PHYSICAL TESTS AND ANALYSES OF COMPOSITE STEEL-CONCRETE
BEAM-COLUMNS
By S. Ali Mirza,! Fellow, ASCE, Ville Hyttinen,:Z and Esko Hyttinen3
ABSTRACT: The composite steel-concrete beam-columns in which steel shapes are encased in concrete andsecond-order effects are significant were studied from 16 specimens loaded to failure. Loading included combinations of axial and transverse forces producing a wide range of different external eccentricities. Observationsfrom the physical tests indicate that, for static loads, the bonding condition at the interface of steel rib connectorsand the surrounding concrete has a small effect on ultimate strength. The tests also show that the ACI 318assumption of maximum usable strain of 0.003 at concrete extreme compression fibers near ultimate load isvalid for such beam-columns. Analyses based on ACI 318, Eurocode 4, and finite-element modeling procedureswere compared to test results that provided further insight into understanding the structural behavior of suchbeam-columns.
umn tests. Steel rib connectors with three different bondingconditions were used for the beam-column specimens reportedon in this study (Fig. 2). The objective of the study was fourfold: (1) to investigate the behavior and ultimate strength ofcomposite steel-concrete beam-columns in which steel shapes
L = 4000
9 V~ .J,.Vu
~ Itllt tllllll til"~
~"'~---~----~~m
1500 I 1000 I 1500
a"Ia
<a)
INTRODUCTION
During the past few decades, several composite steel-concrete structural systems have been used in the construction oftall buildings. One such system employs composite columnsthat consist of steel shapes encased in concrete and compositegirders that use metal deck between the steel section and concrete slab. This system combines the rigidity and formabilityof reinforced concrete with the strength and speed of construction associated with structural steel to produce an economicstructure (Griffis 1986). The concrete used for encasing astructural steel section not only increases its strength and stiffness, but also protects it from fire damage. As a result, the useof such columns is gaining popularity in building constructionin addition to applications in marine structures.
The lateral loads acting on a completed structure are resistedby stiff shear walls, frame action, or both. Regardless of howthe lateral loads are resisted, most columns are subjected tothe combined effects of axial force and bending moment andare classified as beam-columns. Past studies on compositebeam-columns have mostly concentrated on specimens inwhich eccentric axial loads are applied at member ends. Consequently, the physical tests on composite beam-columns withsteel shapes encased in concrete and subjected to axial andtransverse loads seem to be rare in the literature reviewed(Morino et al. 1986; Ricles and Paboojian 1994; Zang andYamada 1992). This is particularly valid for slender beamcolumns. This paper describes experimental and analyticalstudies in which slender composite steel-concrete beam-columns were subjected to the combined effect of proportionallyapplied static axial and transverse loads, as indicated by thetest setup shown in Fig. l(a).
Several studies have reported physical tests conducted oncomposite girders and push-out specimens in which interconnection between the steel section and concrete slab was successfully achieved by welding the steel ribs with holes (perfobond strips) to the flanges of the steel sections (Leonhardtet al. 1987; Oguejiofor and Hosain 1992, 1994). However,such interconnection has rarely been investigated in beam-col-
'Prof., Dept. of Civ. Engrg., Lakehead Univ., Thunder Bay, Ontario,Canada.
2Acad. of Finland Res. Assoc., Struct. Engrg. Res. Lab., Univ. ofOulu,Oulu, Finland.
'Prof., Dept. of Civ. Engrg., Univ. of Oulu, Oulu, Finland.Note. Associate Editor: W. Samuel Easterling. Discussion open until
"The maximum (fracture) strain Em was not measured for these tests.
are encased in concrete and second-order effects are significantover almost the entire range of the interaction diagram; (2) tostudy the effect of different bonding conditions at the interfaceof steel ribs and surrounding concrete; (3) to examine the applicability of ACI 318 (Building 1995), Eurocode 4 (Design1992), and nonlinear finite-element modeling procedures tosuch beam-columns; and (4) to compare the results from threecomputational procedures with each other and with those obtained from physical tests.
