Aleksander KozlowskiEMPLOYMENT (last three): Rzeszów University of Technology, Poland, University of Beira Interior, Covilha, PortugalMAIN SCIENTIFIC ACHIEVEMENTS: •books, monographs: - Brodka J., Kozlowski A.: Strength and Stiffness of Semi-Rigid Joints. Monograph, 322 pages. (inPolish).OficynaWydawniczaPolitechnikiRzeszowskiej.Rzeszow,1996. - Kozlowski A.: Shaping of the Steel and Composite Skeletons with Semi-Rigid Joints. Monograph, 206pages.(inPolish).OficynaWydawniczaPolitechnikiRzeszowskiej.Rzeszow,1999. -BrodkaJ.,Kozlowski.:SkeletonSteelBuildings.Academicbook(inPolish).OficynaWydawnicza PolitechnikiRzeszowskiej.Rzeszow,2003. -BrodkaJ.,BarszczA.,GizejowskiM.,KozlowskiA.:Stiffnessandstrengthofswayframeswith semi-rigidjoints.2004. •publications: -authorandco-authorof139papersandconferencereports.PROFESSIONALACHIEVEMENTS:designof78projectsofsteelandconcretestructures,and96expertopinionsandconsulting on steel and concrete structuresMEMBERSHIPSininternationalassociations:EuropeanresearchprojectsCOST:C1,C12,C16,C25,C26
Rzszard Kowalczyk PRESENT AFFILIATION: Full Professor, Dept. of Civil Engineering and Architecture, University of Beira Interior since 1992.SCIENTIFICCAREER:MSc-WarsawUniversityofTechnologyin1951,PhDin1957,andDrScin1967. In1992TitleofProfessor.HonoraryProfessor:CracowUniversityofTechnology(2001)andSilesianUniversityofTechnology(2004).PROFESSIONALCAREER:over50yearsinresearch,consultingandteachinginvariousuniversitiesandresearchin-stitutesinhisnativePolandaswellasabroad(WarsawUniversityofTechnology,BialystokUniversityofTechnology,Institute of Building Research, Institute of Fundamental Technological Research of the Polish Academy of Sciences, Fritz LeonhardtDesignOffice,Stuttgart,Germany,TheUniversityofCalgary,Canada,LehighUniversity,Bethlehem,USA).UNESCOexpertinvocationalandtechnicaleducationintheMiddleEast(1983–1989)MAIN RESEARCH AREAS: structures, dynamics of structures, structural systems of tall buildings. Author or co-author ofover80papersintechnicaljournalsandconferenceproceedingsand7booksandmonographs.Member of Steering Committee of CTBUH, and Permanent Committee of IABSE
Estimation of the initial stiffness and moment resistance of steel and composite joints
Aleksander Kozlowski1, Ryszard Kowalczyk2 and Marian Gizejowski3
1Rzeszow University of Technology, Rzeszow, Poland, Tel: +48 17 854 11 27, Email: kozlowsk@prz,edu.pl 2University of Beira Interior, Covilha, Portugal, Email: [email protected]
3Warsaw University of Technology, Warsaw, Poland, Email: [email protected]
Abstract In the advanced design of framed multi-storey buildings, actual properties of joints and connection should be taken into account. It is namely: initial stiffness and moment resistance of a joint. The best way to obtain theses characteristics is experimental testing, but tests are very costly and time consuming. Based on the results from experiments and numerical analysis, few analytical methods were developed, amongst them component method, to estimate the moment-rotation characteristic of joints. This method was applied also in design codes. In the lately approved Eurocodes – Eurocode 3 (EC-3, 2005) and Eurocode 4 (EC-4, 2004), procedures allowing calculation of the initial stiffness and moment resistance of steel welded and end-plate bolted joints as well as composite joints are introduced. Eurocodes comprise also the method of classification of joints according to their strength as well as methods of global analysis correlated to this classification. Calculation of moment resistance and initial stiffness of a joint, following Eurocode procedures is rather troublesome and time consuming, so there is a need to develop design tools in the form of computer programs, diagrams or simple formulas for estimation of these values for everyday design practice. For this reason a computer program CRSJAE was developed, which includes full Eurocode procedures. Using this program wide parametric study was conducted, resulting, after regression analysis, in simple formulas for calculation of the main semi-rigid joint characteristics. Comparison with some available experimental test results shows quite good agreement.
Keywords: steel joints, composite joints, stiffness of joints, moment resistance, Eurocodes
Introduction Amongst structural systems applied in multi-storey
building, framed structures are still widely used in practice. In advanced design of steel framed structures, applying semi-rigid philosophy, actual properties of joints and connection i.e. moment resistance and stiffness, should be taken into account. In the pre-design phase of the structural engineer activity, it is required to estimate not only preliminary member section sizes but also joint properties. Especially important is the initial stiffness of joints, used in the classification of joints with regard to their stiffness (rigid, semi-rigid, nominally pinned), as well as in initial stability analysis of frames and in global analysis carried out for the calculation of member forces with regard to the actual stiffness of structural joints (Gi ejowski, 2006).
