Finite Element Analysis for RC Deep Beams under an Eccentric Load

Periodica Polytechnica Civil Engineering

In this paper, reinforced concrete (RC) deep beams (DBs) have been analyzed numerically and a new approach is proposed to the nonlinear numerical modeling of such structural members. The effect of shear deformations and the interaction between reinforcing steel bar and concrete are considered in modeling and analysis. In order to consider the effect of shear deformations, the Timoshenko beam theory has been applied to formulate the analysis method. In the modeling, the RC DB is divided into several sub-elements which are composed of concrete and reinforcing steel bars. Individual degrees of freedom have been assigned to each reinforcing steel bar. Thus, each reinforcing steel bar is able to slip relative to its surrounding concrete and the bond effect is simulated by nonlinear springs. To consider the interaction between reinforcing steel bar and concrete, the concrete segment acts as a beam element, and each reinforcing steel bar acts as a truss element. The reliability of this met...

The shear size effect refers to the phenomenon that the shear strength of reinforced concrete (RC) beams decreases as the beam depth increases. The shear strength of RC deep beams is sensitive to boundary conditions (in this case, load-and support-bearing plate (or column) sizes), which in turn affect the shear size effect of deep beams. In this study, to separate and identify the influences of the bearing plate size on the shear size effect, existing deep beam tests on shear size effect are classified. It is verified that the shear size effect of deep beams with a fixed bearing plate size is stronger compared to deep beams with proportionally varied plate sizes. By using a non-linear analysis software ATENA based on concrete fracture and plasticity theory and a mechanical model called cracking strut-and-tie model (CSTM), the shear size effects of the classified test groups are accurately predicted, and the maximum height of each beam group is extrapolated to 4 m. Through in-depth analysis of the finite element model and CSTM results, it is inferred that the possible reasons that lead to the shear size effect of RC deep beams are: (1) bearing plate size effect, that is the reduced relative strut width caused by the disproportionately varied bearing plate size with the beam height; and (2) beam depth effect, which refers to the deterioration of the shear transfer strength by aggregate interlock of the critical shear crack due to the increase of the beam depth. In addition, based on the prediction results for the 4 m high beams and the existing test results, the STM in the ACI 318-14 is evaluated. The results show that the ACI STM can not inherently consider the beam depth effect, resulting in the safety of large-size deep beams designed according to the ACI STM is lower than that of small-size deep beams. For this reason, proposals for considering the beam depth effect in STM design are put forward.

Structures, 2020

The end support of deep beams could have different effects on behavior of the beams. In this paper, experimental results of 43 deep beams with span-to-depth ratio of less than 3, different reinforcement arrangements and boundary conditions were investigated and discussed. Results indicated that, boundary conditions have important effects on ultimate loads, modes of failure and deflections; but crack formation and their patterns are almost the same irrespective of applied boundary conditions. Furthermore, the ultimate loads of the beams with fixed ends are 1.2-6 times of simply supported and continuous deep beams, depending on amount of main bottom and top reinforcements. Furthermore, in fixed-end deep beams, modes of failure and ultimate loads mostly depend on top main reinforcement. To examine the beams theoretically, available standards and published proposed methods were used. Results indicated that, none of existing methods is suitable for fixed-end deep beams, except proposed method. However, the methods proposed by ACI 318-14 and CIRIA Guide 2 yielded very conservative results for simply supported deep beams.

A spatial finite element model of reinforced concrete (RC) beams with rectangular cross sections, typical side aligned stirrups and distributed or edge concentrated longitudinal reinforcement is presented. It is parameterised in its properties of geometry, material, discretisation and loads in biaxial directions. The concrete volume is discretisised into 8 or 20node solid elements. Truss elements discretely model each single reinforcement bar. They are coupled to the concrete elements using the ″embedded modelling″ technique. The ″concrete damage plasticity″ model of ABAQUS is used to describe the nonlinear material behaviour of concrete. Suitable material functions and material parameters are derived and verified to experimental data of (cyclic) uniaxial, biaxial or triaxial stress tests. Energy criteria and internal length parameters ensure almost mesh independent results of the simulations. An elasto-plastic material model with a gradually rising plastic branch is adopted for the reinforcing steel. The parametric model is verified to experimental data of uniaxial shear tests taken from the literature. Afterwards, it is used to establish a data base of biaxial shear resistances to check developed biaxial shear design formulas that base on simple strut and tie models. More than 100 simulations guarantee an extended and reliable verification that experiments -almost none of them are available in the literature -are not able to give. Moreover, the arrangement of the stirrups is optimised in dependence upon the distribution of the longitudinal reinforcement to minimise reinforcement amounts and increase bearing capacities.

International Journal of Engineering, 2019

Reinforced Concrete (RC) deep beams are commonly used in structural design to transfer vertical loads when there is a vertical discontinuity in the load path. Due to their deep geometry, the force distribution within the RC deep beams is very different than the RC shallow beams. T here are some strut and tie model (STM) already been developed for RC deep beams. However, most of these models are developed for RC deep beams with the simply supported boundary condition, which do not apply for RC deep beams with the fix-ended condition. In this paper, five fixed-end RC deep beams have been tested experimentally which were subjected to monotonic and cyclic loads. Also, a simple ST M was proposed to simulate the load capacity and failure mode of fix-ended RC deep beams. T he proposed ST M has the main strut and sub struts to simulate the force distribution within the RC deep beams. T his ST M were verified using five fixed-end RC deep beams subjected to monotonic and cyclic loads and compared to the response of 31 additional independent experimental tests. T he result shows the newly proposed ST M can simulate the load capacity and failure mode of fix-ended RC deep beams very well.

