Advances in Steel Structures - part 48 ppt

450 S.F. Chen et al. convergence of the solution of the neutral axis orientation for all cross-sectional conditions. Six composite column specimens of rectangular cross-section with asymmetrically placed structural steel were first analyzed. The results agree well with the test results. The bending moment capacity of a composite column of asymmetric polygonal section is then checked and the required bar diameter is successfully designed. Quick convergence was observed in all cases studied herein. The proposed method has thus been shown to be effective and accurate, and is directly applicable in practical design. ACKNOWLEDGMENTS The work presented in this paper is the result of a collaborative effort between the Department of Civil Engineering of Zhejiang University and the Department of Civil and Structural Engineering of The Hong Kong Polytechnic University. The authors wish to thank The Hong Kong Polytechnic University for its financial support provided through the Area of Excellence Scheme and Dr. Y. L. Wong for helpful discussions. REFERENCES ACI Committee 318 (1992). Building Code Requirements for Structural Concrete (ACI 318-92) and commentary (A C1318R-92) , ACI, Detroit, MI. AISC-LRFD (1993). Load and Resistance Factor Design Specification for Structural Steel Buildings, AISC, Chicago, IL. Brondum-Nielsen T. (1985). Ultimate Flexural Capacity of Cracked Polygonal Concrete Sections under Biaxial Bending. ACI Struct. J., 82:6, 863-870. Chen S. F., Teng J. G. and Chan S. L. (1999). Biaxial Bending Design of RC and Composite Columns of Arbitrary Cross-Section. To be published. E1-Tawil S., Sanz-Picon C. F. and Deierlein G. G. (1995). Evaluation of ACI 318 and AISC (LRFD) Strength Provision for Composite Beam-Colunms. J. Construct. Steel Res., 34, 103-123. Eurocode 4, (1994). Eurocode 4: Design of Composite Steel and Concrete Structures, Commission of the European Communities, British Standards Institution, London. Johnson R. P. and Smith D. G. E. (1980). A Simple Design Method for Composite Columns. Struct. Engr., 58A:3, 85-93. Lachance L. (1982). Ultimate Strength of Biaxially Loaded Composite Sections. J. Struct. Div., ASCE, 108:10, 2313-2329. Manual of Steel Construction (1986). Load and Resistance Factor Design, 1st Ed., Amer. Inst. Steel Construct., Chicago, Ill. Mirza S. A. and Skrabek B. W. (1991). Reliability of Short Composite Beam-Clolumn Strength Interaction. J. Struct. Engrg., ASCE, 117:8, 2320-2339. Munoz P. R. and Hsu C. T. T. (1997). Biaxially Loaded Concrete-Encased Composite Columns: Design Equation. J. Struct. Engrg., ASCE, 123:12, 1576-1585. Roik K. and Bergmann R. (1984). Composite Columns-Design and Examples for Construction. Composite and Mixed Constructions, Proc. U. S Japan Joint Seminar, ASCE, Univ. Washington, 267-278. Roik K. and Bergrnann R. (1990). Design Method for Composite Columns with Unsymmetrical Cross- Sections. J. Construct. Steel Res., 15, 153-168. Rotter J. M. (1985). Rapid Exact Inelastic Biaxial Anlysis. J. Struct. Engrg., ASCE, 111:12, 2659- 2674. Yau C. Y., Chan S. L. and So A. K. W. (1993). Biaxial Bending Design of Arbitrarily Shaped Reinforced Concrete Column. ACI Struct. J., 90:3, 269-278. Yen J. R. (1991). Quasi-Newton Method for Reinforced Concrete Column Analysis and Design. J. Struct. Engrg., ASCE, 117:3, 657-666. EFFECTS OF LOADING CONDITIONS ON BEHAVIOUR OF SEMI-RIGID BEAM-TO-COLUMN COMPOSITE CONNECTIONS Y. L. Wong, J. Y. Wang and S. L. Chan Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong ABSTRACT In the design and analysis of moment resistance framed structures, the internal joints are generally modeled as two separate connections with independent characteristics. However, in the case of composite frames, the interaction between two connections located on both sides of the column can be significant, especially under the action of anti-symmetrical moments. In this paper, the experimental results of four composite beam-column internal joints are presented. The specimens were constructed using either flush endplate connections or partial depth endplate connections. Three different loading conditions were considered, namely, (1) hogging moment developed at connection of one side of the joint; (2) sagging moment developed at connection of one side of the joint; (3) hogging moment developed at one connection and sagging moments developed at the other connection simultaneously. Test results indicate that the connection subjected to loading case (1) or (2) has the moment capacity over 20% higher than the corresponding value developed under the loading case (3). Finally, the experimental results are compared with the calculations of an advanced component-based model. It is demonstrated that the analytical results were in good agreement with the experimental results. KEYWORD Composite, End-plate connection, Loading condition, Unbalanced moment, Component-based model. 