EC-3 (EC-3, 2005) and EC-4 (EC-4, 2004) provide methods of classification of joints according to their strength and stiffness, together with methods of global analysis correlated to this classification. Also methods of the calculation of initial stiffness and design moment resistance of structural steel and steel-concrete composite joints are there included. Hand calculation of the above mentioned joint properties is rather troublesome and time consuming. It is enough to say, that hand calculation of the moment resistance and initial stiffness of bolted joint, takes more that two hours of work of an experienced
person. Such calculation should be done in the final phase of design process, when checking the safety of a joint must be proved and this is very often done with the help of computer programs. For pre-design or for a conceptual phase of design it is necessary to supply designers with tools in the form of simple formulas and/or tables, which would allow for the estimation of main parameters of the joint characteristic in an easy way (Steenhuis, 1994), (Steenhuis, 1996).
The task of this paper is to provide design guidelines for the evaluation of moment resistances and initial stiffnesses of different types of steel and composite joints in the form of simple formulas. Since considered joints are commonly used in steel tall buildings, the results of this study may be interesting for structural engineers involved in design of framed steel and steel-concrete composite buildings.
Parametric study of moment resistance and initial stiffness
Eurocodes EC-3 (EC-3, 2005) and EC-4 (EC-4, 2004) comprise design procedures to calculate the moment resistance and initial stiffness of joints. These procedures are based on the component method. Analysis of design procedures used in these codes for the calculation of initial stiffness and moment resistance of steel bolted end-plate joints shows that these
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Estimation of the initial stiffness and moment resistance of steel and composite joints
Aleksander Kozlowski1, Ryszard Kowalczyk2 and Marian Gizejowski3
1Rzeszow University of Technology, Rzeszow, Poland, Tel: +48 17 854 11 27, Email: kozlowsk@prz,edu.pl 2University of Beira Interior, Covilha, Portugal, Email: [email protected]
3Warsaw University of Technology, Warsaw, Poland, Email: [email protected]
Abstract In the advanced design of framed multi-storey buildings, actual properties of joints and connection should be taken into account. It is namely: initial stiffness and moment resistance of a joint. The best way to obtain theses characteristics is experimental testing, but tests are very costly and time consuming. Based on the results from experiments and numerical analysis, few analytical methods were developed, amongst them component method, to estimate the moment-rotation characteristic of joints. This method was applied also in design codes. In the lately approved Eurocodes – Eurocode 3 (EC-3, 2005) and Eurocode 4 (EC-4, 2004), procedures allowing calculation of the initial stiffness and moment resistance of steel welded and end-plate bolted joints as well as composite joints are introduced. Eurocodes comprise also the method of classification of joints according to their strength as well as methods of global analysis correlated to this classification. Calculation of moment resistance and initial stiffness of a joint, following Eurocode procedures is rather troublesome and time consuming, so there is a need to develop design tools in the form of computer programs, diagrams or simple formulas for estimation of these values for everyday design practice. For this reason a computer program CRSJAE was developed, which includes full Eurocode procedures. Using this program wide parametric study was conducted, resulting, after regression analysis, in simple formulas for calculation of the main semi-rigid joint characteristics. Comparison with some available experimental test results shows quite good agreement.
Keywords: steel joints, composite joints, stiffness of joints, moment resistance, Eurocodes
Introduction Amongst structural systems applied in multi-storey
building, framed structures are still widely used in practice. In advanced design of steel framed structures, applying semi-rigid philosophy, actual properties of joints and connection i.e. moment resistance and stiffness, should be taken into account. In the pre-design phase of the structural engineer activity, it is required to estimate not only preliminary member section sizes but also joint properties. Especially important is the initial stiffness of joints, used in the classification of joints with regard to their stiffness (rigid, semi-rigid, nominally pinned), as well as in initial stability analysis of frames and in global analysis carried out for the calculation of member forces with regard to the actual stiffness of structural joints (Gi ejowski, 2006).
EC-3 (EC-3, 2005) and EC-4 (EC-4, 2004) provide methods of classification of joints according to their strength and stiffness, together with methods of global analysis correlated to this classification. Also methods of the calculation of initial stiffness and design moment resistance of structural steel and steel-concrete composite joints are there included. Hand calculation of the above mentioned joint properties is rather troublesome and time consuming. It is enough to say, that hand calculation of the moment resistance and initial stiffness of bolted joint, takes more that two hours of work of an experienced
person. Such calculation should be done in the final phase of design process, when checking the safety of a joint must be proved and this is very often done with the help of computer programs. For pre-design or for a conceptual phase of design it is necessary to supply designers with tools in the form of simple formulas and/or tables, which would allow for the estimation of main parameters of the joint characteristic in an easy way (Steenhuis, 1994), (Steenhuis, 1996).
