermal and me-chanical testing system e tensile testing machine is anelectronic servo system with 100 kN capacity which wascalibrated before testing A high-temperature stove with a
Table 2 Manufacturing key temperatures of S350 S420 and G500 steels
Manufacturing key process Hot rolling (degC) Final rolling (degC) Annealing (degC)S350 1220 Room temperature 730S420 1200 Room temperature 700G500 1200 870 500
0
Tem
pera
ture
Time
Full annealing
Stress relieving annealing
Ac3
Ac1
Figure 1 Annealing process
Table 1 Chemical compositionlowast of S350 S420 and G500 steels
S350 (10mm) C () Mn () Al () S () Nb ()006 08 0045 002 0015
S420 (10mm) C () Mn () Al () S () Nb ()006 06 0045 0015 009
G500 (12mm) C () Mn () Al () S () B ()004 022 0038 0015 0002
lowastPercentage of element by mass
Advances in Civil Engineering 3
maximum temperature of 1200degC was employed in thetesting ree pairs of thermocouples binding separately onupper rod surface of specimen and lower rod in a range of150mm provided signals for accurate feedback control ofspecimen temperatures presented in Figure 4 In this way auniform temperature zone would be generated when thetemperature of three thermal couples remained stable ematerial for fixing thermocouples herein is the refractory heatinsulation ceramic fiber cloth band shown in Figure 5 A setof linear displacement gratings including high-temperatureresistance extension rods with a range of 125mm relative to50mm gauge was used to acquire the deformation of spec-imens between the gauge lengths e extensometer systemdetailed in Figure 6 created a 50mm gauge which was able tocollect more displacement data from the gauge scope beforethe coupon failed and was also calibrated before testing
Tensile coupon tests were carried out by adopting thesteady-state testmethod First the specimenwas heated up to apreselected temperature at a rate of 20degCmin Free thermalexpansion was allowed when heating up by keeping tensileload zero e temperature levels selected in this experiment
were 20degC 100degC 200degC 300degC 400degC 500degC 600degC and700degC e specimen was kept for 30sim40min at this constanttemperature until it reached the steady condition en theload was applied by controlling the displacement of theelectronic tensile grip until failure while maintaining the settemperature degreee displacement rate was set to 024mmmin which was specifically in elastic stage equivalent to astrain rate of 000007s as the minimum rate specified by ISOstandard [22] Moreover the sampling frequency was 10HzMost of the specimens were repeated twice for doublechecking Some additional experiments have been conductedfor verification (500degC for G500 steel) and supplement (350degCand 700degC for S350 and S420 steels) at several temperaturepoints Summary of tested specimens is present in Table 3
Temperature control is the most critical part in a high-temperature material test undoubtedly During tests pro-cedure real-time temperatures at three different pointsalong the specimen were detected by thermocouples andrecorded by data acquisition system Figure 7 gives a set oftypical temperature curves from three thermal couples overtime for a certain specimen at a certain temperature con-dition (take 500degC for example) At about 25min thecoupon temperature reached preselected 500degC in the grosshowever the temperature was quite uneven and unstable atthat point Until the 45min under the working of feedbackcontrol system the heat conduction and thermal convectionin the furnace were balanced dynamically Consequentlythree curves narrowed into a tiny range and the entirespecimen was clearly and steadily at the target temperatureAt that moment the coupon was ready to be elongated
4 Test Results and Discussion
In this section based on the purses of investigating thedifference between two kinds of cold-rolled thin-walledsteels on material properties at elevated temperatures theresults of tests are discussed in the way of comparison
41 Failure Mode Figures 8ndash10 present the failure modes ofthree grades of tested coupons All specimens fractured within
(a)
15 plusmn
02
15 plusmn 02
2 times ϕ8 0+0015
15 0+0
3
4 times R25 B
t22
46 (46)18 18
22
30
58
186
005 A
A
(b)
Figure 2 Test specimens and dimensions
Figure 3 Testing system (Doli control system)
4 Advances in Civil Engineering
the gauge length scope expectedly which means the stress-strain curves recorded from data acquisition system were realstress-strain relationships within the gauge length Meanwhilethe carburization layer coated the specimen for all tested grades
when temperature reached 500degC illustrated by the darksurface of those coupons in Figures 8ndash10 is carburizationcoating was incompact and could be scratched using thin sheetmetal Specifically steel plates presented a blue brittle
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
6 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
(high strength and low ductility) come from stress relievingannealing process [6] on production line
3 Experimental Study
