High-strength Concrete Deep Beams Research Articles

Experimental Study of Shear Performance of High-Strength Concrete Deep Beams with Longitudinal Reinforcement with Anchor Plate.

As a transfer member at the discontinuous place of vertical load, the deep beam has a complex stress mechanism and many influencing factors, such as compressive strength of concrete, shear span ratio, and reinforcement ratio. At the same time, the stress analysis principle of traditional shallow beams is no longer applicable to the design and calculation of deep-beam structure. The main purpose of this paper was to use the strut-and-tie model to analyze its stress mechanism, and to verify the applicability of the model. Nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate of the same size were tested by two-point concentrated loading method. The effects of shear span ratio (0.3, 0.6, and 0.9), longitudinal reinforcement ratio (0.67%, 1.05%, and 1.25%), horizontal reinforcement ratio (0.33%, 0.45%, and 0.50%), and stirrup reinforcement ratio (0.25%, 0.33%, and 0.50%) on the failure mode, deflection curve, characteristic load, crack width, steel bar, and concrete strain of the specimens were analyzed. The results showed that the failure mode of deep-beam specimens was diagonal compression failure. The normal section cracking load was about 15 to 20% of the ultimate load, and the inclined section cracking load was about 30~40% of the ultimate load. The shear span ratio increased from 0.3 to 0.9, and the bearing capacity decreased by 32.9%. When the longitudinal reinforcement ratio increased from 0.67% to 1.25%, the ultimate load increased by 42.6%. The shear span ratio and longitudinal reinforcement ratio have a significant effect on the bearing capacity of the high-strength concrete deep beams with longitudinal reinforcement with an anchor plate. The shear capacity of nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate was calculated by national standards, and the results were compared with the calculation results of the Tan-Tang model, the Tan-Cheng model, SSTM, and SSSTM. The analysis showed that the softened strut-and-tie model takes into account the softening effect of compressive concrete, and is a more accurate mechanical model, which can be applied to predict the shear capacity of high-strength concrete deep-beam members with longitudinal reinforcement with an anchor plate.

Experimental Study and Calculation Methods of Shear Capacity for High-Strength Reinforced Concrete Full-Scale Deep Beams.

The shear behavior of 8 high-strength concrete full-scale deep beams with high-strength steel bars was studied. The depth beam size was 100 mm × 900 mm × 2200 mm, the test parameters included the shear span-to-depth ratio ( = 0.9, 0.6, 0.3), longitudinal reinforcement ratio (.66%, 1.06%, 1.26%) and stirrup reinforcement ratio ( = 0, 0.26%, 0.34%, 0.5%). The ratio of the cracking load of the inclined section to the ultimate load is between 30% and 50%, and the bending deformation of the deep beam is small, showing the characteristics of brittle failure for deep beams. Under the action of a concentrated load, the failure mode of deep beams with a small shear span ratio is the failure of the diagonal compression struts, which is very different from that of shallow beams with a large shear span ratio. With the increase of shear span ratio from 0.3 to 0.9, the ultimate shear capacity of deep beams decreases by 19.33%. With the increase of longitudinal reinforcement ratio from 0.67% to 1.27%, the ultimate shear capacity of deep beams increased by 45.02%. With the increase of vertical stirrup reinforcement ratio from 0% to 0.5%, the ultimate shear capacity of deep beams increased by 8.93%. Increasing the area of longitudinal bars or stirrups limited the transverse tensile strain of the compression struts, which is conducive to improving the compressive strength of the compression struts of deep beams and then improving the bearing capacity of deep beams. The strut-and-tie model (STM) is more suitable for analyzing the shear capacity of deep beams. The calculation methods for calculating the shear capacity of deep beams were compared with ACI 318-19, CSA A23 3-19, EN 1992-1-1:2004, Tan–Tan model, Tan–Cheng model, softened STM (SSTM) and simplified SSTM (SSSTM). The results showed that the shear capacity of deep beams could be well predicted by reasonably determining the STM parameters.