The task of this paper is to provide design guidelines for the evaluation of moment resistances and initial stiffnesses of different types of steel and composite joints in the form of simple formulas. Since considered joints are commonly used in steel tall buildings, the results of this study may be interesting for structural engineers involved in design of framed steel and steel-concrete composite buildings.
Parametric study of moment resistance and initial stiffness
Eurocodes EC-3 (EC-3, 2005) and EC-4 (EC-4, 2004) comprise design procedures to calculate the moment resistance and initial stiffness of joints. These procedures are based on the component method. Analysis of design procedures used in these codes for the calculation of initial stiffness and moment resistance of steel bolted end-plate joints shows that these
CTBUH 8th World Congress 2008 �
characteristics depend on the following parameters (see Fig. 1):
- thickness of the end plate tp, - beam section height, - column section height, - diameter and grade of the bolts, - member steel properties, - horizontal distance of bolts "w", - vertical distance of bolts "mx", - width of end plate.
Fig. 1. Key geometric parameters for end-plate joints
To investigate influence of above mentioned factors on the main properties of a joint, a wide parametrical study was conducted. Calculation of the initial stiffness and moment resistance of joints was made by computer program CRSJAE (Koz owski and Pisarek, 1997) developed in Rzeszow University of Technology, Poland. This program was built in the form of EXCEL spreadsheet routine that includes full EC-3 (EC-3, 2005) and EC-4 (EC-4, 2004) design procedures.
Few examples of the relationship of initial stiffness of the steel joint Sj.ini vs some of the above mentioned parameters are shown in Figs. 2 to 6 (denoted there by Sj). Each joint was considered either as unstiffened, i.e. not stiffened (without stiffeners), or as partially or fully stiffened.
Fig. 2. Relationship between initial steel joint stiffness and height of the
column
Fig. 3. Relationship between initial stiffness of the steel joint and height
of the beam
Fig. 4. Relationship between initial stiffness of the steel joint and
thickness of the end plate
Fig. 5. Relationship between initial stiffness of the steel joint and bolt
diameter
Fig. 6. Relationship between initial stiffness of the steel joint and
vertical spacing of the bolt rows
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Development of simple formulas Results presented in Figs. 2 to 6 and conclusions
drawn from the parametrical studies carried out indicate that the initial stiffness of steel joint depends mainly on the height of beam and column sections, bolt diameter and end-plate thickness. These parameters were taken as variables to obtain simplified formulas.
As constant parameters, the following ones were considered as the most commonly used in practice:- steel grade S235 (Fe 360), - bolt grade 10.9, - beam sections IPE, - column sections HEB, - horizontal distance of bolts w = 3.5 d, - vertical distance of bolts mx = 1.5 d,
- width of end plate b
b bbp
fc fbfb2
but bp.
As variable parameters xi and boundary limits, the following was adopted: - thickness of end plate:
mmin)30,12(tx p1 ,
- height of the beam section (IPE):
mmin)400,160(hx b2 ,
- height of the column section (HEB):
mmin)400,140(hx c3 ,
- bolt diameter:
mmin)24,16(dx 4 .Theory of experiment design was used to find
simple formula for the evaluation of initial stiffness and moment resistance of considered steel joints. Detailed description of this method was presented elsewhere (Koz owski and Pisarek, 1995), (Koz owski, 1997). All numerical simulations were made using CRSJAE program and their results were used in regression analysis to obtain simplified equations of the following format:
BdhhtA=S ecc
bb
apj.ini (1)
DdhhtC=M nkc
gb
fpRd (2)
where: A, B (C, D)– constants for the evaluation of initial stiffness (moment resistance) obtained from the regression analysis,
a, b, c, e (f, g, k, n) – exponents for the evaluation of initial stiffness (moment resistance) obtained from the
regression analysis. Final formulas for various types of welded and
end-plate bolted steel joints are shown in Table 1. The following explanation is provided for Table 1:
- thickness of end-plate: tp in mm, - height of the beam section (IPE): hb in mm, - height of the column section (HEB): hc in mm, - bolt diameter: d in mm.
Simple formulas for the evaluation of initial stiffness and moment resistance of steel-concrete composite joints were obtained also using program CRSJAE, in which reinforcement concrete part components are activated as to the EC-4 procedure. The bases for numerical simulations were: characteristics of bare steel joints (their initial stiffness and moment resistance) and additionally, thickness of the concrete slab tr and the reinforcement ratio µ. Employing regression analysis, formulas for composite joint properties were obtained. The final results are presented in Table 2.