31 Test Method Two major methods [11ndash19] may be usedto evaluate the mechanical behavior of construction mate-rials under high-temperature environment [11ndash19] emost common method currently used for investigating themechanical properties of steels at elevated temperatures isthe steady-state test in which the specimen is heated up to atarget temperature and held for a period of time until thetemperature is stable and uniform along the specimen thengradually subjected to a tensile load through to fractureAnother well-known method is the transient-state test inwhich the specimen applied a static load and then is heatedup slowly until failure criteria are met Most researchersemploy steady-state test technique since it is able to obtainstress-strain curves directly avoids fluctuant temperatureenvironment eliminates the influence of thermal expansionand generally saves resources According to current papersthere is no final conclusion [11 13 16] yet on which methodis more accurate for testing and predicting the mechanicalproperties of steels at elevated temperatures Also the mainfocus of this investigation is on the prediction of different
types of steels for CFS structures material properties underhigh temperatures erefore the steady-state test methodwas adopted in this test study
32 Test Specimens All coupons were cut by a wire cuttingmachine from original coils of S350 and S420 steels withnominal thickness of 10mm and G500 steels with nominalthickness of 12mm e dimension of the test specimenswas determined by ISO standard [22] as presented inFigure 2 ere were four small lugs at the edge of parallelpart for fixing extensometer system and two holes forpinning extension tension rods e metal thickness andgage width of the specimens were average of those valuesmeasured at three points within gauge lengths by using amicrometer before testinge base metal thickness and realgage width were used in the calculations of the initial crosssectional area
33 Test Devices and Procedure e experiment setup is theEDC222 Doli testing system shown in Figure 3 which is anintegrated closed loop digital control thermal and me-chanical testing system e tensile testing machine is anelectronic servo system with 100 kN capacity which wascalibrated before testing A high-temperature stove with a
Table 2 Manufacturing key temperatures of S350 S420 and G500 steels
Manufacturing key process Hot rolling (degC) Final rolling (degC) Annealing (degC)S350 1220 Room temperature 730S420 1200 Room temperature 700G500 1200 870 500
0
Tem
pera
ture
Time
Full annealing
Stress relieving annealing
Ac3
Ac1
Figure 1 Annealing process
Table 1 Chemical compositionlowast of S350 S420 and G500 steels
S350 (10mm) C () Mn () Al () S () Nb ()006 08 0045 002 0015
S420 (10mm) C () Mn () Al () S () Nb ()006 06 0045 0015 009
G500 (12mm) C () Mn () Al () S () B ()004 022 0038 0015 0002
lowastPercentage of element by mass
Advances in Civil Engineering 3
maximum temperature of 1200degC was employed in thetesting ree pairs of thermocouples binding separately onupper rod surface of specimen and lower rod in a range of150mm provided signals for accurate feedback control ofspecimen temperatures presented in Figure 4 In this way auniform temperature zone would be generated when thetemperature of three thermal couples remained stable ematerial for fixing thermocouples herein is the refractory heatinsulation ceramic fiber cloth band shown in Figure 5 A setof linear displacement gratings including high-temperatureresistance extension rods with a range of 125mm relative to50mm gauge was used to acquire the deformation of spec-imens between the gauge lengths e extensometer systemdetailed in Figure 6 created a 50mm gauge which was able tocollect more displacement data from the gauge scope beforethe coupon failed and was also calibrated before testing
Tensile coupon tests were carried out by adopting thesteady-state testmethod First the specimenwas heated up to apreselected temperature at a rate of 20degCmin Free thermalexpansion was allowed when heating up by keeping tensileload zero e temperature levels selected in this experiment
were 20degC 100degC 200degC 300degC 400degC 500degC 600degC and700degC e specimen was kept for 30sim40min at this constanttemperature until it reached the steady condition en theload was applied by controlling the displacement of theelectronic tensile grip until failure while maintaining the settemperature degreee displacement rate was set to 024mmmin which was specifically in elastic stage equivalent to astrain rate of 000007s as the minimum rate specified by ISOstandard [22] Moreover the sampling frequency was 10HzMost of the specimens were repeated twice for doublechecking Some additional experiments have been conductedfor verification (500degC for G500 steel) and supplement (350degCand 700degC for S350 and S420 steels) at several temperaturepoints Summary of tested specimens is present in Table 3
Temperature control is the most critical part in a high-temperature material test undoubtedly During tests pro-cedure real-time temperatures at three different pointsalong the specimen were detected by thermocouples andrecorded by data acquisition system Figure 7 gives a set oftypical temperature curves from three thermal couples overtime for a certain specimen at a certain temperature con-dition (take 500degC for example) At about 25min thecoupon temperature reached preselected 500degC in the grosshowever the temperature was quite uneven and unstable atthat point Until the 45min under the working of feedbackcontrol system the heat conduction and thermal convectionin the furnace were balanced dynamically Consequentlythree curves narrowed into a tiny range and the entirespecimen was clearly and steadily at the target temperatureAt that moment the coupon was ready to be elongated
4 Test Results and Discussion
