Optimized design of RC deep beams based on performance metrics applied to strut and tie model and in-plane stress conditions

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.

NLFEA of Reinforced Concrete Corbels: Proposed Framework, Sensibility Study, and Precision Level

“…Therefore, the tensile stress-strain behavior model of concrete in tension was modeled according to Hordijk [28] in the next analyses. The use of models based on the concept of fracture energy is widely employed in numerical simulations found in the literature [11,12,36,[42][43][44] because it decreases the mesh dependence of the results [12]. In fact, in tests performed with Guo's model [41] that varied the mesh discretizations, the numerical results presented larger changes.…”

“…When µ = 0, no viscoplastic regularization is considered. In the literature, viscosity values are frequently found between 10 −3 [50], 10 −4 [51], and 10 −5 [12,43]. The default value considered for CDP is 0.…”

NLFEA of one-way slabs in transition between shear and punching: Recommendations for modeling

“…Many studies contributed to predicting the sectional shear capacity of reinforced concrete (RC) beams [11,12] and the punching capacity of flat slabs or slab-column connections [13,14] using three-dimensional (3D) non-linear finite element analyses (NLFEA). However, the following gaps were identified: (i) A limited number of studies addressed the challenge of using the same modeling strategy to assess the ultimate capacity of RC members that may develop different shear failure mechanisms (one-way shear and punching shear), such as one-way slabs under concentrated loads [15,16].…”

One-way shear and punching strength of reinforced concrete slabs without transverse reinforcement under concentrated loads

“…A large number of studies contributed to predicting the sectional shear capacity of reinforced concrete (RC) beams (RIBEIRO et al, 2020;SANTOS et al, 2019) and the punching capacity of flat slabs or slab-column connections (SOUSA et al, 2021b; GENIKOMSOU; POLAK, 2015) using three-dimensional (3D) non-linear finite element analyses (NLFEA).…”