Arab J Sci Eng DOI 10.1007/s13369-015-1678-x RESEARCH ARTICLE - CIVIL ENGINEERING Behavior of RC Shallow and Deep Beams with Openings Via the Strut-and-Tie Model Method and Nonlinear Finite Element Waleed E. El-Demerdash 1 · Salah E. El-Metwally 1 · Mohamed E. El-Zoughiby 1 · Ahmed A. Ghaleb 1 Received: 22 January 2015 / Accepted: 23 April 2015 © King Fahd University of Petroleum & Minerals 2015 Abstract The strut-and-tie model (STM) has been widely applied for the design of reinforced concrete (RC), mem- bers particularly discontinuity regions. In this paper, on the basis of available experimental results of crack patterns, fail- ure modes, and trajectories of internal stresses from elastic finite element analysis (FEA), STMs have been suggested for many shallow and deep beams with openings, which had been tested experimentally. In addition, for comparison pur- poses, 3-D nonlinear FEA using ANSYS-12 package has been performed for selected beams. Some of the important factors affecting the behavior of RC beams, namely con- crete compressive and tensile strength, span-to-depth ratio, shear span-to-depth ratio, physical and mechanical prop- erties of horizontal, vertical web reinforcement and main steel, loading position, opening dimensions, and location, are investigated via a parametric study with the aid of 3-D nonlinear FEA. With such analysis, results of crack pattern, deflection, failure mode, and strain and stress distributions, which cannot be determined using the STM, are obtained. A comparison of the FEA with test results and proposed STMs has been carried out. The present study reveals the reliability of the STM method in obtaining a reasonable lower bound estimate of the load carrying capacity of RC ordinary/deep beams with openings. In addition, the 3-D nonlinear FEA of simple and continuous NSC and HSC ordinary/deep beams with/without openings yields accurate predictions of both the ultimate load and the complete response. B Salah E. El-Metwally selmetwally@yahoo.com 1 Structural Engineering Department, Mansoura University, El-Mansoura, Egypt Keywords Strut-and-tie model · 3-D nonlinear finite element analysis · Shallow and deep beams · Openings · Normal-strength concrete · High-strength concrete 1 Introduction Inserting openings in the web of a reinforced concrete, RC, beam is associated with not only a sudden change in the dimensions of its cross section, but also a concentration of stresses at the corners of the opening, and it is possible to induce transverse cracks in the beam. Openings also reduce the stiffness, which leads to excessive deformations and con- siderable redistribution of forces. In this paper, the behavior of selected RC shallow and deep beams with openings, constructed from normal-strength concrete, NSC, and high-strength concrete, HSC, is exam- ined. Current codes, e.g., ACI 318M-11 [1], define a beam to be deep when the span-to-overall-depth ratio L / h ≤ 4, or the shear span-to-overall-depth ratio a/ h ≤ 2. As a result of its proportions, the beam strength is usually con- trolled by shear, rather than by flexure, provided that normal amount of longitudinal reinforcement is used. Nevertheless, the shear strength of deep beams is significantly greater than that predicted using expressions developed for shallow beams. The method of strut-and-tie model, STM, has proved to be a rational method for the analysis and design of discontinu- ity regions [2, 3], D-regions; therefore, the method is utilized to carry out this investigation. In addition, the finite element package ANSYS-12 [4] is used to perform a 3-D nonlinear finite element analysis, FEA, of selected tested shallow and deep beams. The FEA, on one hand, is used to check the output results obtained from the STM and completes, on the other hand, the understanding of the behavior of the con- 123