Behavior of Waste Glass Powder in Concrete Deep Beams with Web Openings

Waste Glass Powder (WGP) could be used as a cement replacement additive to manufacture concrete and solving the problem of environmental pollution. The experimental program was made up of ten simply supported reinforced High-Strength Concrete (HSC) deep beams tested under static loadings. Five beams were with WGP, while the other five beams were without WGP. Eight beams had web openings while two reference beams were without openings. The principal studied parameters were the effect of using WGP, and the location and size of web openings. Using the three-dimensional finite element computer program ABAQUS, a numerical simulation for comparing the shear strength and behavior of tested deep beams has been suggested. The comparison between experimental failure loads of studied beams with that estimated by the Strut-and-Tie model was carried out. Three codes of practice were used to make this comparison: the American Concrete Institute (ACI 318-19), the New Zealand Code (NZS-06), and the Japan Society of Civil Engineering (JSCE-07). The results showed that using WGP in similar deep beams with web openings enhances the cracking shear strength (by about 17–25%) and the ultimate shear strength (by about 12–41%). The improvement in the ultimate failure load could be attributed to the developed concrete microstructures caused by WGP’s very fine grains, producing further gel, and decreasing the number of voids in the concrete matrix. The suggested finite element simulation accurately predicts the behavior of HSC deep beams with and without WGP beams and with web openings.

Flexural behavior of high strength concrete deep beams reinforced with GFRP bars

This paper presents an experimental and numerical study of the flexural behavior of high concrete deep beams reinforced with locally produced glass fiber reinforced polymers (GFRP) bars using high strength concrete (HSC). Both studies were carried out to study the effect of using (GFRP) bars with different ratios of reinforcement and concrete compressive strengths on the behavior of these beams.A total of eight beams, measuring 150 mm wide 500 mm depth and 1800 mm length, were cast, and tested up to failure under two-point loading. The main parameters were the types of reinforcement used, whether steel or GFRP bars. Also, concrete compressive strengths of 50 MPa and 60 MPa were used. In addition, different reinforcement ratios of 0.0033 for steel reinforcement and ratios (0.8, 1.0 and 1.2) of the balanced condition were used. The mid-span deflections, failure loads and GFRP reinforcement strains of the examined deep beams were recorded and compared with each other.The test results revealed that the crack widths and mid-span deflections significantly decreased when using 1.2μb of GFRP reinforcement ratio compared with beams reinforced with steel bars where μb is balanced reinforcement ratio of beam. The decrease in deflection varied between 20%–39.0% for specimens having 50 and 60 MPa respectively, with a significant decrease in the concrete cracks’ widths. Also, the ultimate load slightly increased by 2.5 % and 4.0 % as the concrete strengths increased.A Non-Linear finite element analysis (NLFEA) using ANSYS 2019-R1 was constructed to simulate the flexural behavior of the tested deep beams, in terms of failure load, crack pattern and load deflection behavior. Comparison between the experimental and numerical methods showed good agreement between both results.

Effect of Anchorage Length on the Shear Capacity of High Strength Concrete Deep Beams

Ten simply supported deep beams with high strength concrete (C55 MPa) have been casted and subjected to a four-point loading test. Different parameters were examined for their influence on specimen behavior. These parameters were the shear span to overall depth ratio (a/h), the overall depth of deep beams (h), and additional anchorage length beyond the centerline of support (la). The experimental results show that the beam capacity decreases as the shear span to the overall depth ratio increases, and the overall depth and embedment length decrease. The major effect of anchorage length on the shear strength is studied. Different failure modes were observed which do not match strut-and-tie failure modes. The shear compression and anchorage failures were con-trolled in the high compressive concrete deep beams due to bottom steel yielding. Finally, the ex-perimental test results are compared with predictions of the strut-and-tie method according to the ACI 318-14 and a good agreement was found.

Normal and High-Strength R/C Deep Beams under Pure Torsion and Codes Evaluation.(Dept.C)