PHYSICAL TESTS
The behavior of slender tied composite beam-columns wasobserved from 16 specimens tested to failure. The failure loadsconsisted of concentric axial load N. and a pair of transverseloads V. acting simultaneously on pin-ended specimens, asshown in Fig. 1. Since the specimens were cast and tested
1318/ JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 1996
horizontally, they were also subjected to uniformly distributedtransverse load g due to the self-weight of the specimen.
The externally applied (first-order) bending moment at thefailure section (midlength) of a specimen is given by M.e =V.a + gL2/8, where a = shear span and L = length of thespecimen, and the external eccentricity at the same location iscomputed from e =M.e/N•. This eccentricity was nondimensionalized by dividing it by the overall depth h of the composite cross section in the plane of bending. The resulting eccentricity ratio e/h, ranging approximately from 0.17 to 2.6(Table 1), were used to investigate the beam-column behaviorover almost the entire practical range of the axial load-bendingmoment interaction diagram.
Axial and transverse loads were applied through load-controlled methods and monitored by readings from the load cells.The distribution of forces within the specimens could be traced
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by means of electric strain gauges that were attached to thecompression face of the concrete cross section at rnidlengthand to the outside faces of the structural steel flange overhangs. The transverse deflections of the specimens were alsomeasured. The loading procedure involved monitoring of response to service load forces before loads were increasedenough to create a failure condition. The testing time rangedfrom 19 to 69 min. The ratio of transverse to axial loads waskept constant at all stages of loading for a given specimen butvaried from specimen to specimen. The loads produced singlecurvature bending in all beam-column specimens with bendingmoments acting about the major axis of the steel cross section.
All specimens had the same structural steel shape and overall dimensions of the concrete cross section which was squareand symmetrical about both axes. Specific cross-section detailsare given in Fig. 2. The ratio of the cross-sectional area ofstructural steel to the area of overall concrete cross sectionwas 4.2%. To avoid local buckling of component plates, astocky steel shape was used with width-to-thickness ratio ofthe flange overhangs of 5.8 and that of the web of 15.5.
Nominal amounts of longitudinal and transverse reinforcingsteel were provided for all specimens. Four corner bars havinga cross-sectional area of about 0.55% of the gross cross sectionwere used in the longitudinal direction, whereas closed rectangular ties having a volumetric ratio of approximately 0.25%were placed at 150 mm on centers over almost the entirelength of the specimens. Near the specimen ends, the volumetric ratio of the ties was increased to approximately 2.65%and the tie spacing was decreased to 50 mm. This was doneto control the bursting effect in end regions due to the highbearing stresses caused by applied axial loads.
Ribs were welded to both sides of the steel section (Fig. 2)to enhance interconnection between the steel section and concrete for some specimens. Based on the type of steel ribs used,specimens were grouped into three series as indicated by Table1: (1) RHB refers to six specimens that contain ribs with holesbonded to concrete; (2) RNHB' stands for five specimens having ribs without holes bonded to concrete; and (3) RHNB represents five specimens consisting of ribs with covered holesthat are not bonded to concrete. The last mentioned involveda series of specimens (series RHNB) in which rib holes werefilled with wooden disks and then covered with smooth plastic
tape that was coated with a layer of oil to break the bondbetween the steel ribs and surrounding concrete. For specimens of the RHB series, reinforcing steel ties passed throughevery third rib hole, acting as mechanical connectors betweensteel and concrete. This mechanical interconnection was notavailable for the specimens of the other two series, becausethe ties passed over the ribs for those specimens. As a result,for specimens of series RHB, the resistance to horizontal shearforce at the interface of ribs and concrete was provided bylateral ties acting as mechanical connectors plus the bearingand shearing of concrete inside the rib holes in addition to thebond due to adhesion and friction at the interface of ribs andsurrounding concrete. The bond due to adhesion and frictionalone resisted the horizontal shear force at the interface of ribsand concrete for specimens of series RNHB. As observed earlier, the bond was broken at the interface of ribs and concretefor series RHNB specimens. Bond due to adhesion and frictionexisted at the interface of the steel section and surroundingconcrete for specimens of all three series.