451 452 Y.L. Wong et al. INTRODUCTION In design practice, the moment-rotation properties of connections located at two sides of internal joints have been modeled as two separate connections with independent. The influences of loading conditions are often ignored. However, in the case of composite frames under lateral loads, the interaction between connections located in interior joints, especially under the action of unbalanced moments may be significant. Previous experimental study of composite frames (Leon et al 1987) indicated that the positive moment capacity of an exterior connection was about 25% higher than that of the interior connection, while their capacities under negative moments were comparable. This is mainly because the improvement in strength and stiffness of composite structures, as compared with the steel counterparts, is achieved through the composite action of the slab. However, the linkage between the concrete slab and the column has been considered as a weak point and some researchers (Zandonini 1989, Kato and Tagawa 1984) emphasized the importance of interaction between column and slab. However, up to date, systematic study on this aspect is not available. The objective of this study is to experimentally quantify the interaction between connections under unbalanced moments. Theoretical analysis using a component-based model was also carried out. The contents of this paper are arranged as follows. In the first section, an experimental programme was presented. In the next section, a component-based model is introduced. The test results and the verification of the analytical results are presented in the third section. Finally, conclusions are drawn at the end of the paper. SPECIMEN DESCRIPTION AND TEST ARRANGEMENT Four specimens (SPFM1, SPPM2, SPMM3 and SPMM4) were constructed and tested. Connection types of flush endplate and partial depth endplate were selected (see Figure 1), where 'L' and 'R' denote the left and right connections respectively. All test specimens comprised two 305x127UB37 steel beams. The conventional metal decking floor system comprising a concrete slab supported by a profiled steel decking was chosen. The concrete slab was 1200mm width and 130mm overall depth filled with normal weight concrete with design strength of 40 N/mm 2. The steel decking was 1.0mm BONDEK II. Headed connectors of 19mm diameter and 100mm pre-welded length were adopted with Figure 1 Steel connection details Effects of Loading Conditions on Behaviour of Beam-Column Connections 453 one connector per trough. Longitudinal reinforcement was 10T10, and the corresponding ratio was 0.86% of the concrete area above the ribs of the decking. All bolts used in connections were 20mm diameter of grade 8.8 and tightened to 180 Nm by a hand torque wrench to provide the comparability and consistency of the specimen. Figure 2 Test set-up Figure 3 Different loading conditions and beam-end supports The general arrangement of the test set-up including a reaction flame and a loading system is illustrated in Figure 2. The column of a test specimen is hinge-connected to a ground-beam at the 454 Y.L. Wong et al. bottom, while the top of the column is connected with the actuator by low-friction swivel hinge bearings, which allow free rotation of the actuator as the specimen deforms. Load cells were fixed at the beam far ends through rigid bars to record the reaction forces for calculating the connection moments. The beam length from the column centerline to the beam-end support is 2.0m. The overall height of the column measured from the bottom hinge to the center of the actuator is 2.165m. The connection rotation is defined as the change in angle of steel beam relative to the column centerline. The lateral load was applied to the specimen at the column head by a computer-controlled double- acting hydraulic actuator