Fourteen reinforced concrete deep beams were tested under pure torsion in order to evaluate the torsion design provisions of ACI 318-02 Building Code, the Egyptian code (ECCS-2001), the New Zealand code (NZS 3101-95), and the Eurocode 2 (EC-2) when applied to High Strength Concrete (HSC) deep beams. The results of these tests have been used to compare the torsional behavior of reinforced deep beams constructed from Normal-Strength Concrete (NSC with characteristic cube compressive strength fcu of about 35 MPa) and HSC (with fcu of about 81 MPa). The main parameters examined in this study were the design compressive strength, the provided transverse reinforcement ratio, the quantity of longitudinal and skin reinforcement and the size of the tested beams in the form of the tested span to total height ratio (L/h=1.0, 2.0 and 3.0). The results showed that the reserve in the torsional strength of the HSC deep beams aster cracking is considerably less than that of the similar NSC deep beams. The cracking torsional strength of the tested NSC deep beans is about 38-54% of the measured ultimate torsional strength, while the same ratio for the similar HSC deep beams is about 57-77% of the measured ultimate strength. The design torsional strength equations of the four international codes considered in this study were safe and conservative when applied to NSC and HSC deep beams. The predictions of the ultimate torsional strength of the deep beams according to the method of ACI 318-02 and using a value of the angle between the concrete struts and the longitudinal axis of the beam θ equal to 45 deg may give a conservative results less than that calculated using this angle between 30 and 60 deg.

Behaviour of Rectangular Concrete Deep Beams with Hybrid Fibre Reinforced Polymer Reinforcements Considering Web Openings

The use of non-corrosive reinforcements in the place of steel reinforcements has therefore been focused as an alternative to improve the life span of the concrete structures. Fibre Reinforced Polymer (FRP) reinforcements offer many advantages over steel reinforcements including resistance to electrochemical corrosion, high strength to weight ratio and easy in fabrication and electromagnetic insulating properties. Further, the use of hybrid FRP reinforcements, in lieu of conventional steel reinforcements requires better understanding under different parametric conditions. Therefore the present study deals mainly with the behaviour of Concrete Deep beams with and without openings reinforced internally with hybrid type Fibre Reinforced Polymer (FRP) reinforcements under static loading conditions. In structural applications, deep beams are commonly used as large span structures such as transfer girders in buildings, bridges, foundation walls, shear walls and offshore structures. In this study,high strength concrete deep beams are investigated. Among the eight beams, four beams are reinforced internally using conventional reinforcements with and without web opening, four beams are reinforced internally using hybrid FRP reinforcements with and without web openings. Different parameters like, high strength concrete, web opening positions (Top, Middle and Bottom), span sprinkled FRP hybrid reinforcements are considered. Based on this study, static load carrying capacities and their modes of failures of deep beams reinforced internally with FRP hybrid type reinforcements for various web openings positions are compared by finite element modelling using ANSYS software with the existing theories for better under standings. Based on the modelling and theoretical work, final conclusions of the present study are derived.

Effect of longitudinal opening on the structural behavior of reinforced high-strength self-compacted concrete deep beams

Deep beams are loaded as a simple beam in which the load is taken to the supports by a compressive force. Beam is classified as a deep beam if the beam has a depth larger than quarter of the clear span. Openings are very important in deep beams in order to allow the passage of conduits and other mechanical purposes. Bridge beams with a longitudinal opening are suitable for all services (electrical or mechanical). The present study carried out an investigation on the behavior of nine reinforced high-strength self-compacted concrete (RHSSCC) deep beams with longitudinal opening with different openings shape, size, and location. Two shapes (square and circular), two opening positions (compression and tension zone) were chosen and one-sixth of depth and one-quarter of depth side length or circular diameter dimension are used. The load capacity, deflection, absorbed energy and cracks pattern were recorded and discussed. The experimental program shows that longitudinal openings makes a reduction in the loading capacity of RHSSCC deep beams, increase in opening size decreases capacity load of deep beams, the change in longitudinal opening shape slightly affected and the longitudinal opening located in compression zone gave more reduction than openings located in the tension zone.

Behavior of high strength self compacted concrete deep beams with web openings

Deep beams transfer loads through loading face to supports in an inclined direction and mostly fail in shear. These beams are with a small span-to-depth ratio. Openings are used to facilitate the passage of utility pipes and service ducts. However, it will cause increasing in cracking and deflection and reduction in the ultimate load of the loaded deep beam. This research investigates and analyses the behavior of reinforced high-strength self-compacted concrete deep beams (RHSSCC) with web opening. Sixty-one deep beams were cast to investigate the effect of size (75 mm and 50 mm two opening's size were used), shape (square, circular and relatively new type “rhombus” shape) and location of openings with respect to a neutral axis (upper or lower N.A.) and with respect to the load path (in or out load path) on the behavior of RHSSCC deep beam with three types of web openings (symmetrical, unsymmetrical and centered web openings). Load-deflection curves, crack pattern, absorbed energy and crack pattern for the tested beams is discussed.