The concrete strengths were measured on standard (150 X150 X 150 mm) cubes. The strengths shown in Table 1 arethe averages of three cube tests. For equivalent cylinderstrengths, a conversion factor of 0.81 was used for strengthanalyses presented in the later part of this paper. This value isthe average conversion factor for the 16 cube strengths listedin Table I and was computed from the equation given byL'Hermite (1955)
in which I~Ube = measured compressive strength of standardcubes; and I~Ylinder = equivalent compressive strength of standard cylinders.
The modulus of elasticity of steel sections, ribs, and reinforcing bars was 200,000 MPa whereas the yield strength ofsteel ribs was 293.4 MPa. The yield strengths IY, tensilestrengths !u' and maximum (fracture) strains Em of structuralsteel given in Table 1 are averages of five to 11 tests conductedon coupons approximately 211 X 25 X 5 mm in size thatwere machined from flanges of the steel sections. Similarly,j;"f", and Em values of reinforcing steel in Table 1 are averagesof three tests conducted on lO-mm diameter (cross-sectionalarea = 79 mm2
) bars 241 mm in length.
TABLE 2. Test Results at Failure
Lateral Test Strengths MomentExternal deflection magnification
Specimen eccentricity at midheight Ilm Nu Vu Mu• Mum factordesignation ratio e1h (mm) (kN) (kN) (kN ·m) (kN'm) 0= Mum/Mu•
(1 ) (2) (3) (4) (5) (6) (7) (8)
(a) Series RHB' ribs (with holes) bonded to concrete
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TEST RESULTS
Ultimate Strengths
Table 2 contains a summary of test results at failure condition. The table displays for each specimen the ultimate axialand transverse loads that could be resisted by the specimenand the corresponding lateral deflection am recorded at midlength of the specimen. The externally applied (first-order)bending moment Mu• and the magnified bending moment Mum,both acting at the failure section (midlength) of the specimens,were computed from the following:
M u• =aVu + Mg = l.5Vu + 3.2 (kN'm) (2)
Mum =M u• + Nuti.m (3)
in which Mg = bending moment caused by the self-weight ofthe specimen = gL2/8. The term Nuti.m in (3) represents thesecond-order bending moment caused by the transverse deflection of the specimen at the failure section. The momentmagnification factor for a beam-column was defined as theratio of the magnified bending moment to the externally applied bending moment, both acting at the failure section (& =Mum/Mu.). The computed values of Mue> Mum, and l) are listedin Table 2.
The moment magnification factors shown in Table 2 arequite high, especially for test specimens with eccentricity ratios (e/h) lower than 0.9. This is because the specimens had ahigh slenderness with L/h = 16.7. This corresponded to theL/r ratios of 71.6 (series RNHB) or 72.9 (series RHB andRHNB), where r = radius of gyration of the composite crosssection in the plane of bending computed according to ACI318 (Building 1995). A comparison of moment magnificationfactors for specimens from the three series shows small differences in their values (Table 2), indicating insignificant effectof the bonding condition at the interface of rib connectors andconcrete.
The effect of the bonding condition at the interface of ribsand concrete was further investigated by comparing the nondimensionalized axial load ratios Nu/No for the tests from threeseries. No is the pure axial force capacity of the compositecross section and was computed from
sum of cross-sectional areas of structural and reinforcingsteels; and L/yAs = sum of compressive yield forces resistedby structural and reinforcing steels. Again, the plotted valuesof Nu/No shown in Fig. 3 indicate the small effect of the bonding condition at the interface of ribs and concrete. This impliesthat the bond due to adhesion and friction at the interface ofthe steel section and surrounding concrete provides sufficientinterconnection and additional interconnection through shearconnectors may not be necessary for beam-columns, especiallywhen they are subjected to low eccentricities. However, thisobservation may not be applicable to beam-columns subjectedto seismic forces or fatigue effects, since the specimens investigated here dealt with static loads alone. In this regard, theACI 318 provisions (Building 1995) require shear connectorsfor the transfer of forces between steel and concrete at all axialload levels, whereas the American Institute of Steel Construction (AISC) load and resistance factor design (LRFD) provisions (Load 1993) require shear connectors to develop the fullplastic moment resistance of beam-columns at low axial loads.
