Title: Determining Efficient Strut and Tie Models for Simply Supported Beams Using Minimum Strain Energy

Author(s): Qinang Hu, M. Tyler Ley, and Bruce W. Russell

Publication: Structural Journal

Volume: 111

Issue: 5

Appears on pages(s): 1015-1026

Keywords: deep beams; design methods; strain energy; strut-and-tie model.

DOI: 10.14359/51686824

Date: 9/1/2014

Abstract:
Strut-and-tie modeling is a design tool that can be used to address complicated problems where common assumptions made in sectional (beam) analysis do not apply. One early step in strut-and-tie modeling requires the user to envision a series of load paths within a structure. The literature contains little guidance on how to choose these load paths. This paper demonstrates how strain energy calculations can be used to quantify differences between different strut-and-tie models (STMs). The results provide insight and guidance for choosing an STM with minimum strain energy for simply supported beams. In addition, methodologies are provided that give the engineer the ability to judge the STM chosen and to affect positive changes if desired. Important conclusions include: 1) a three-panel STM shows improved efficiency over a single-panel STM; 2) the most efficient three-panel STM shows a characteristic geometry with a perpendicular compression strut and tension diagonal; 3) an analytical approach is discovered that supports using distributed longitudinal steel in D-regions; and 4) a simple method is presented to find the STM with the minimum strain energy. The work is directly applicable to deep beams and members in bending near reactions.