Strut-and-tie models make the design of portions of complex structures transparent. This example, a pier table from a cable stayed bridge, is developed to show how strut-and-tie modeling can be used for an area that may be exposed to cyclic loading and how the results from alternate loads may be superimposed upon one another. The pier table transmits forces from the pylon, through an integral superstructure connection, to individual support legs. The pier table also creates an area for the transmission of superstructure forces. This example briefly describes the model development based upon the perceived flow of forces within the structure. The tie reinforcement is then detailed and the nodal zones checked.

A single corbel projecting from a 14 in. (356 mm) square column is designed using the strut-and-tie method according to ACI 318-02 Appendix A. The corbel is to support a precast beam reaction force, Vu of 56.2 kips (250 kN) acting at 4 in,(102 mm) from the face of the column. A horizontal tensile force, Nuc of 11.2 kips (49.8 kN) is assumed to develop at the corbel top, accounting for creep and shrinkage deformations. The structure and the loads are described in Fig. (3.1-1). Normal-weight concrete with a specified compressive strength, fc of 5 ksi (34.5 MPa) is assumed. The yield strength of reinforcement, fy is taken as 60 ksi (414 MPa). The selected corbel dimensions including its bearing plate are shown in Fig. (3.1-2). The corresponding shear span to depth ratio, a/d, is 0.24. A simple strut-and-tie model shown in Fig. (3.1-3) is selected to satisfy the code requirements. The main tie reinforcement provided is 5 #4 (#13 mm) bars. These bars are welded to a structural steel angle of 31/2 in. x 31/2 in. x 1/2 in. (89 mm x 89 mm x 13 mm). The reinforcement details are shown in Fig. (3.1-5).

At the ends of dapped-end beams, the transfer of load from the support into the beam is a D-region. The STM is excellent for modeling such a region. In a number of applications, for example parking structures, dapped-end beams are used in conjunction with inverted T-Beams. At each point where the load of the dapped-end beam sets on the inverted T-beam, a D-region is formed. The following example used ACI 318-02 Appendix A to design both the end region of thedapped-end beam as well as the tie back and vertical reinforcement needed for each point load on the inverted T-beam. Conventional B-regions in the dapped-end beam are designed using conventional AC1 beam design.

This paper documents the decisions made by ACI Committee 3 18 to introduce strut-and-tie models into the 2002 ACI Code. Sections 3 and 4 of this paper review code statements concerning the layout of strut-and-tie models for design. The format and values of the effective compression strength of struts are presented in Sec. 5. The first step was to derive an effective compression strength which gave the same cross-sectional area and strength using Appendix A as required by another code for the same concrete strength and same unfactored loads. The final selection of design values of the effective compression strength considered test results, design values from the literature, values from other codes, and ACI Code design strengths for similar stress situations. A similar derivation of the effective compression strengths of nodal zones is summarized in Sec. 6 of the paper. The description of the geometry of nodal zones in code language proved difficult. The design of ties is described in Sec. 7 of this paper and requirements for nominal reinforcement are in Sec. 8. Nominal reinforcement is provided to add ductility, to improve the possibility of redistribution of internal forces, and to control cracks at service loads.

A double corbel projecting from an interior column is designed using the strut-and-tie method according to ACI 318-02 Appendix A. The corbel transfers precast beam reaction forces, Vu of 61.8 kips (275 kN) acting at 6 in. (152 mm) from the face of the column at both ends. To account for beam creep and shrinkage deformations, a factored horizontal force, Nuc of 14.3 kips (63.6 kN) is assumed to develop at each side of the corbel top. The column is 14 in. (356 mm) square. The upper column carries a factored compressive axial load, Pu of 275 kips (1223 kN). The compressive strength of concrete, fc and yield strength of steel reinforcement, fy are taken as 4 ksi (27.6 MPa) and 60 ksi (414 MPa), respectively. Normal-weight concrete is assumed. The selected dimensions including the bearing plates are shown in Fig. (3.2-2). The shear span to depth ratio, a/d, is 0.38. A simple strut-and-tie model shown in Fig. (3.2-3) was used for the design. The provided main tie reinforcement is 7 #4 (#13 mm) bars. The anchorage of these bars is provided by welding each end of the bars to a structural steel angle of 4 in. x 4 in, x 1/2 in. (102 mm x 102 mm x 13 mm). The reinforcement details are shown in Fig. (3.2-5).