Structural Steel Stresses
The variation of stresses in flanges of the steel section between applied transverse loads (in the central part of the specimen) is shown in Fig. 4. These stresses were measured fromthe strain gauges attached to the outside faces of the top andbottom flanges. Twelve strain gauges were used for each specimen and were located at midlength and 500 mm each sidefrom the midlength along the axis of the specimen.
Three different load levels are used for plotting these steelstresses: (1) 33% of the failure load; (2) 66% of the failureload; and (3) failure load. If the service live load and service
II-Eltl !!!!! 1)1111!!I~fj--
-400 .----..,...----..----.,-----,
-e/l1-0.410 --- e/h-0.858 - -e/l1-2.584
in which Ag = gross area of the concrete cross section; LAs =
FIG. 4. Variation of Stress in Flanges of Structural Steel Section
0.0 1...-__...L-__-.1.-__---l. l...-__...L-__-J
0.0 1.0 2.0External Eccentricity Ratio (e/h)
FIG. 3. Effect on Strength of Bonding Condition at InterfaceofSteel Ribs and Surrounding Concrete
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FIG. 6. Typical Failure Mode
of the failure load) are well within elastic limits (Fig. 4). Atfailure load, the bottom flange of all three specimens yieldedin tension although yielding did not occur over the full lengthof the central region in the specimen with elh = 0.410, asindicated by Fig. 4. However, the stresses in the top (compression) flange were lower than the yield stress for specimenswith elh = 0.410 and 0.858 and much lower than the yieldstress for the specimen with elh = 2.584. This is expectedbecause high eccentricity ratios involve low axial forces, resulting in decreased stresses due to axial compression.
To avoid congestion of Fig. 4, the structural steel stressesfor specimens with elh = 0.247 and 0.174 are not plotted. Thestresses in the top flange of these specimens at all three load
FIG. 5. Variation of Strain In Extreme Compression Fibers ofConcrete
dead load are assumed to be equal in magnitude, the 66% ofthe failure load approximately represents the total service deadand live load, whereas the 33% of the failure load approximately equals the service dead load alone. The steel stressesin Fig. 4 are plotted from data from specimens RHNB-3,RHNB-4, and RHNB-5, having external eccentricity ratios ofelh =0.410, 0.858, and 2.584, respectively. According to ACI318 (Building 1995), these eccentricity ratios would producecompression, balance, and tension failure condition, respectively, at the fai'ure section of the beam-column specimens.
As expected, the structural steel stresses at service dead load(33% of the failure load) and service dead plus live load (66%
TABLE 3. Comparison of Code Strengths with Test Strengths
Note: Overall average value for columns 7 and 8 =1.14 and 1.03, respectively; and overall coefficient of variation for columns 7 and 8 =8.9 and11.8%, respectively.
'Average value for columns 7 and 8 =1.13 and 1.05, respectively; and coefficient of variation for columns 7 and 8 =12.5 and 13.6%, respectively.bAverage value for columns 7 and 8 = 1.16 and 1.06, respectively; and coefficient of variation for columns 7 and 8 = 6.8 and 12.9%, respectively."Average value for columns 7 and 8 = 1.12 and 0.98, respectively; and coefficient of variation for columns 7 and 8 =7.5 and 8.1%, respectively.
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levels were similar to, although somewhat lower than, thosefor the specimen with e/h = 0.410. For the bottom flange,however, the stresses in specimens with e/h = 0.247 and 0.174were significantly lower than the stresses in the specimen withe/h = 0.410, regardless of the load level considered. Fig. 4shows the data for series RHNB specimens. The structuralsteel stresses in specimens of the other two series (RHB andRNHB) were similar to those plotted in Fig. 4.
Concrete Strains
The variation of maximum compressive strain of concreteis plotted in Fig. 5. These strains were measured from thestrain gauges mounted on the top (compression) face at midlength of each specimen. Fig. 5 indicates that the maximumcompressive strain of concrete at failure load varied from approximately 0.0028 to 0.0044. This means that the ACI 318(Building 1995) assumption of maximum usable strain of0.003 at concrete extreme compression fiber near ultimatestrength is also valid for the type of composite beam-columnstested. For the other two load levels, representing dead loadalone and dead plus live load (33 and 66% of the failure load),the concrete strains are much lower than those at the failureload, as indicated by Fig. 5. Again, the data for series RHNBspecimens are shown; the data for specimens of the other twoseries were similar to those plotted in Fig. 5, especially thoseat failure load. The maximum compressive strain of concreteat failure load varied approximately from 0.0025 to 0.0044 for
specimens of series RHB and from 0.0035 to 0.0043 for specimens of series RNHB.
