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.

"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."

fib Bulletin 61 is a continuation of fib Bulletin 16 (2002). Again the bulletin’s main objective is to demonstrate the application of the FIP Recommendations “Practical Design of Structural Concrete”, and especially to illustrate the use of strut-and-tie models to design discontinuity regions (D-regions) in concrete structures. Bulletin 61 presents 14 examples, most of which are existing structures built in recent years. Although some of the presented structures can be considered to be quite important and, in some instances, complex, the chosen examples are not intended to be exceptional. The main aim is to look at specific design aspects, by selecting D-regions of the presented structures that are designed and detailed according to the proposed design principles and specifications for the use of strut-and-tie models. Two papers at the end of the bulletin deal with the role of concrete tension fields in modelling with strut-and-tie models, and summarize the experiences gained by the Working Group in applying strut-and-tie models to the examples in the bulletin. It is hoped that fib Bulletin 61 will be of interest to engineers involved in the design of concrete structures, supporting the use of more consistent design and detailing tools such as strut-and-tie models.

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.

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.