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Elastic Stiffness Equation of Composite Beam Element
4.1 CHARACTERISTICS AND CLASSIFICATION OF COMPOSITE BEAM Concrete slabs are generally laid on the steel beams in multi-storey, high-rise steel buildings. A slab on a beam will bend independently due to vertical floor loads, and a relative shear slip occurs on the interface if there is no connection between them (Figure 4.1). In this case, the concrete slab and the steel beam resist vertical loads jointly but as individual components. A shear connector can be designed and laid on the slab–beam interface to restrain the relative shear slip (see Figures 4.2 and 4.3), in which case the beam is a concrete–steel composite one and resists vertical floor loads as an integrity (Viest et al., 1997). Composite beams can be categorized into the following two types according to the performance of shear studs connecting concrete slabs and steel beams: Composite beams with full composite action (Figure 4.2). Sufficient shear connectors are designed for the fully composite beams so that they can resist the shear force on the interface between concrete slabs and steel beams, and the relative slip is small. The full bending capacity of the composite beams can be ensured in this case. Composite beams with partial composite action (Figure 4.3). Insufficient shear connectors are designed for the partially composite beams so that they cannot fully resist the shear force on the interface between concrete slabs and steel beams, and the relative slip is relatively large. The full bending capacity of the partially composite beams cannot be achieved. When the number of shear connectors is less than 50 % of that required for fully composite beams, the composite action between concrete slabs and steel beams is actually small, and it is negligible in engineering practice. A partially composite beam may be a practical option in structural design for the consideration of construction economy, under the condition that the relative slip between the concrete–slab flange and the steel beam is taken into account in the design. The most efficient and effective way for the analysis of steel frames is the finite element method (FEM) with beam–column members. Inconsistency of degree of freedom (DOF) will occur in finite element analysis of composite frames if two independent axial DOFs are introduced at the two ends of composite beams to consider effects of the relative shear slip (Dissanayeke, Burgess and Davidson, 1995; Faella, Martinelli and Nigro, 2001). To avoid such inconsistency, the elastic stiffness equation of a composite beam element, considering effects of relative slip, is derived based on elastic interaction theory proposed by Newmark, Siess and Viest (1951) through the solution of the governing differential equilibrium equation of the composite element. Advanced Analysis and Design of Steel Frames. Guo-Qiang Li and Jin-Jun Li # 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-03061-5