Use of Strut-and-Tie Models to Calculate the Strength of Deep Beams with Openings

Abstract

Strut-and-tie modeling is a method applicable to almost every design situation in reinforced concrete. This is a behavioral theory proposed as a alternative to past design strategies utilizing empirical formulas and parameters. Since the original presentation of this method in the 60' s numerous experimental studies have been conducted, yet the topic of deep beams with large web openings has not been widely covered. Design codes and guidelines also do not commonly cover this topic. However empirical design equations have been proposed based on previous research in the field. An empirical method is presented and the relation to the beam geometry and behavior is discussed. A discussion of the strut-and-tie method is also given including the limited previous research and application of the method. These two methods are compared using previous experimental results of deep beams with openings. The comparison includes analysis of predicted loads and ultimate loads as well as predicted behavior using the strut-and-tie method for beams with and without web reinforcement. For beams with reinforcement a model was constructed to compare a realistic reinforcement detail. This generates a fairly accurate assessment of strength and behavior with the experimental results. In beams without reinforcement a model is presented using ties only where available. This general model was then adapted to three of the experimental beam geometries. This model gives consistent prediction of the ultimate load and beam behavior in each beam. The results presented reinforce the strut-and-tie method as a safe approach in structurally diverse situations where empirical methods may have a limited range of application.