Tests of high-strength concrete deep beams

This study reports the test results of 16 high-strength concrete deep beams. Loads on the deep beams were transferred downwards between the columns to simulate real structures. The main variables studied were the shear span-to-depth ratios, and the parameter of horizontal and vertical stirrups. The test results indicate that the shear strengths of deep beams increase with decreasing shear span-to-depth ratio. The shear strengths can be significantly enhanced for deep beams with both horizontal and vertical stirrups. The shear strengths of deep beams with horizontal stirrups are higher than those of deep beams without horizontal stirrups. The normalised shear strengths of deep beams are not affected by the effective depth; the size effect on the normalised shear strength is not pronounced. A method for determining the shear strengths of deep beams is proposed.

Experimental verification of strut and tie model for HSC deep beams without shear reinforcement

The strut and tie model (STM) has emerged as an alternative effective design methodology particularly for D-regions and complex structural concrete members. This paper verifies the applicability of STM for predicting the shear capacity of high strength concrete (HSC) deep beams without web reinforcement. A total of 18 deep beams were constructed and tested in four-point bending up to failure. The test variables included the longitudinal reinforcement ratio, the shear span to depth ratio, and the beam depth. The load carrying capacity of the beams was predicted using STM. The accuracy of the predictions was examined considering two critical assumptions related to the upper strut height. The predicted load carrying capacity of the beams was compared with the experimental values. The results of the comparison indicated that the two assumptions of the upper strut height showed good prediction capability of the test results for HSC deep beams without shear reinforcement capturing the effects of the test variables.

Shear strength estimation of RC deep beams using the ANN and strut-and-tie approaches

Reinforced concrete (RC) deep beams are structural members that predominantly fail in shear. Therefore, determining the shear strength of these types of beams is very important. The strut-and-tie method is commonly used to design deep beams, and this method has been adopted in many building codes (ACI318-14, Eurocode 2-2004, CSA A23.3-2004). In this study, the efficiency of artificial neural networks (ANNs) in predicting the shear strength of RC deep beams is investigated as a different approach to the strut-and-tie method. An ANN model was developed using experimental data for 214 normal and high-strength concrete deep beams from an existing literature database. Seven different input parameters affecting the shear strength of the RC deep beams were selected to create the ANN structure. Each parameter was arranged as an input vector and a corresponding output vector that includes the shear strength of the RC deep beam. The ANN model was trained and tested using a multi-layered back-propagation method. The most convenient ANN algorithm was determined as trainGDX. Additionally, the results in the existing literature and the accuracy of the strut-and-tie model in ACI318-14 in predicting the shear strength of the RC deep beams were investigated using the same test data. The study shows that the ANN model provides acceptable predictions of the ultimate shear strength of RC deep beams (maximum <TEX>$R^2{\approx}0.97$</TEX>). Additionally, the ANN model is shown to provide more accurate predictions of the shear capacity than all the other computed methods in this study. The ACI318-14-STM method was very conservative, as expected. Moreover, the study shows that the proposed ANN model predicts the shear strengths of RC deep beams better than does the strut-and-tie model approaches.

Fuzzy modelling approach for shear strength prediction of RC deep beams

This study discusses the use of Adaptive-Network-Based-Fuzzy-Inference-System (ANFIS) in predicting the shear strength of reinforced-concrete deep beams. 139 experimental data have been collected from renowned publications on simply supported high strength concrete deep beams. The results show that the ANFIS has strong potential as a feasible tool for predicting the shear strength of deep beams within the range of the considered input parameters. ANFIS‟s results are highly accurate, precise and therefore, more satisfactory. Based on the Sensitivity analysis, the shear span to depth ratio (a/d) and concrete cylinder strength (f) have major influence on the shear strength prediction of deep beams. The parametric study confirms the increase in shear strength of deep beams with an equal increase in the concrete strength and decrease in the shear span to-depth-ratio.