Failure Mode
All specimens failed in a similar mode. As the load wasincreased close to the failure condition, wide cracks appearedon the bottom (tension) face of the specimen. These crackswere accompanied by tension yielding of the bottom longitudinal reinforcing bars and, if e/h was greater than 0.4, by tension yielding of the bottom flange of the structural steel sectionas well. Just prior to failure, concrete strain in the extreme top(compression) fibers near the midlength of the specimenreached around 0.0025 -0.0044, depending on the externale/h ratio. Finally, the failure took place by the crushing ofconcrete in these fibers, as indicated in Fig. 6.
COMPARISON WITH ACI AND EUROCODESTRENGTHS
The ultimate strengths of beam-column specimens werecomputed using the ACI 318 (Building 1995) and Eurocode 4(Design 1992) methods and compared to the test strengths. Allcomputations for both methods were carried out as given inthese codes except that the understrength factors for ACI 318and the so-called partial safety factors (material resistance factors) for Eurocode 4 were taken equal to 1.0. The computedstrengths, therefore, represent the unfactored code strengths.
Segments
Nodes
1
I[I] 0 [II[£]0 0 [2] 01
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1.7
I: 8x250
2000
Segment m
•
15•
16•250
(a)
17•
.1
•
••
•
m+-----X----m
ConcreteIntegration points 15 x 15
RelnfcrcementlsteellIntegration points1 polnt/bar
Steel memberIntegration points5+9+5
Steel ribsIntegration points5+5
(b)
FIG. 7. Finite-Element Model of Composite Beam-Columns: (a) Side View of Element Model; (b) Cross Sections of Elements
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FIG. 8. Schematic Stress-5train Curves Used for FEM Method
The Eurocode 4 method is somewhat different from the ACIcode in the sense that it adopts the European buckling curvesfor steel columns as the basic design curves for compositecolumns. It also uses a simplified axial force-bending momentinteraction curve for the composite cross sections. The equivalent compressive strengths of standard cylinders computedfrom (1) were used for both design methods. The modulus ofelasticity of concrete was taken as 4,750Vf~Ylinder for the ACIcode and as 30,500 MPa for Eurocode 4.
Table 3 shows the values of Nu and M ue computed from theACI code and Eurocode 4 methods for all beam-column specimens. Also given in this table are the ratios of test to codestrengths (strength ratios) for the two methods. An examination of these strength ratios indicates that both methods predictthe composite beam-column strength with reasonable accuracy, with the exception of specimen RHB-2 in Table 3 wherethe Eurocode 4 method somewhat overestimates the teststrength. Table 3 also shows that the ACI 318 procedure produces somewhat more conservative and less variable resultsthan the Eurocode 4 method. This can be seen by comparingthe average strength ratios and related coefficients of variationobtained from the two methods (footnotes of Table 3) for thebeam-column tests of individual series and all three seriescombined. This is not surprising because ACI 318 uses thestrain-compatibility solution for the cross-section strength,whereas Eurocode 4 uses a modified plastic strength analysisin which the cross section is assumed to have been yieldedpartly in compression and partly in tension.