The explanation introduced for Table 1 holds also for Table 2, and additionally: - concrete slab thickness: tr in mm, - reinforcement ratio: in %.
Comparison of proposed simplified formulas for selected steel joints
To verify these formulas, a comparison of properties of selected steel joints is made, using fully documented experimental test results taken from data base Sericon (Weynand, 1992). A summary of the main test data is presented in Table 3. Figs. 7 to 9 show, as examples, the comparison of initial stiffness and moment resistance of steel joints as reproduced from experimental tests, evaluation according to EC-3 full procedure and estimation using simplified formulas presented in Table 1.
Fig. 7. Comparison for test no. 101.010 – experimental results, EC-3
component method and proposal of this study
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Table 1. Formulas for the estimation of the moment resistance MRd and initial stiffness Sj.ini of steel joints.
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..
Table 2. Formulas for estimation of the moment resistance MRd and initial stiffness Sj.ini for composite joints
Table 3. Summary of experimental test data of selected steel end-plate joints
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Fig. 8. Comparison for test no. 101.013 – experimental results, EC-3
component method and proposal of this study
Fig. 9. Comparison for test no. 109.001 – experimental results, EC-3
component method and proposal of this study
Comparison of results presented in Figs. 7 to 9 shows that proposed computational estimation of main characteristics of joints gives an approximation to test results within the range of ca 30% for the initial stiffness and moment resistance of joints. Moreover, although there are differences between the initial stiffness values obtained from full EC-3 design procedure and those obtained from developed simple formulas, they are small and this constitutes a proof that proposed formulas might be recommended for practical applications, especially for the pre-design stage of structural engineering activity.
ConclusionsThe results of calculations presented in this study
allow for the formulation of the following conclusions: The suggested procedure of using simple formulas
for the estimation of initial stiffness and moment resistance of joints proved to be very useful and easy for preliminary design of framed structures with semi-rigid joints.
Developed in the paper formulas based on Eurocodes 3 and 4 can estimate the main parameters of the moment-rotation characteristic of joints with accuracy not lower than 30%. This is not an excellent result, but taking into account the complicity and interrelationship of parameters involved and relatively simple procedure, it can be considered as sufficient from engineering point of view.
The suggested procedure gives to the engineer a tool to estimate by computation the values, which previously were proposed to be assessed by “good
guessing” procedure (Steenhuis, 2004) and relates these values to real parameters involved in joint functioning, such as for instance: bolts diameters, end-plate thickness and column sizes.
The method, thanks its simplicity, can be easy applied for pre-design of multi-story buildings, in which there are many different types of joints with various dimensions and solutions. Using simple formulas, it allows on considerable shortening of computation time for estimation of the necessary main characteristics of joints.
References Eurocode 3 (2005). EN 1993-1-8. Design of steel structures - Part 1-8: Design of joints. CEN, Brussels. Eurocode 4 (2004). EN 1994-1-1. Design of composite steel and concrete structures – Part 1-1: General rules and rules for buildings. CEN, Brussels. GIZEJOWSKI M.A., BARSZCZ A.M., KOZLOWSKI A., Sleczka L.(2006). Modelling, analysis and design of steel semi-continuous frames. In: Progress in Steel, Composite and Aluminium Structures (Eds. M.A. Gizejowski, A. Kozlowski, L. Sleczka, J. Ziolko). Taylor & Francis, London. KOZLOWSKI A. (1997). Research activity in the field of semi - rigid joint in Rzeszow University of Technology. COST C1. Doc. C1/ WD2/ 97 -14. Rzeszow. KOZLOWSKI A., Pisarek Z. (1995). Moment resistance and stiffness of end plate connections according to PN and EC3. Proceedings XLI Conf. KILiW PAN i KN PZITB. Krynica (in Polish). KOZLOWSKI A, Pisarek Z. (1997). Program CRSJAE for calculation the moment resistance and stiffness of steel joint according to EC-3.Rzeszow University of Technology. Rzeszow (in Polish). STEENHUIS M., GRESNIGT N., WEYNAND K. (1994). Pre-design of semi-rigid joints in steel frames. Proceedings of the Second State of the Art COST C1 Workshop. Prague. STEENHUIS M., EVERS H., GRESNIGT N. (1996). Conceptualdesign of joints in braced frames. Proceedings of the Twelfth IABSE Colloquium „Semi - Rigid Structural Connections”. Istambul. WEYNAND K. (1992). SERICON - databank on joints in building frames. COST C1 "Semi-Rigid Behaviour of Civil Engineering Structural Connections". Doc. C1/WD2/93-22. Strasbourg.