Size effect on shear resistance of high strength concrete deep beams

Size effect on the shear strength of high strength concrete deep beams was investigated. A total of 12 full-scale reinforced concrete beams without web reinforcement were constructed and tested up to failure. The test variables included the beam depth and the concrete compressive strength. The beams were simply supported and were tested in four point bending. The test results showed that the shear stresses at failure decreased with the increase in beam depth indicating the existence of size effect. Beams of higher concrete strength exhibited more size effect than beams of normal concrete strength. The shear strength of the beams was analyzed using the ACI 318 strut and tie model (STM) provisions, Zhang and Tan’s STM, and kinematic model. The results of the analysis showed that conservative predictions by ACI 318 STM provisions were obtained for the tested deep beams. However, the ACI 318 STM did not capture the size effect. On the other hand, both Zhang and Tan’s STM and kinematic model were found to reflect the effect of beam size in their predictions.

High-strength concrete deep beams with web openings strengthened by carbon fiber reinforced plastics

The objective of this study is to examine the effect of carbon fiber reinforced polymer (CFRP) on the shear strengths of deep beams with web openings. A total of 18 high-strength concrete deep beams with web openings were tested. Twelve were externally wrapped with four layers of CFRP, six of them strengthened in the horizontal direction and the others in the vertical direction. The parameters of the configuration of CFRP, the sizes of the openings and the locations of the openings were covered in this study. The test results indicates the shear strengths of deep beams with openings sized <TEX>$60{\times}40mm$</TEX> were about 16% higher than that with openings sized <TEX>$68{\times}68mm$</TEX>. For deep beams with openings sized <TEX>$60{\times}40mm$</TEX>, the lower the locations of openings the higher the shear strengths were. The test results also indicate the shear strengths of deep beams with web openings strengthened by CFRP wrapped in the vertical direction can be enhanced by about 10%. However, the shear strengths of deep beams with web openings strengthened by CFRP wrapped in the horizontal direction can only be enhanced by about 6%. The shear strengths of deep beam, with different size and location of web openings and strengthened by different configuration of CFRP can be reasonably predicted by the empirical formulas of Kong and Sharp.

Environmental Studies and Researches Institute, University of Sadat City, Egypt

Reinforced concrete deep beams may exist in many structural applications such as offshore structures,transfer girders, pile caps, tall buildings and water tanks. The depth of deep beams is much greaterthan normal in relation to their span. Since the beam is short in this case, shear deformations are moreimportant and special design methods should be applied in this case rather than normal beam theory.Continuous deep beams are defined in the Egyptian Code of Practice (2012) [2]as those beams whoseheight to effective span ratio greater than 0.4. Deep beams are members with special features. In suchbeams, plane sections do not remain plane after bending, with significant warping of the crosssectionsbecause of high shear stresses. The resulting strain distribution is no longer linear andflexural stresses are not linearly distributed even in the elastic range. Recently, high strengthconcrete, defined by the American Concrete Institute ACI318-08[3], as concrete with cylindercompressive strength greater than 60Mpa, is being widely used in the construction industry.However, limited research efforts were directed towards the study of the behavior and shear strengthof reinforced high strength concrete continuous deep beams. Furthermore, sometimes web openingshave to be provided in deep beams for the purpose of access or for providing services. The presenceof such openings may affect the shear strength of deep beams. However, limited investigations weredirected towards the study of continuous deep beams with openings. Also, strengthening simplysupported deep beams using carbon fiber reinforced polymers (CFRP) was investigated by manyresearchers. However, limited research papers were directed towards CFRP strengthening ofcontinuous deep beams. Experimental tests have been carried out on rectangular reinforced concretecontinuous deep beams with a/d=1.17, under static loading up to failure. The study takes intoconsideration the following parameters: Percentage of web reinforcement (ρh), Positions ofopenings and number of openings. Also, strengthening of openings in continuous deep beams usingglass fiber reinforced polymer (GFRP) was studied in this research. Test results indicated that thepresence of web openings within exterior or interior shear spans had great effect on the beamcapacity and its behavior. Existence of web openings within exterior or interior shear spans caused ahigh reduction in the shear capacity of the beams by about 35%. Therefore and whenever should be kept clear of the natural load path joining the loading and reaction points (solid) free from openings.Also, the strengthening of openings contains the cracks and increase the crack and ultimate load.Finally we will compare the test results with the theoretical values for beam A1 which were evaluatedusing strut and tie analysis according to Egyptian code (2012). The strut–and tie method can be used forthe design of Disturbed regions (D- regions) of structures where the basic assumption of flexure theorynamely plane sections remaining discontinuities arising from concentrated forces or reactions and neargeometric discontinuities such as abrupt changes in cross section etc. The strut – and- tie method ofdesign is based on the assumption that the D-regions in concrete structures can be analyzed and designusing hypothetical pin-jointed trusses consisting of struts and ties interconnected at nodes. The usualdesign practice for continuous deep beams has been to employ empirical equations which are invariablybased on simple span deep beams testes. Given the unique behavior pattern of continuous deep beams,this practice is unreliable. Since continuous deep beams contain significant extents of D-regions and theyexhibit a marked truss or tied arch actions, the strut- and – tie method offers a rational basis for theanalysis and design of such beams. The mechanics and behavior of continuous deep beams are brieflydiscussed from which a strut–and–tie model for such a beam is developed.

