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After a brief summary of the contents of the SP and the examples, several general points are discussed which are based on observations made about the examples. The choice of a strut-and-tie model is a major issue and different engineers may propose various modles for the same task. This leads to a discussion of the uniqueness of models and whether it is acceptable that different engineers may choose different models and thus different reinforcement arrangements and detailing for the same D-region. A further issue identified in some of the examples was the transition of a B-region to a D-region, and the procedure of modeling is shown. Finally the role and the importance of detailing is emphasized and some examples for this are given. Also some observations are made which led to recommendations for reconsidering some code provisions.

The following example illustrates use of STM's for design of a pile cap. Two load cases are considered: 1) axial load only, and 2) axial load and overturning moment. The design is based on Appendix A of ACI 318-02 Results are compared to section design procedures per ACI 318-99. Compared to section design metods, STM design is more rational and leads to a more reliable structure. Because the reinforcing bars are located above the piles, overall footing depth is increased compared to traditional design in which the bars are placed between piles.

In this example, application of the new strut-and-tie modeling provisions of ACI 318-02 to the design of a wall with openings is summarized. Because the openings constitute a significant portion of the wall, earlier Code versions provide little relevant guidance fro ensuring that the wall provides adequate resistance to the applied loads. Previous examples fo the application of strut-and-tie models (STM's) to multiple load cases and/or lateral loads are rare. The wall in this example is designed to resist multiple combinations of both gravity and in-plane lateral loads. Construction of the STM for each load eombination is outlined. In addition, employment of statically indeterminate STM's to improve the efficiency and serviceability of the wall design is discussed. The example also covers selection and anchorage of tie reinforcement, as well as capacity checks for struts and nodal zones.

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.

The design of the end region of a prestressed beam according to Appendix A of the 2002 ACI Building Code is presented. Two alternatives are considered, the first with straight strands and debonding toward the ends of the member in order to control stresses at transfer. The second case is with draped strands. Strut-and-tie modles corresponding to each of the two alernatives are developed, analyzed, and the reinforcement is proportioned to reseist the calculated internal forces. Anchorage length requirements were a critical factor in selecting the configuration of the truss model.

Inadequate design of indirect supports resulted in a lot of structural damage and near failure of structural concrete beams. Most codes, including ACI 318, do not properly cover this case. However, strut-and-tie models almost automatically lead to correctly reinforcing these critical discontinuity regions. This example combines indirect supports as well as indirectly applied loads and demonstrates the application of strut-and-tie models following Appendix A of ACI 318-2002.

The example problem of a deep beam with a rectangular opening represents a strong example of the application of Strut-and-Tie modeling of reinforced concrete structures. Since the entire beam constitutes a D-region, this example demonstrates the principles and methods that can be utilized to solve a wide range fo problems. Example #4 has been fully evaluated per the requirements of Appendix A of ACI 318-02.

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).

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.