Abstract
Abstract Deep beams do not behave according to classical beam theory. The nonlinearity of strain distribution within these elements requires application of strut and tie models (STM) or other alternatives to evaluate the complex stress field. Although the design of these elements is a common task for structural engineers, limited research is found on assessing effectiveness of the results. The purpose of this work is to compare, in a systematic approach, different design solutions for a deep beam using selected performance metrics which are strain energy, reinforcement ratio, maximum load, structural efficiency, safety factor and cracking behavior. A deep beam (2.85 m of height, 4.20 m of length and 0.2 m of thickness) with a square opening (0.7 m x 0.7 m) close to one of the supports was subjected to a uniform loading at the top surface while resting on supports at both ends. A simplified finite element model (FEM) of this beam was developed simulating concrete with elastic linear stress-strain behavior and disregarding steel reinforcements. This model allowed determination of elastic stress fields necessary to subsequent analyses. Four STM were then developed, supposing the total load respectively represented by one (STM-1), two (STM-2), four (STM-4) or eight (STM-8) concentrated loads equally spaced along the top of the beam. Additionally, an in-plane stress field method (SFM) was applied to the design of the same beam subjected to uniform loading on the top surface. After design and detailing of the reinforcement for each situation, nonlinear FEMs were used to predict the ultimate conditions. The strain energy reduced significantly comparing results from STM-1 to STM-2 and subsequently to STM-4 and remained at a low level in STM-8 and SFM. The reinforcement ratio reduced systematically from STM-1 to STM-8, was minimum with the SFM and the same behavior was followed by maximum load. The structural efficiency (maximum load/reinforcement ratio) increased from STM-1 to STM-8, with maximum efficiency at STM-8 and was slightly below with SFM. The safety factor reduced systematically from STM-1 to STM-8 and was slightly lower with SFM, but in all cases was above acceptable limits found in design codes.
Highlights
Design of reinforced concrete elements frequently relies on Euler-Bernoulli kinematic hypothesis, which admits a linear strain distribution along the cross-section of the structural elements
The present study focused on developing of numerical analysis to investigate the deep beams behavior in reinforced concrete
The beams were evaluated from strut and tie model for different design solutions by four load discretizations
Summary
Design of reinforced concrete elements frequently relies on Euler-Bernoulli kinematic hypothesis, which admits a linear strain distribution along the cross-section of the structural elements. Optimized design of RC deep beams based on performance metrics applied to strut and tie model and inplane stress conditions discontinuity in geometry or load configuration, such as pile caps, corbels, footings, beam column connections, deep beams and elements with openings. The Strut and Tie Model is attributed to Schlaich et al (1987) and is based on discretization of the structure in compression (struts) and tension (ties) bars connected by nodes The forces in this truss can be evaluated, allowing verification of concrete stresses and determination of steel reinforcement areas. All the models were evaluated from six performance metrics: factor of safety, reinforcement ratio, structural efficiency, maximum load, cracking behavior and the minimum energy strain, allowed to determine with precision the effectiveness of each model
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call