Salah E. El-Metwally/et al/Engineering Research Journal 141 (March 2014) C50 – C70 05 C STRUT-AND-TIE MODEL AND 3-D NONLINEAR FINITE ELEMENT ANALYSIS FOR THE PREDICTION OF THE BEHAVIOR OF RC FSHALLOW AND DEEP BEAMS WITH OPENINGS Waleed E. El-Demerdash 1 , Salah E. El-Metwally 2 , Mohamed E. El-Zoughiby 3 , Ahmed A. Ghaleb 4 1 Teaching Assistant MET Academy, 2 Prof. of Structural Concrete, 3 Associate Prof., 4 Associate Prof. Structural Engineering Department, Mansoura University, El-Mansoura, Egypt ABSTRACT: The Strut-and-Tie Model, STM, has been widely applied for the design of non- flexural and deep members in reinforced concrete structures. In this paper, strut-and-tie models for selected (shallow and deep) beams with openings, have been suggested based on the available experimental results of; crack patterns, modes of failure, and internal stresses trajectors obtained from elastic finite element analysis. The proposed STM approach is, then, applied to one group of simple shallow beams and one group of simple deep beams tested experimentally. In addition, a three-dimensional nonlinear finite element analysis using ANSYS 12.0 computer program has been employed for two selected (shallow and deep) beams which were analyzed using the STM method. Some of the important factors affecting the behavior of reinforced concrete beams (named: concrete compressive and tensile strength, span to depth ratio, shear span to depth ratio, physical and mechanical properties of horizontal, vertical web reinforcement and main steel, loading position, opening dimensions and location) are investigated throughout a parametric study with the aid of the nonlinear finite element analysis. With such analysis, results of cracking patterns, deflections, failure mode and strain and stress distributions, that cannot be determined using the strut-and-tie model, are obtained. A comparison of the finite element results with test results and STM results has been carried out. Keywords: Strut-and-Tie model; Finite element method; Shallow and deep beams; Openings; Normal strength concrete; High strength concrete. 1. INTRODUCTION As per the ACI 318M-11 code [2], each shear span (a v ) of the beam in Fig. 1a, where a v < 2h, is a D-region. If two D-regions overlap or meet as shown in Fig. 1b, they can be considered as a single D-region for design purposes. The maximum length-to-depth ratio of such a D-region would approximately equal 2. Thus, the smallest angle between the strut and the tie in a D-region is arctan (1/2) = 26.5 degrees, rounded to 25 degrees. If there is a B-region between the D-regions in a shear span, as shown in Fig. 1c, the strength of the shear span is governed by the strength of the B-region if the B- and D-regions have similar geometry and reinforcement. This is because the shear strength of a B-region is less than that of a comparable D-region. Figure 1 Description of deep and slender beams (ACI 318-2011).