Design and Modeling of Slender and Deep beams with Linear Finite Element Method

Abstract

This study deals with the finite element analysis to determine the behavior of reinforced concrete beams and high walls. It is assumed that the behavior of these members can be described by a plane stress field. This thesis consists of two major parts. The first part is about reinforcing of slender beams with the Linear Elastic Finite Element Method (LE-FEM). The aim is to determine whether LE-FEM is able to provide safe and reliable reinforcement designs for slender beam specimens. In this thesis a new method of reinforcement design with the Scia Engineer 2D Finite Element (FE) module is developed. This new method is called the ‘step by step method’ or SSM. Capacity checks in accordance with the Eurocode are done with the help of the Scia 1D beam model. The nonlinear analysis of the specimens is done with the help of the NLE-FEM package called ATENA. This software can simulate the actual behavior of the concrete elements inclusive cracking and plasticity/yielding phases. A nonlinear analysis is set as the reference point for the actual behavior of the specimens and is validated by using laboratory research carried out by Van Hulten in 2010. Two main conclusions are drawn from the comparison of the linear elastic analysis and nonlinear analysis. First, the ‘step by step’ method of reinforcement design resolved the problem which was reported by Romans. He reported (2010) that, crack width criterion for the bottom of the cross section of the slender beams when the normal design method is used in Linear elastic finite element method does not satisfy the crack width criterion according to Eurocode. The second conclusion is that in the serviceability limit state, the LE-FEM cannot meet the Eurocode crack criterion requirements for most of the specimens due to large cracks in the web of the cross-section. It is found that shear reinforcement has a major effect on the control of cracking in the serviceability limit state in the web of the cross section. One possible solution is a combination of skin reinforcement with extra shear reinforcement. In this thesis this combination is introduced in three different categories, each with a different reinforcement ratio of the slender beam specimens. Their results in terms of ultimate and serviceability limit state (ULS and SLS) are presented as well. The second part of this thesis is about deep beams. In addition to slender beams, deep beam specimens will be examined as well. Deep beam specimens with span-depth ratios (a/d) smaller or bigger than 1 are investigated. Different reinforcement configurations are made using the following four analysis methods: standard beam method (SBM), the ‘strut-and-tie’ method (STM), the LE-FEM (Scia Engineer) and the NL-FEM (Scia Engineer). As in the first phase for slender beams, ATENA functions as a reference point. An evaluation procedure is carried out in order to properly model with ATENA. The conclusion is that for deep beam specimens with an a/d ratio of less than 1, all different reinforcing methods give satisfying results in SLS and ULS. However, the most efficient method that uses fewer reinforcements is the method based on NL-FEM (Scia Engineer) and STM. For deep beam specimens with an a/d ratio of more than 1 but still within the range of deep beams, the crack width criterion does not satisfy in the web of the cross-section. This problem is solved by doubling the amount of longitudinal mesh net at the bottom half of the cross-sectional area. All related documents can also be found on the website below: http://www.babak-dadvar.com/thesis/babak.html