In this section based on the purses of investigating thedifference between two kinds of cold-rolled thin-walledsteels on material properties at elevated temperatures theresults of tests are discussed in the way of comparison
41 Failure Mode Figures 8ndash10 present the failure modes ofthree grades of tested coupons All specimens fractured within
(a)
15 plusmn
02
15 plusmn 02
2 times ϕ8 0+0015
15 0+0
3
4 times R25 B
t22
46 (46)18 18
22
30
58
186
005 A
A
(b)
Figure 2 Test specimens and dimensions
Figure 3 Testing system (Doli control system)
4 Advances in Civil Engineering
the gauge length scope expectedly which means the stress-strain curves recorded from data acquisition system were realstress-strain relationships within the gauge length Meanwhilethe carburization layer coated the specimen for all tested grades
when temperature reached 500degC illustrated by the darksurface of those coupons in Figures 8ndash10 is carburizationcoating was incompact and could be scratched using thin sheetmetal Specifically steel plates presented a blue brittle
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
6 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
maximum temperature of 1200degC was employed in thetesting ree pairs of thermocouples binding separately onupper rod surface of specimen and lower rod in a range of150mm provided signals for accurate feedback control ofspecimen temperatures presented in Figure 4 In this way auniform temperature zone would be generated when thetemperature of three thermal couples remained stable ematerial for fixing thermocouples herein is the refractory heatinsulation ceramic fiber cloth band shown in Figure 5 A setof linear displacement gratings including high-temperatureresistance extension rods with a range of 125mm relative to50mm gauge was used to acquire the deformation of spec-imens between the gauge lengths e extensometer systemdetailed in Figure 6 created a 50mm gauge which was able tocollect more displacement data from the gauge scope beforethe coupon failed and was also calibrated before testing
Tensile coupon tests were carried out by adopting thesteady-state testmethod First the specimenwas heated up to apreselected temperature at a rate of 20degCmin Free thermalexpansion was allowed when heating up by keeping tensileload zero e temperature levels selected in this experiment
were 20degC 100degC 200degC 300degC 400degC 500degC 600degC and700degC e specimen was kept for 30sim40min at this constanttemperature until it reached the steady condition en theload was applied by controlling the displacement of theelectronic tensile grip until failure while maintaining the settemperature degreee displacement rate was set to 024mmmin which was specifically in elastic stage equivalent to astrain rate of 000007s as the minimum rate specified by ISOstandard [22] Moreover the sampling frequency was 10HzMost of the specimens were repeated twice for doublechecking Some additional experiments have been conductedfor verification (500degC for G500 steel) and supplement (350degCand 700degC for S350 and S420 steels) at several temperaturepoints Summary of tested specimens is present in Table 3
Temperature control is the most critical part in a high-temperature material test undoubtedly During tests pro-cedure real-time temperatures at three different pointsalong the specimen were detected by thermocouples andrecorded by data acquisition system Figure 7 gives a set oftypical temperature curves from three thermal couples overtime for a certain specimen at a certain temperature con-dition (take 500degC for example) At about 25min thecoupon temperature reached preselected 500degC in the grosshowever the temperature was quite uneven and unstable atthat point Until the 45min under the working of feedbackcontrol system the heat conduction and thermal convectionin the furnace were balanced dynamically Consequentlythree curves narrowed into a tiny range and the entirespecimen was clearly and steadily at the target temperatureAt that moment the coupon was ready to be elongated
4 Test Results and Discussion
In this section based on the purses of investigating thedifference between two kinds of cold-rolled thin-walledsteels on material properties at elevated temperatures theresults of tests are discussed in the way of comparison
41 Failure Mode Figures 8ndash10 present the failure modes ofthree grades of tested coupons All specimens fractured within
(a)
15 plusmn
02
15 plusmn 02
2 times ϕ8 0+0015
15 0+0
3
4 times R25 B
t22
46 (46)18 18
22
30
58
186
005 A
A
(b)
Figure 2 Test specimens and dimensions
Figure 3 Testing system (Doli control system)
4 Advances in Civil Engineering
the gauge length scope expectedly which means the stress-strain curves recorded from data acquisition system were realstress-strain relationships within the gauge length Meanwhilethe carburization layer coated the specimen for all tested grades
when temperature reached 500degC illustrated by the darksurface of those coupons in Figures 8ndash10 is carburizationcoating was incompact and could be scratched using thin sheetmetal Specifically steel plates presented a blue brittle
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
6 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
the gauge length scope expectedly which means the stress-strain curves recorded from data acquisition system were realstress-strain relationships within the gauge length Meanwhilethe carburization layer coated the specimen for all tested grades