with a maximum capacity of + 500kN and an available stroke up to 250mm. Different loading conditions (see Figure 3) were considered, namely, (1) only hogging moment achieved in connection (Case 1); (2) only sagging moment achieved in connection (Case 2); (3) hogging and sagging moments achieved at both connections simultaneously (Case 3). COMPONENT BASED MODEL OF COMPOSITE JOINT Figure 4 shows the modeling of an interior composite joint. The rigid bars on the left and right sides represent the boundary between connections and composite beams. The central rigid body coincides with the centroidal axis of the column. The rigid body and bars are connected by a continuum of nonlinear distributed springs in axial compression or tension to simulate the behaviour of connection components. Four types of elements are used to represent the connection components, including: (1) elements corresponding to beam flanges with endplate attached; (2) elements corresponding to beam webs with endplate attached; (3) elements of reinforcement; (4) elements of concrete slab. The idealized configuration for the tension and compression regions in concrete slab is illustrated in Figure 5. The constitutive rule and detailed derivation of properties for those elements may refer to Wang (1999). Rigid body d bar ,,lement 9 Y~ am 'ange 1 !! ! (a) Connection model (undeformed) (b) Connection model (deformed) Figure 4 Modeling of composite joint Effects of Loading Conditions on Behaviour of Beam-Column Connections 455 Figure 5 Idealized configuration of slab Figure 6 Force equilibrium in connections The discrete bodies of left and right connections are shown in Figure 6. For the sake of easy and clear expression, it is assumed that the left connection is under sagging moment and the right one is under hogging moment. According to the force equilibrium, we have, nsR n sL n con Ef i + F r + F; = N. ; Zf + Zf + Fr = NL (1) i=1 i=1 i=1 nsR nr ~"~fi(YoR - Yi) + ~ fi(YoR - Yi) + M*~ = M R (2) i=1 i=1 nsL nson ~-~fi(YoL - Yi) + ~-'~f (YoL - Yi) + Mr = ML (3) i=1 i=1 456 Y.L. Wong et al. where nsL and n,R are the number of elements in the left and right steel connections respectively; rt r and n co . are element numbers of reinforcing bars and concrete slab respectively; YoL and Yon are neutral line positions in left and right connections respectively; N z and N R are axial forces in left and right beams. F* indicates the force transferred from the opposite connection, and the additional moment then achieved is denoted by M*. Those values are calculated as follows, n r Fr =Fr =~~fi (4) i=I nr M; = ~ '~f/(YoL -Yi) (5) i=l b; F~ = be9" + b ~ 2 f (6) M;= b; beff q- b~ Ei:I f/(Yo. - Yi ) (7) in which, bef f and b~ are the effective widths of concrete slab corresponding to the contacted column flange and fill-in concrete and the opposite side respectively. The force f/of each element can be directly obtained from the constitutive rule of elements. fi = fi (di) (8) whereas the element deformation d i in the left and right connections is expressed as" di =(Y0L Yi)OL (i = 1, 2 nsL ) & (i = 1, 2 nco. ) di =(YOR Yi)On (i = 1, 2 nsR ) (9) (10) Special attention should be paid to the reinforcement elements, where d i is calculated as: di = OR(Yon Yi) + OL (YoL Yi) ( i = 1, 2 rt r ) (11) Since the nonlinear constitutive relations of connection elements, a numerical procedure with iteration is needed to determine the moment-rotation curve of connection(s). EVALUATION OF EXPERIMENTAL AND MODELING RESULTS Table 1 lists the experimental ultimate moments of connections with various configurations and under different loading conditions. As expected, flush endplate connections achieve higher resistance than partial depth endplate connections. It is worth to note that the connection resistance without concerning the interaction (Case 1 and 2 for specimens SPMM3 and SPMM4 respectively) was over 20% higher than that encountered by the influence from the opposite connection (Case 3 for specimens SPFM 1 and SPPM2). Effects of Loading Conditions on Behaviour of Beam-Column Connections 457 TABLE 1 COMPARISON OF ULTIMATE MOMENTS UNDER DIFFERENT LOADING CONDITIONS i i Loading Specimen Mult ~ Flush Partial Depth ( a )/( b ) \ ~~ (a) (b) (c) Ilml Case 1 SPMM3 (i) -239.01 -172.85 1.38 Case 2 SPMM4 ( ii ) 227.88 171.23 1.33 Case 3 SPFM1L/SPPM2L ( iii ) 175.03 128.89 1.36 Case 3 SPFM1R/SPPM2R (iv) -171.69 -142.11 