The strength comparisons given in Table 3 are based on theassumption that the cylinder strength is equal to 0.81 timesthe cube strength. When this conversion factor was increasedto 0.85 and 0.9, the average ratios of test to code strengths inTable 3 decreased by 2.5 and 4.5%, respectively, for ACI 318and by 1 and 2%, respectively, for Eurocode 4. The coefficients of variation remained unaffected in both cases. Thisindicated the nearly insignificant effect of the concrete strengthconversion factor within the range studied (0.81-0.9), whichwas expected because the cross-sectional area of longitudinal
E
-0
E
(a) Stress-Strain Relationship for Concrete
E
(b) Stress-Strain Relationship forStructural and Reinforcing Steel
-E
TABLE 4. Comparison of FEM Strengths with Test Strengths
External FEM Strengths Ratios of Test to FEM Strengths
Specimen eccentricity Nu Vu Mu• Mum N.. V.. ordesignation ratio elh (kN) (kN) (kN'm) (kN·m) Mu• ratios Mum ratios
(1 ) (2) (3) (4) (5) (6) (7) (8)
(a) Series RHB: ribs (with holes) bonded to concrete'
Note: Overall average value for columns 7 and 8 = 1.01 and 1.04, respectively; and overall coefficient of variation = 9.3 and 7.6%, respectively.'Average value for columns 7 and 8 = 1.02 and 1.04, respectively; and coefficient of variation for columns 7 and 8 = 12.4 and 7.9%, respectively.bAverage value for columns 7 and 8 = 1.03 and 1.07, respectively; and coefficient of variation for columns 7 and 8 = 9.0 and 9.4%, respectively.<Average value for columns 7 and 8 = 0.97 and 1.02, respectively; and coefficient of variation for columns 7 and 8 = 3.6 and 5.8%, respectively.
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200
20 40 60 80External Bending Moment, Mue (kN-m)
1000-r------tt--""/----,
20 40 60 80External Bending Moment, Mue (kN-m)
800
200
20 40 60 80External Bending Moment, Mue (kN-m)
" Test Results
+ ACI318
x Eurocode4
o FEM
FIG. 9. Comparison of FEM, AC1318, Eurocode 4, and Test Strengths: (a) Series RHBj (b) Series RNHBj (c) Series RHNB
(structural and reinforcing) steel was 4.75% of the area of theoverall concrete cross section.
FINITE-ELEMENT MODELING
The finite-element modeling (FEM) of beam-column specimens was carried out by using a nonlinear FEM software(ABAQUS I 989a,b). The objective was to model the ultimatestrength and load-deflection response of these specimens. Thespecimens were modeled with three-node, three-dimensionalbeam elements as shown in Fig. 7. I-beam elements were usedto model the structural steel section whereas eccentric rectangular elements were employed for steel ribs. Ribs in seriesRHB and RHNB beam-column specimens had holes spacedalong the rib length as indicated in Fig. 2. Parts of these ribswere modeled with narrower rectangular elements having thesame cross-sectional area as the ribs at the hole location. Theelements for concrete, reinforcing bars, structural steel section,and steel ribs had common nodal points. The integration pointsof the element cross sections used for taking into account theproperties of different materials are shown in Fig. 7.
The schematic stress-strain relationships for concrete andsteel are given in Fig. 8. As shown in this figure, the elasticplastic stress-strain curves were used for reinforcing and structural steels. The stress-strain relationship for concrete in uniaxial compression was represented by the following expression(Saenz 1964):
1324/ JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 1996
(5)
in which I; = compressive strength; Eo = strain correspondingto compressive strength = 0.002; and Ec = modulus of elasticity of concrete. The stress-strain curve for concrete in uniaxialtension was taken from BaZant and Dh (1984):
CT = EcE for E S E,p (6a)
CT =1: - E,(E - E,p) for E,p < E < Elf (6b)
CT =0 for E ~ Elf (6c)
in which I: = tensile strength; E, = tension softening modulus= 0.48E/(0.39 + I:); E,p = strain corresponding to tensilestrength = 1:IEc ; and Elf = final strain when tensile stress reduces to zero = E,p + (/:IE,).