when temperature reached 500degC illustrated by the darksurface of those coupons in Figures 8ndash10 is carburizationcoating was incompact and could be scratched using thin sheetmetal Specifically steel plates presented a blue brittle
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
6 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
phenomenon like normal steels around 300degC evidenced bythe dark blue colored oxidation film on the fracture section ofspecimens shown in Figure 11 for the fracture details
For two full annealed steels visually noticeable elon-gation and necking of the coupons occurred from ambientand continued to higher temperatures For G500 steelssignificant elongation and necking could not be observeduntil temperature exceeds 500degC Considering the distinc-tion on heat treatment temperatures between full annealedand stress relieving annealed steels the G500 steel is more
brittle at ambient temperature since the cold work formingeffect is not eliminated during annealing However whentemperature went up to 600degC which was higher than thecritical temperature Ac1 for low carbon steel it was possiblethat the steel was partially annealed in the oven and lost partof the hardening influence Afterwards significant changeon the failure mode of G500 at 600degC could partially supportthis assumption and we still need more data investigation toexplore the relationship between temperatures and materialproperties for various steels used in CFS structures
10 20 30 40 500Time (min)
0
100
200
300
400
500
600
Tem
pera
ture
(degC)
Upper temperature
Middle temperature
Lower temperature
Figure 7 Typical temperature curves
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 8 Failure modes for S350 steels
20degC
100degC
200degC
300degC
350degC
400degC
500degC
600degC
700degC
Figure 9 Failure modes for S420 steels
6 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
Some of the failed specimens appear to be distorted after500degC During the tests at temperatures above 500degC thespecimens were stretched at a much higher displacementrate after the extensometer range was exceeded In this casethe fracture of these specimens seems to be abnormal Itshould be pointed that both ends of the tested specimenshave been clamped tightly in the slot of extension loadingrods by inserting shims at two sides of the coupon to avoideccentric load
42 Ductility In this part percentage elongation afterfracture [22] as shown in equation (1) calculated fromoriginal gauge length and final gauge length after fracture isused to indicate the ductility of specimens e final gaugelength for fractured and cooled down specimens wasmeasured by piecing the segments of specimens tightly at thefracture Table 4 presents the average percentage elongationafter fracture at different temperatures for specimens and itscurves are shown in Figure 12
AT lut minus l0
l0times 100 (1)
It is interesting to find that S350 and S420 steels whenthe temperature increased from 20degC to 200degC lose theirductility obviously Some researchers [11 12] noted a similarbehavior for full annealed steels is material behavior maybe attributed to chemical transformations taking place in thesteel base After 300degC since chemical reactions were takenover by temperature effects as the dominate factor theductility grows continually as expected At the same timeS350 and S420 steels presented a very close trend on ductilitydevelopment with temperature rising
Stress relieving annealed steels showed lower ductilitythan that of full annealed steels at ambient temperature dueto the different heat treatments in manufacturing process asmentioned before Under 200degC the ductility of G500 steels
maintained low values even close to room temperaturevalue en there was a higher platform of ductility in therange of 300degCsim500degC though it was still lower than that offull annealed steel at the same temperatures Up to 600degC theeffect of strain hardening and heat treatment has beeneliminated so that both full annealed and stress relievingannealed steels showed the same level of ductility Since the
20degC
100degC
200degC
300degC
400degC
500degC
600degC
Figure 10 Failure modes for G500 steels
Figure 11 Blue brittle phenomenon for steel plates
Table 4 Average percentage elongation after fracture (cooleddown)
Figure 12 Average percentage elongation after fracture at differenttemperatures
Advances in Civil Engineering 7
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
flashover temperature of fire is over 600degC the lack ofductility cannot be considered as a characteristic for stressrelieving annealed steels at fire conditions
43 Constitutive Relationship Since the measurement rangeof the displacement grating is 125mm the stress-straincurves are given within the strain of 02 as shown inFigures 13ndash15 All stress-strain curves of tested specimens(shown in Figure 3) are summarized together for S350 S420and G500 steels respectively For each of the temperatureconditions (marked in the same black circles) curves ofrepeated tests accord well with each other indicating thestability of tested materials test devices and test operations