1.21 ( i)/( iv ) ( v ) 1.39 1.22 - ( ii )/( iii ) ( vi ) 1.30 1.33 - 458 Y.L. Wong et al. Figure 7 Moment-rotation curves of specimens The complete moment-rotation curves of test specimens obtained experimentally and analytically are illustrated in Figure 7. In general, good agreement between the experimental and theoretical results has been achieved, at least up to the maximum moment levels. It is also evident that the proposed model can simulate the interaction effect existing between composite connections located at two sides of the column. The dashed line in Figure 7(a) to (d) represents the moment-rotation performance of a connection with the absence of the opposite connection. CONCLUSION Experimental work and rational analysis based on an advanced component-based model indicate that the interaction effects between composite connections of interior joints are significant when they are subjected to the unbalanced moments. This effect should be considered in the design of unbraced composite frames. Reference Kato B. and Tagawa Y. (1984). Strength of composite beams under seismic loading, Composite and Mixed Construction (edited by Roeder, C. W.), Proc. of the US/Japan joint seminar, ASCE, 42-49. Leon R. T., Ammerman D., Lin J. and McCauley R. (1987). Semi-rigid composite steel frames, Engineering Journal AISC, 4th quarter, 147-155. Wang J. Y. (1999). Nonlinear analysis of semi-rigid composite joints under lateral loading m Experimental and theoretical study, Ph. D thesis, the Hong Kong Polytechnic University. Zandonini R. (1989). Semi-rigid composite joints, Structural Connections: Stability and Strength (edited by Narayanan, R.), Elsevier Applied Science, 63-120. STEEL - CONCRETE COMPOSITE CONSTRUCTION WITH PRECAST CONCRETE HOLLOW CORE FLOOR D. Lam l, K. S. Elliott 2 and D. A. Nethercot 2 1School of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK 2 School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK ABSTRACT Precast concrete hollow core floor units (hcu) are widely used in all types of multi-storey steel framed buildings where they bear onto the top flanges of universal beams. In the current UK market, hcu's account for about 50% of all floors used in steel framed buildings, with an annual production of about 4 million square metres worth s The steel beam is normally designed in bending in isolation from the concrete slab and no account is taken of the composite beam action available with the precast units. A programme of combined experimental and numerical studies has been conducted, with the aim of deciding on a suitable approach for the design of composite steel beams that utilise precast concrete hollow core slabs. The results show that the precast slabs may be used compositely with the steel beams in order to increase both flexural strength and stiffness at virtually no extra cost, except for the headed shear studs. For typical geometry and serial sizes, the composite beams were found to be twice as strong and three times as stiff as the equivalent isolated steel beam. The failure mode was ductile, and may be controlled by the correct use of small quantities of tie steel and insitu infill concrete placed between the precast units. KEYWORDS Composite, concrete, hollow core, precast, push-off, shear studs, steel, structural design INTRODUCTION An effective way to improve structural efficiency is to utilise the favourable structural properties of the basic components and to combine them in a manner that leads to maximum performance in a safe and cost effective way. Composite action between steel beams and concrete slabs through the use of shear connectors is responsible for a considerable increase in the load-carrying capacity and stiffness of the steel beams, which when utilised in design, can result in significant savings in steel weight and / or in 459 . considerable increase in the load-carrying capacity and stiffness of the steel beams, which when utilised in design, can result in significant savings in steel weight and / or in 459 . the US/Japan joint seminar, ASCE, 4 2-4 9. Leon R. T., Ammerman D., Lin J. and McCauley R. (1987). Semi-rigid composite steel frames, Engineering Journal AISC, 4th quarter, 14 7-1 55. Wang J Figure 3 Different loading conditions and beam-end supports The general arrangement of the test set-up including a reaction flame and a loading system is illustrated in Figure 2. The column