The compressive strength, tensile strength, and modulus ofelasticity of concrete used in (5) and (6) included the rate ofloading effect on beam-column specimens and were calculatedfrom
in which/;ylinder = equivalent compressive strength of standardcylinders computed from (1); and t = time (in seconds) taken
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F-~E.STl~EMJ
10 20 30 40 50 60 70
f> [mm]
10 20 30 40 50 60 70
f> [mm]
Specimen RHNB-2
Specimen RHNB-4
50
40
~3020
>10(b) 0 L...__- _
10 20 30 40 50 60 70 0
f> [mm]
50
40
~ 3020
>10
(d) O¥----------10 20 30 40 50 60 70 0
f> [mm]
Spe.lmen RHNB·l
Specimen RHNB-3
50
40
~3O> 20
10(a) 0 L- _
o
50 Specimen RHNB.540 _._-__..-
~30> 20
10
(e) 0¥---------o 10 20 30 40 50 eo 70
f> (mm]
FIG. 12. Load-Deflection Curves for Series RHNB Specimens
Load-Deflection Behavior
In Figs. 10, 11, and 12, the transverse loads (V) are plottedagainst the transverse midlength deflections (a) for seriesRHB, series RNHB, and series RHNB tests, respectively. Inthese figures, the load-deflection response measured from thephysical tests is compared to that obtained from the FEM procedure. These plots indicate an excellent predictability of theload-deflection behavior by the FEM analysis in almost allcases. Again, the only exception is specimen RHB-2 in Fig.10, where the actual response is somewhat "softer" than thatcomputed by FEM analysis.
strengths with reasonable accuracy for almost all specimens.The only exception is specimen RHB-2 in Table 4 where theFEM procedure somewhat overestimates the test strength.However, the average ratios of test to FEM strengths are closeto 1.0 and the related coefficients of variation are small (footnotes of Table 4), indicating the predication acceptability ofthe FEM procedure used.
The strength comparisons given in Table 4 are based onf:yllnder = 0.81f:ube· When this conversion factor was increasedto 0.85 and 0.9, the average ratios of test to FEM strengths inTable 4 decreased by 1-3% and 3-5%, respectively, whilethe coefficients of variation remained unaffected, indicatingagain the near insignificance of the concrete strength conversion factor within the range studied for these specimens.
Fig. 9 compares the Nu-Mut strength interaction diagramscomputed from the FEM method (Table 4), from the ACI 318and Eurocode 4 procedures (Table 3), and from test results(Table 2). Three sets of plots are shown in the figure. Eachset represents a different series of tests and, hence, a differentbonding condition at the interface of the steel ribs and surrounding concrete. Fig. 9 shows that although there are somedifferences in strengths obtained from the three computationalmethods, particularly at e/h ratios less than 0.9, all three methods predict the beam-column specimen test strengths withinreasonable accuracy over the entire range of e/h ratios tested.This seems valid regardless of the bonding condition at theinterface of steel ribs and surrounding concrete.
SUMMARY AND CONCLUSIONS
The structural behavior and ultimate strength of slendercomposite steel-concrete beam-columns was observed from 16
FIG. 10. Load-Deflection Curves for Series RHB Specimens
10 20 30 40 50 60 70
f> [mm)
FIG. 11. Load-Deflection Curves for Series RNHB Specimens
by a beam-column specimen to reach its failure load. The termshown inside the square brackets in (7) represents the effectof rate of loading on the strength of in-situ concrete and isdocumented in a study by Mirza et al. (1979). This term variedfrom 0.87 to 0.91 for the 16 beam-column specimens reportedhere.
The possible effects of concrete confinement due to lateralties, of slip between longitudinal steel and surrounding concrete, and of the presence of shear forces on resistance in combined axial compression and bending were neglected for FEM.
Ultimate Strengths
The values of Nu, Vu, Mu.. and Mum computed from the FEMprocedure are given in Table 4 for all beam-column specimens.Also given in this table are the ratios of test to FEM strengths.Table 4 indicates that the FEM procedure predicts the test
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specimens loaded to failure under the combined effect of axialand transverse forces. The external eccentricity covered theentire practical range of the axial force-bending moment interaction diagram. Three bonding conditions at the interfaceof steel rib connectors and surrounding concrete were investigated. The structural steel stresses and concrete strains weremeasured and the typical failure mechanism was identified.
Observations from the physical tests indicate that, for staticloads, the bonding condition at the interface of steel ribs andsurrounding concrete had a small effect on the ultimatestrength. The tests also show that the present ACI 318 andEurocode 4 procedures adequately estimate the ultimatestrength of composite beam-columns, and that the ACI 318assumption of maximum usable strain of 0.003 at concreteextreme compression fibers near ultimate load is valid for suchbeam-columns. Predictions from a nonlinear finite-elementmodeling procedure provide good comparisons to the ultimatestrength and load-deflection response obtained from the physical tests.