As shown in Figures 13 and 14 the stress-strain curves ofS350 and S420 steels present a similar variation trend (1) Fortemperatures below 200degC an obvious yield plateau occurswhen the load reaches the ultimate strength and disappearsafter temperatures beyond 200degC (2) From 20sim300degC thestrain-hardening ranges at different temperatures pinch intoa small zone which illustrates that only yield strength ex-periences degradation at those temperature cases but ulti-mate strength dose not (3) At temperatures beyond 200degCthe stress-strain curves were of the gradual yielding type andboth yield strength and ultimate strength deteriorate withtemperature rising e yield plateaus with multiple yieldpoints are the result of interrupted motion of the Ludersband along the specimen e movement of dislocationsnear the band front becomes locked when temperaturereaches 300degC and thus yield plateaus disappeared overthese temperatures [23]
Unlike the full annealed steels the G500 steel gavegradual yielding type stress-strain curves at both ambientand elevated temperatures referring to Figure 15 en itappears that the yield strengths do not decrease much up to200degC Furthermore the stress-strain curves have a similarshape and ultimate deformation at temperatures from 300degCto 500degC When temperature reaches 600degC the ultimatestrain increases significantly Meanwhile the load decreasesvery slowly after the ultimate strength at this condition andthe corresponding failure mode changes to ductile fracturewith clear necking
44 Retention Factors Primarily Table 5 shows the tensiletest results of all three steels at ambient temperature whichare fundamental parameters for calculating high-tempera-ture material properties Besides the apparent higherstrength of G500 steels the elastic modulus of this highstrength steel is also higher than that of full annealed steels atroom temperature
Retention factors for the elastic modulus yield strengthand ultimate strength were computed as the ratios of ma-terial properties at high temperatures to their values atambient conditions which is 20degC in this paper e elasticmodulus was calculated by fitting the initial portion of thestress-strain curves via using the least squares methodfollowing ISO standard [22] For the curves with smooth andlong yield plateau the yield strength was taken as the averagevalue of stresses in the plateau en for the gradual yielding
cases the yield strength was determined by the 02 proofstress method which uses the intersection point of thestress-strain curve and the proportional line offset by 02strain Results are shown in Table 6
Figures 16 and 17 provide the retention factors for fullannealed and stress relieving annealed steels obtainedthrough steady-state tests from this study and current steelstructural fire design codes
By comparing tests data in this paper for cold-rolledthin-walled steels with current design codes retentionfactors from existing steel design codes are generally unsafeespecially for yield strength prediction As for elasticmodulus retentions factors predicted by Eurocode 3 [9] andAISC 360 [7] agree well with the present full annealed steelstests data before 500degC but somewhat are unsafe beyond500degC ese two curves are also suitable for G500 steelsalthough being a little conservative around 300degC andslightly unsafe beyond 400degC In addition the elasticmodulus retention factors curve provided by AS 4100 [8] areunsafe beyond 400degC for both full annealed and stress re-lieving annealed steels Yield strength retentions factorsfrom hot-rolled steel experimental data provisioned by AISCand Eurocode 3 were the most unsafe whereas AS 4100 andBS5950-8 [10] are less unsafe relatively is confirms thatby directly using retention factors developed for hot-rolledsteel to calculate yield strength they are not suitable for cold-rolled thin-walled steels
erefore the provisioned curves in current codescannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study
In order to investigate the relationship on high-tem-perature material properties between the steels for CFSstructures with different manufacturing process this papercollected the existing test data of cold-rolled thin-walledsteels at elevated temperatures in the recent 20 years aspresented in Table 7 Specifically based on previous dis-cussion S420 steel shares a very similar trend on failuremode ductility constitutive relationship and retentionfactors with S350 steel (typical full annealed steels) eventhough its nominal yield strength is close to G450 steel(stress relieving annealed steels)us in Table 7 the level ofductility (elongation) is the reliable and significant classi-fication standard for commonly used steels for CFS struc-tures which is mainly due to the different annealing processduring manufacturing
Figures 18 and 19 illustrate the retention factors for fullannealed and stress relieving annealed steels in this test studyand other publications available in the literature
ose two scatter diagrams show a significant dispersionin the existing data on the retention factors of elasticmodulus and yield strength which can be mainly attributedto the measuring method strain rate heating rate materialtype and the criteria used to determine the parametersConsequently most of the provisioned equations based onpast investigations are not suitable for predicting the deg-radation properties of cold-rolled thin-walled steels due tosignificant scatters existence
Despite the discrete of those scatters there are still basicregulations to follow when scatters have been divided into
8 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