IJMER

ABSTRACT: Several reinforced concrete deep beams with different L/D ratios (1.5, 1.6, 1.71) were cast and tested in order to investigate the strain distribution pattern at mid-section of the beam. This paper describes analysis of deep beams subjected to two point loading with three different L/D ratios (1.5, 1.6, 1.71) using Non-linear Finite element method (ANSYS 9.0 software). In ANSYS 9.0 software, SOLID 65 and LINK 8 element represent concrete and reinforcing steel bars. Non-linear material properties were defined for both elements. Using ANSYS software Flexural Strains and deflections were determined at mid-section of the beam. The failure crack-patterns were obtained. Variations of flexural strains were plotted at mid-section of the beam. The beams were designed by I.S.456-2000 (Indian Standard Code of Practice for Plain and Reinforced Concrete). Flexural strains were measured experimentally at mid-section of the beam using Demountable mechanical strain gauge. The failure crack-patterns of the beam for different L/D ratios were also observed. The comparison between ANSYS results and experimental test results were made in terms of strength, flexural strain and deflection of concrete beams. The analytical and experimental flexural strains were compared at mid-section of the beam for different L/D ratios. It was found that the smaller the span/depth ratio, the more pronounced was the deviation of strain pattern at midsection of the beam. As the depth of the beam increases the variation in strength, flexural steel and deflection were found to be more experimentally than the non-linear finite element analysis.

International Journal of Engineering Research and Technology (IJERT), 2015

https://www.ijert.org/nonlinear-behavior-of-reinforced-concrete-continuous-deep-beam https://www.ijert.org/research/nonlinear-behavior-of-reinforced-concrete-continuous-deep-beam-IJERTV4IS040460.pdf This paper presents numerical investigation of nine continuous reinforced concrete deep beams were experimentally tested and collected from literature. The collected specimens cover several parameters which usually influenced on strength and behavior of continuous deep beams as shear span to depth ratio, the reinforcement ratio, the effective depth, and the concrete compressive strength. All beams had the same longitudinal top and bottom reinforcement and no web reinforcement to assess the effect of changing the beam depth on the shear strength of such beams. A three-dimensional finite element model using (ANSYS 12) program is used. It was found that the general behaviors through the linear and nonlinear ranges up to failure of the finite elements model show good agreement with observations and data from the experimental beam tests.

2015

This paper presents numerical investigation of nine continuous reinforced concrete deep beams were experimentally tested and collected from literature. The collected specimens cover several parameters which usually influenced on strength and behavior of continuous deep beams as shear span to depth ratio, the reinforcement ratio, the effective depth, and the concrete compressive strength. All beams had the same longitudinal top and bottom reinforcement and no web reinforcement to assess the effect of changing the beam depth on the shear strength of such beams. A three-dimensional finite element model using (ANSYS 12) program is used. It was found that the general behaviors through the linear and nonlinear ranges up to failure of the finite elements model show good agreement with observations and data from the experimental beam tests.

The paper deals with the comparison between experimental and analytical deflection results of reinforced (M20 grade) concrete deep beams. Three deep beams were designed according to the Indian Standard (IS) code provisions with different length to depth (L/D) ratios (1.5, 2, and 2.5). The beams were cast and tested by subjecting it to single central point loading (three point bending test). The loads at first crack and failure, deflections at first crack and failure and the crack widths were observed. Those parameters were also analyzed using software, ANSYS 9.0., which uses non-linear FEM. A graphical plot of load versus deflection was obtained for both experimental and numerical deflection values separately. The comparison between the experimental and analytical behaviour of the beams are also discussed.

This research presents an experimental study of shear behavior of RC deep box beam strengthened internally by reinforced concrete transverse ribs. Eight beam specimens were tested, six box-deep beams and two solid-deep beams. The effect of type of concrete (NSC and SCC) and the number of internal cells on the behavior of deep box beam were tested. All beams were (2000mm) long and have been tested over a clear span of (1900mm) with a width of (450 and 200 mm) for top and bottom flanges respectively and (500mm) depth, the shear span-depth ratio (a/d) was (2) and longitudinal reinforcement ratio (ρ) was (0.00835). All beam specimens were simply supported under the effect of single point loading at mid span. The beam length, shear span-depth ratio (a/d), longitudinal and transverse reinforcement were kept constant for all tested beams. Test results indicated that all tested beams failed by shear and the failure took place by diagonal splitting mode for all tested beams except one beam, where its shear failure took place by diagonal compression mode. The results reveal that as (fʹR c R) increased from (30.7 MPa) to (58 MPa), increase in the first diagonal cracking load of (solid, one cell, two cells, and four cells) beams were about (17%, 27%, 23%, and 24%) respectively. Also, It was found that as (fʹR c R) increased from (30.7 MPa) to (58 MPa) increase in the ultimate load of (solid, one cell, two cells, and four cells) beams were about (63%, 56%, 45% and 59%) respectively. Test results indicated, also, that the box-deep beams which have two cells and four cells have the highest first diagonal cracking and ultimate loads as compared with box-deep beam which has one cell.