APPENDIX I. REFERENCES
ABAQUS version 4.8 theory manual. (1989a). Hibbit, Karlsson, and Sorensen Inc., Pawtucket, R.I.
ABAQUS version 4.8 users' manual and example problems. (1989b). Hibbit, Karlsson, and Sorensen, Inc., Pawtucket, R.I.
Bafant, Z. P., and Oh, B. H. (1984). "Deformation of progressively cracking reinforced concrete beams." ACI J., 81(3), 268-278.
Building code requirements for structural concrete (ACI 318-95) andCommentary (ACI 3I8R-95). (1995). Am. Concrete Inst. (ACI), Detroit, Mich.
Design of composite steel and concrete structures-part I-I: general rulesand rules for buildings (Eurocode 4). (1992). Euro. Committee forStandardization, Brussels, Belgium.
Griffis, L. G. (1986). "Some design considerations for composite-framestructures." AlSC Engrg. J., 23(2), 59-64.
Leonhardt, F., Andrii, w., Andrii, H.-P., and Harre, W. (1987). "Neues,vorteilhaftes Verbundrnittel fUr Stahlverbund-Tragwerke mit hoherDauerfestigkeit." Beton- und Stahlbetonbau, Berlin, Germany, 12,325-331.
L'Herrnite, R. (1955). Idees actuelles sur la technologie du beton. Collection de L'lnstitut Technique du Batiment et des Travaux Publics,Paris, France.
Load and resistance factor design specification for structural steel buildings. (1993). Am. Inst. of Steel Constr. (AISC), Chicago, Ill.
Mirza, S. A., Hatzinikolas, M., and MacGregor, J. G. (1979). "Statisticaldescriptions of strength of concrete." J. Struct. Div.. , ASCE, 105(6),1021-1037.
Morino, S., Matsui, C., and Yoshikai, S. (1986). "Local buckling of steelelements in concrete encased columns." Proc., Pacific Struct. SteelConf, New Zealand Heavy Engrg. Res. Assn., Auckland, New Zealand,Vol. 2, 319-335.
Oguejiofor, E. C., and Hosain, M. U. (1992). "Perfobond rib connectors
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for composite beams." Proc.• Compos. Constr. in Steel and ConcreteII, ASCE. New York, N.Y., 883-898.
Oguejiofor, E. C., and Hosain, M. U. (1994). "A parametric study ofperfobond rib shear connector." Can. J. of Civ. Engrg., Ottawa, Canada, 21(4), 614-625.
Ric1es,1. M., and Paboojian, S. D. (1994). "Seismic performance of steelencased composite columns." J. Struct. Engrg., ASCE, 120(8),24742494.
Saenz, L. P. (1964). "Discussion of 'Equation for the stress-strain curveof concrete,' by Prakash Desayi and S. Krishnan." ACI J., 61(9),1229-1235.
Zhang, F., and Yamada, M. (1992). "Composite columns subjected tobending and shear." Proc., Compos. Constr. in Steel and Concrete II,ASCE, New York, N.Y., 483-498.
APPENDIX II. NOTATIONThe following symbols are used in this paper:
a shear span;Ec = modulus of elasticity of concrete (E, =tension softening
modulus);e = external eccentricity acting at the failure section =
MuJNu;f; = compressive strength of concrete used for finite-element
modeling;f~ = measured compressive strength of standard concrete
cubes;f~YUnder = equivalent compressive strength of standard concrete
cylinders;f: = tensile strength of concrete used for finite-element mod-
eling;fu = ultimate tensile strength of steel;h = yield strength of steel;g = transverse load due to self-weight of the specimen;h = overall depth of composite cross section in plane of
bending;L length of specimen;
M u• external (first-order) bending moment acting at failuresection;
Mum = magnified bending moment acting at failure section;No = pure axial force capacity of the composite cross section;Nu applied concentric axial load at failure;
t = time (in seconds) taken to reach the failure load in abeam-column test;
V = applied transverse load (at failure = Vu);
d = transverse deflection at rnidlength (at failure =d m);
8 = moment magnification factor = Mum/Mu.;E = strain;
Em = maximum (fracture) strain of steel;Eo = strain corresponding to f;;Elf = final strain when tensile stress in concrete reduces to