two groups full annealed and stress relieving annealedsteels As shown in Figure 18 there is a consistent trend forretention factors of elastic modulus for both full annealedsteels and stress relieving annealed steels erefore theinfluence from different manufacturing process on elasticmodulus of steels for CFS structures is less obvious In the
yield strength case contrarily as Figure 19 red scatters andblack scatters went to two different shapes obviouslythough they agree well generally with the distribution ofthemselves Under 300degC the yield strength of full annealedsteels reduces much faster than stress relieving annealedsteels when temperatures rise From 300degC to 600degC the
0
100
200
300
400
500
600
Stre
ss (M
Pa)
400degC
20degC200degC100degC
300degC
500degC
600degC
700degC
350degC
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 13 Stress-strain curves of S350 steels at different temperatures
400degC
20degC
200degC100degC
300degC
500degC
600degC
700degC
350degC
0
100
200
300
400
500
600
Stre
ss (M
Pa)
002 004 006 008 01 012 014 016 018 020Strain
20degC20degC100degC100degC
200degC200degC300degC
300degC350degC400degC
400degC500degC500degC
600degC600degC700degC
Figure 14 Stress-strain curves of S420 steels at different temperatures
Advances in Civil Engineering 9
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
yield strength for stress relieving annealed steels dropsdrastically with temperatures elevating although those forfull annealed steels fall smoothly at this stage After 600degCthe descending slope of stress relieving annealed steelsbecomes gentler than full annealed steels again In this casesteels with different manufacturing process behave totallydifferent for reduction rules on yield strength at elevatedtemperatures
In conclusion it is meaningful to produce statisticalconclusion and raise general equations for predicting the
reduction of material properties on steels used for CFSstructures at elevated temperatures
5 Prediction Equations
51 Retention Factors Prediction for Elastic Modulus Due tothe weak dependence of manufacturing procedure of steelsfor CFS structures on the elastic modulus reduction de-velopment a single equation is provided here for calculatingretention factors of elastic modulus by fitting the scatters
400degC
500degC
600degC
300degC
20degC 100degC 200degC
0
100
200
300
400
500
600
700
800
Stre
ss (M
Pa)
002 004 006 008 01 012 0140Strain
20degC20degC100degC
100degC200degC200degC
300degC300degC350degC
400degC400degC500degC
500degC600degC600degC
Figure 15 Stress-strain curves of G500 steels at different temperatures
Table 5 Mechanical properties of cold-rolled thin-walled steels at ambient temperature
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
(polynomial regression) in the entire database (compiled inTable 6)
ET
E20 4826E minus 16T
5+ 1224E minus 12T
4minus 5808E minus 10T
3
minus 1742E minus 06T2
minus 2070E minus 04T + 1004
20degCleTle 800degC
(2)
Figure 20 shows the fitting curve of the retention factorsfor elastic modulus with original scatters and Figure 21 givesthe comparison of the proposed equation curves with codecurves for predicting elastic modulus Recommended re-tention factors for the elastic modulus extracted from fittingequation at temperatures of hundreds are provided inTable 8
52 Retention Factors Prediction for Yield StrengthConsidering the separation of full annealed and stress re-lieving annealed steels on retention factors for yield strengthtwo sets of equations were promoted here through poly-nomial and exponential regressions for predicting retentionfactors of yield strength correspondingly as equation (3) forfull annealed steels and equation (4) for stress relievingannealed steels Figures 22 and 23 show the fitting curves ofthe retention factors for yield strength of full annealed steelsand stress relieving annealed steels separately MeanwhileFigure 24 gives the comparison of the proposed equationcurves with code curves for predicting yield strengthRecommended retention factors for the yield strengthextracted from fitting equation at temperatures of hundredsare provided in Table 9 In general as revealed by Figures 21and 24 equations provided by current standards [1ndash6] areunsafe for predicting elastic modulus and yield strength
E TE
20
0
02
04
06
08
1
12
100 200 300 400 500 600 700 8000T (degC)
AS 4100S350 096mmS420 096mm
G500 116mmAISC 360Eurocode 3
Figure 16 Comparison of the retention factors of elastic modulus according to test results with the current design codes
F yT
Fy2
0
00
02
04
06
08
10
12
100 200 300 400 500 600 700 8000T (degC)
BS 5950-8S350 096mmS420 096mm
G500 116mmAISC 360
Eurocode 3AS 4100
Figure 17 Comparison of the retention factors of yield strength according to test results with the current design codes
Advances in Civil Engineering 11
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
Table 7 Compilations of basic information for current test data
Year Researchers Grade ickness (mm) Elongationlowast ()Full annealed steels
1999 Qutinen [11] S350 200 gt20
2003 Lee et al [12] G300040 No information060 No information100 No information
2009 Ranawaka and Mahendran [14] G250060 gt30080 gt30095 gt30
2011 Kankanamge and Mahendran [15] G250 155 gt30195 gt30
2013 Ye and Chen [17] Q345 150 gt30
2015 Batista Abreu [18]
S230 144 gt20
S345115 gt20155 gt20258 gt20
2016 Craveiro et al [19] S280 250 gt20
is research S350 100 3202S420 100 2999
Stress relieving annealed steels
2003 Lee et al [12]
G500 120 No information
G550042 No information060 No information095 No information
2007 Chen and Young [13] G450 190 113G550 100 98
