scope:

Introduction

Strut-and-tie models provide an excellent tool for the design of structural concrete where sectional design procedures for flexure and shear do not apply. This is the case in discontinuity regions (D-regions), which may exhibit structural damage or even brittle failure if not properly designed and detailed. This special publication presents further examples for the use of strut-and-tie models following Appendix A of ACl 318-2008 for designing structural concrete members with D-regions. This SP is a follow-up of ACl SP 208. which was published in 2002 when the Appendix A was first introduced into ACl 318. The major part of this Special Publication presents 13 different examples designed with strut-and-tie models using Appendix A of ACl 318-2008. Most of these examples were taken from design practice of buildings and bridges:

• The Examples 1 and 2 dealing with hammerhead bent caps, and Example 3 dealing with a foundation grade beam represent D-regions. which so far have been designed by sectional design for flexure and shear.

• The Example 4 deals with the design of end-regions of prestressed beams, which represent a classical problem in the design of prestressed concrete beams.

• The Examples 5 and 6 deal with the design of beams in buildings which contain critical D-regions.

• The Example 7 covers a dapped end beam with a curved bar node, which is a valuable addition to the nodes presented in Appendix A of ACl 318.

• The Example 8 presents a dapped girder end with a special steel device, the so- called Cazaly hanger.

• In Example 9 two link beams are designed of a high-rise building.

• The Example 10 presents a strut-and-tie design for a storey-high propped cantilever deep beam with a large opening, and additionally comparisons are made with plastic and non-linear truss analyses, finite element analysis, and with the results from a scale model test.

• The Example 11 presents the design with strut-and-tie models for a 3D-structure, which is a pile cap with tension piles.

• The Examples 12 and 13 present the design of diaphragms in two bridges, a segmental concrete girder bridge and an extradosed cable stayed bridge.

All examples were selected to demonstrate the potential of strut-and-tie models to solve uncommon design problems. The different design steps are shown, starting with the Important step of finding a model, followed by the dimensioning of the struts and ties, up to the steps with detailing and anchoring the reinforcing bars.

The Papers 14 and 15 deal with general topics rather than presenting numerical examples. Paper 14 points out the importance of detailing bydescribingthecollapseoftheConcorde Overpass that was partly due to improper hanger reinforcement details. The evolution of die hanger reinforcement details in dapped end beams given in different versions of the PCI Design Handbook is presented, and the results of a series of experiments on dapped end beams with different hanger reinforcement details are described.

Paper 15 deals with some controversial topics that were discussed in ACl Subcommittee 445-A "Strut-and-Tie Models". The sectional shear design of beams leads to discrepancies with the design of adjacent D-rcgions by the strut-and-tie models, but this is avoided by designing the whole member with the truss model. Furthermore, two important D-regions in beams are dealt with, which is a point load applied near the support and the indirect support. Finally, a list ot references is given lor further guidance in application of strut- and-tie models.