"Prepared by members of ACI Subcommittee 445-1, Strut and Tie Models, for sessions at the Fall Convention in Phoenix, October 27 to November 1, 2002, and sponsored by Joint ACI-ASCE Committee 445, Shear and Torsion and ACI Committee 318-E, Shear and Torsion."

Strut-and-tie modeling (STM) is an experimentally proven technique to analyze and design D-regions. STM is easy to model if the truss configuration is available. The flow of forces and stresses within the beam can be visualized with STM, and an appropriate truss can be assembled to represent the stress pattern. The required reinforcement to resist the tension at different locations can be detailed from the forces in the truss members. The study presented herein analyzes and designs deep beams subjected to point loads and uniformly distributed loads. Beams with high-strength as well as normal-strength concrete were modeled in this study. The clauses from ACI 318 (2008) are followed throughout this research. Strut-and-tie technique is an iterative process. MATLAB programs were written to perform the iterative calculations. The output from the MATLAB programs includes the longitudinal reinforcement as well as shear reinforcement required to resist the applied loads on the beam. The cases considered herein included simply supported beams subjected to single or two point loads. The loads were placed symmetrically as well as asymmetrically. The output from the MATLAB programs was verified with the software CAST. The results from MATLAB were found to be in agreement with CAST output. A comparative study between two different models proposed in literature was performed and the results were included to justify the selection of a particular model in this research. An attempt was made in this research to generate an optimum design. The design was subjected to a large number of iterations. These iterations generated an optimum truss height and, hence, the most efficient deign for the given beam properties. The strut-and-tie model considered in this research requires design of shear reinforcement as well as reinforcement to resist the transverse tensile force in the bottle shaped struts. The required reinforcement to resist the two actions (shear and transverse tension) was detailed such that excessive use of bars was avoided. The detailing of the longitudinal reinforcement was performed in a manner that would ensure ease of field installation. Preference was given to straight developed bars and smaller diameter bars. Similarly, large diameter bars were avoided as shear reinforcement. Adequate space was ensured within the bars from the same layer, with adjacent layers and shear reinforcement to facilitate concreting of the section.

This book examines the application of strut-and-tie models (STM) for the design of structural concrete. It presents state-of-the-art information, from fundamental theories to practical engineering applications, and also provides innovative solutions for many design problems that are not otherwise achievable using the traditional methods.

The contents of this book have been chosen with the following main aims: to review the present coverage of the major design codes and the CIRIA guide, and to explain the fundamental behaviour of deep beams; to provide information on design topics which are inadequately covered by the current codes and design manuals; and to give authoritative revie

First published in 1984, Limit Analysis and Concrete Plasticity explains for advanced design engineers the principles of plasticity theory and its application to the design of reinforced and prestressed concrete structures, providing a thorough understanding of the subject, rather than simply applying current design formulas. Updated and revised th

Strut-and-Tie models are useful in designing reinforced concrete structures with discontinuity regions where linear stress distribution is not valid. Deep beams are typically short girders with a large point load or multiple point loads. These point loads, in conjunction with the depth and length of the members, contribute to a member with primarily discontinuity regions. ACI 318-08 Building Code Requirements for Structural Concrete provides a method for designing deep beams using either Strut-and-Tie models (STM) or Deep Beam Method (DBM). This report compares dimension requirements, concrete quantities, steel quantities, and constructability of the two methods through the design of three different deep beams. The three designs consider the same single span deep beam with varying height and loading patterns. The first design is a single span deep beam with a large point load at the center girder. The second design is the deep beam with the same large point load at a quarter point of the girder. The last design is the deep beam with half the load at the midpoint and the other half at the quarter point. These three designs allow consideration of different shear and STM model geometry and design considerations. Comparing the two different designs shows the shear or cracking control reinforcement reduces by an average 13% because the STM considers the extra shear capacity through arching action. The tension steel used for either flexure or the tension tie increases by an average of 16% from deep beam in STM design. This is due to STM taking shear force through tension in the tension reinforcement through arching action. The main advantage of the STM is the ability to decreased member depth without decreasing shear reinforcement spacing. If the member depth is not a concern in the design, the preferred method is DBM unless the designer is familiar with STMs due to the similarity of deep beam and regular beam design theory.

The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.