2009 Ranawaka and Mahendran [14] G550060 lt3080 lt3095 lt3
2011 Kankanamge and Mahendran [15] G450 150 lt10190 lt10
2012 Chen and Ye [16] G550 100 lt10is research G500 120 276
lowaste elongation here represents the percentage elongation after fracture of specimens at ambient temperatures However most researches have not given theelongation data directly stress-strain curves are major clues to estimate the ductility of steels
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
E TE
20
Full annealed steelsStress relieving annealed steels
Figure 18 Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with availableresearch results
12 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
0 100 200 300 400 500 600 700 80000
02
04
06
08
10
12
T (degC)
F yT
Fy2
0
Full annealed steelsStress relieving annealed steels
Figure 19 Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available researchresults
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
Current test dataEquation (2)
Figure 20 Fitting curve of the retention factors for elastic modulus
00
02
04
06
08
10
12
0 100 200 300 400 500 600 700 800T (degC)
E TE
20
AS 4100AISC 360
Eurocode 3Proposed equation
Figure 21 Comparison of the proposed equation curves with code curves for predicting elastic modulus
Advances in Civil Engineering 13
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
FyT
FY20 minus2272E minus 14T
5+ 4931E minus 11T
4minus 3418E minus 08T
3
+ 7512E minus 06T2
minus 1230E minus 03T + 1023
20degC leTle 800degC
(3)
FyT
Fy20 2855E minus 14T
5minus 9820E minus 12T
4minus 1991E minus 08T
3
+ 8483E minus 06T2
minus 1030E minus 03T minus 1018
20degC leT le 600degC
FyT
Fy20 9467E + 07T
minus 3222 600degC leT le 800degC
(4)
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12F y
TF
y20
Current test dataEquation (3)
Figure 22 Fitting curve of the retention factors for yield strength of full annealed steels
0 100 200 300 400 500 600 800700T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
Current test dataEquation (4)
Figure 23 Fitting curve of the retention factors for yield strength of stress relieving annealed steels
Table 8 Recommendation retention factors for the elastic modulus
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
53 Constitutive Relationship Models In order to carry outadvanced FEA simulation and fire safety design completeconstitutive models are required Generally temperature-dependent constitutive relationship models are based on theRambergndashOsgood three-parameter (elastic modulus yieldstrength and temperature) gradual yielding model [24] Asfor equation (5) εT σT ET and FyT are the strain stresselastic modulus and yield strength at T (degC) respectivelyand KT and ηT are parameters obtained from regressionanalysis
In RambergndashOsgood model KT is strength coefficientand ηT is hardening parameter In past researches some
researchers [13ndash15] use temperature-dependent KT and ηT
simultaneously some researchers [12] use fixed ηT and therest of researchers [16ndash18] use constant KT Consideringthat the yield strength was obtained through the 02 offsetmethod stress-strain data was fitted to equation (5) (ex-ponential regression) with the RambergndashOsgood strengthparameter KT set to 0002 erefore the strain computedat the 02 offset stress corresponds with the yield strainFurthermore the temperature-dependent Ram-bergndashOsgood hardening parameters ηT were fitted toequation (6) (polynomial regression) for the entire tem-perature range
0 100 200 300 400 500 600 700 800T (degC)
00
02
04
06
08
10
12
F yT
Fy2
0
BS 5950-8AISC 360Eurocode 3
AS 4100Proposed full annealed steels curveProposed stress relieving annealed steels curve
Figure 24 Comparison of the proposed equation curves with code curves for predicting yield strength
Table 9 Recommendation retention factors for the yield strength
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
300degC
400degC
500degC
600degC
700degC
002 004 006 008 01 0120Strain
0
50
100
150
200
250
300
350
400
450
500
Stre
ss (M
Pa)
(a)
300degC
400degC
500degC
600degC
700degC
002 004 006 008 01 0120Strain
0
50
100
150
200
250
300
350
400
450
500
Stre
ss (M
Pa)
(b)
Figure 25 Continued
16 Advances in Civil Engineering
εT σT
ET
+σT
FyT
1113888 1113889
ηT
(5)
ηT aT2
+ bT + c (6)
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
εT σT
ET
+σT
FyT
1113888 1113889
ηT
(5)
ηT aT2
+ bT + c (6)
For S350 and S420 steels since there is an obvious yieldplateau for stress-strain curves up to 200degC it was reasonableto apply elastic-perfectly plastic model under 200degCMeanwhile due to the lacking of strengthening stage forG500 steel up to 100degC elastic-perfectly plastic model wasadopted also for G500 steel under 100degC ConsequentlyRambergndashOsgood model regression fitting started from300degC for S350 and S420 steels and from 200degC for G500steel e resulting RambergndashOsgood hardening parametersare shown in Table 10 constants for RambergndashOsgoodhardening parameters are shown in Table 11 and stress-strain fitting curves are compared with test results in Fig-ure 25 Based on Figure 25 there is a very good agreementbetween the predicted stress-strain curves from equations(5) and (6) and test results erefore these equations arerecommended for the determination of the stress-straincurves of S350 (10mm) S420 (10mm) and G500 (12mm)steels at elevated temperatures
6 Conclusions
is paper has reported a detailed experimental study of themechanical properties of steels for CFS structures at elevatedtemperatures Different manufacturing processes and theirinfluence on the properties of steels for CFS structures werediscussed e experimental study included tensile coupontests conducted on S350 S420 and G500 steels via steady-state test methods and a careful discussion of the test results
was provided e failure mode ductility stress-strain re-lationship and material reductions were elaborated in acomparison way en based on the testing and literaturedata retention factors for elastic modulus and yield strengthwere established for the two types of steels used in CFSstructures as functions of temperature At last constitutiverelationship models were proposed based on tests data forS350 S420 and G500 steels separately
Abbreviations
A20 Percentage elongation after fracture at 20degCAT Percentage elongation after fracture at T (degC)E20 Elastic modulus at 20degCET Elastic modulus at T (degC)Fy20 Yield strength at 20degCFyT Yield strength at T (degC)Fu20 Ultimate strength at 20degCFuT Ultimate strength at T (degC)L0 Original gauge lengthluT Final gauge length at T (degC)T TemperatureεT Strain at T (degC)σT Stress at T (degC)KT Strength coefficient in RambergndashOsgood model at T
(degC)ηT Hardening parameter in RambergndashOsgood model at
T (degC)
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
18 Advances in Civil Engineering
Conflicts of Interest
No conflicts of interest exist in the submission of thismanuscript
Acknowledgments
e authors are grateful to the financial support of theNational Key Research and Development Program of China(No 2017YFC0703809)
References
[1] AISIS100North Ameriean Specifieation for the Design of Cold-Formed Steel Structural Members American Iron and SteelInstitute Washington DC USA 2007
[2] ASNZS 4600 AustralianNew Zealand Standard Cold-Formed Steel Structures Standards Australia and StandardsNew Zealand Sydney Australia 2005
[3] EN1993-1-3 Eurocode 3 Design of Steel Structures Part 1ndash3Gerneral Rules Supplementary Rules for Cold-Formed Mem-bers and Sheeting European Committee for StandardizationBrussels Belgium 2006
[4] BS 5950-5 Structural Use of Steelwork in Building-Part 5 Codeof Practice for Design of Cold-Formed Sections British Stan-dards Institution Hemel Hempstead UK 1998
[5] GB 50018-2002 Technical Code of Cold-Formed in-WallSteel Structures GB National Standards Beijing China 2002
[6] C A Rogers D Yang and G J Hancock ldquoStability andductility of thin high strength G550 steel members andconnectionsrdquo in-Walled Structures vol 41 no 2pp 149ndash166 2008
[7] ANSIAISC 360 Specification for Structural Steel BuildingsAmerican Institute of Steel Construction Chicago IL USA2005
[8] A S 4100 Australian Standard Steel structures StandardsAustralia Sydney Australia 1998
[9] EN 1993-1-2 Eurocode 3 Design of Steel Structures Part 1-2Gerneral Rules Structural Fire Design European Committeefor Standardization Brussels Belgium 2005
[10] BS 5950-8 Structural Use of Steelwork in Building-Part 8 Codeof Practice for Fire Resistant Design British Standards Insti-tution Hemel Hempstead UK 2003
[11] J Outinen ldquoMechanical properties of structural steels at el-evated temperaturesrdquo Licentiate thesis Helsinki University ofTechnology Espoo Finland 1999
[12] J H Lee M Mahendran and P Makelainen ldquoPrediction ofmechanical properties of light gauge steels at elevated tem-peraturesrdquo Journal of Constructional Steel Research vol 59no 12 pp 1517ndash1532 2003
[13] J Chen and B Young ldquoExperimental investigation of cold-formed steel material at elevated temperaturesrdquo in-WalledStructures vol 45 no 1 pp 96ndash110 2007
[14] T Ranawaka and M Mahendran ldquoExperimental study of themechanical properties of light gauge cold-formed steels atelevated temperaturesrdquo Fire Safety Journal vol 44 no 2pp 219ndash229 2009
[15] N D Kankanamge and M Mahendran ldquoMechanical prop-erties of cold-formed steels at elevated temperaturesrdquo in-Walled Structures vol 49 no 1 pp 26ndash44 2011
[16] W Chen and J Ye ldquoMechanical properties of G550 cold-formed steel under transient and steady state conditionsrdquoJournal of Constructional Steel Research vol 73 pp 1ndash112012
[17] J Ye and W Chen ldquoElevated temperature material degra-dation of cold-formed steels under steady-and transient-stateconditionsrdquo Journal of Materials in Civil Engineering vol 25no 8 pp 947ndash957 2013
[18] J C Batista Abreu ldquoFire performance of cold-formed steelwallsrdquo Licentiate thesis Johns Hopkins University BaltimoreMD USA 2015
[19] H D Craveiro J P C Rodrigues A Santiago and L LaımldquoReview of the high temperature mechanical and thermalproperties of the steels used in cold formed steel structures-thecase of the S280 Gd+Z steelrdquoin-Walled Structures vol 98pp 154ndash168 2016
[20] G Krauss and M A Grossmann Principles of Heat Treatmentof Steel American Society for Metals Metals Park GeaugaCounty OH USA 1980
[21] K E Easterling Introduction to the Physical Metallurgy ofWelding Butterworth-Heinemann Oxford UK 1992
[22] International Standard of Organzation ISO 6892-2 MetallicMaterials-Tensile Testing-Part 2 Method of Test at ElevatedTemperature International Standard of Organzation GenevaSwitzerland 2011
[23] E O Hall Yield Point Phenomena in Metals and AlloysMacmillan New York NY USA 1970
[24] W Ramberg and W R Osgood Description of Stress-StrainCurves by ree Parameters National Advisory Committeefor Aeronautics Washington DC USA 1943