NONLINEAR ANALYSIS OF HIGH STRENGTH CONCRETE DEEP BEAMS BY USING FINITE ELEMENT METHOD

In this paper, 4 high strength concrete deep beams were analyzed by nonlinear finite element method. The variables that considered in the investigation are shear-span to depth ratio, concrete strength (86-120 MPa). The investigation examines deep beam behavior and compares the analytical results with the ACI 318M-05(ACI318, 2005) and experimental results(Stephen et.al.,1996). In general, good agreement between the finite element and experimental results was obtained in this paper. The behavior of concrete in compression was simulated by an elasto-plastic work hardening model followed by a perfect plastic response, which was terminated at the onset of crushing. On the other hand, the behavior in tension is simulated by implementing a smeared crack model in connection with using a tension-stiffening model that account for the retained post-cracking stresses, and a shear retention model that modifies the shear modulus of rigidity as the crack widens. Several parametric studies have been carried out to investigate the effect of some important finite element and material parameters.

Effect of Type and Position of Shear Reinforcement of High-Strength Reinforced Concrete Deep Beams -ENG

This paper reports experimental data on the behavior and strength of high-strength concrete deep beams reinforced with shear reinforcement. Tests were conducted on eight reinforced concrete deep beams with stirrups in different type and positions using high-strength concrete (compressive strength of about 85.0 MPa). The beams measured 1400 mm long, 100 mm wide and 300 mm deep, and were tested under two point loads. The test variables were type and position of web reinforcements [Shear stress of vertical stirrups (vfy), Shear stress of horizontal stirrups (hfy) and Shear stress of inclined stirrups (αfy)] within shear span, within middle span(between two point loads) and along the beam. Conventional steel bars were used as longitudinal reinforcement in this investigation. The test results indicated that beams with vertical and inclined shear reinforcement within the shear span (B4) resisting the ultimate load of about 417.90kN. While beams with horizontal shear reinforcement (B3), shear reinforcement between two point loads (B7), and the beam without shear reinforcement (B8) resisting, 255.77, 260.18 and 250.55kN respectively. All the beams failed in shear and the optimum position of stirrups is the shear span for high strength concrete deep beams and with combination of vertical and inclined stirrups. Keywords: Concrete; Deep beams; High strength; Position; Shear; Stirrups.

Span-to-depth ratio effect on shear strength of steel fiber-reinforced high-strength concrete deep beams using ANN model

The paper predicts the shear strength of high-strength steel fiber-reinforced concrete deep beams. It studies the effect of clear span-to-overall depth ratio on shear capacity of steel fiber high-strength deep beams using artificial neural network (ANN8). The three-layered model has eight input nodes which represent width, effective depth, volume fraction, fiber aspect ratio and shear span-to-depth ratio, longitudinal steel, compressive strength of concrete, and clear span-to-overall depth ratio. The model predicts the shear strength of high-strength steel fiber deep beams to be reasonably good when compared with the results of proposed equations by researchers as well as the results obtained by neural network (ANN7) which is developed for seven inputs excluding span-to-depth ratio. The developed neural network ANN8 proves the versatility of artificial neural networks to establish the relations between various parameters affecting complex behavior of steel fiber-reinforced concrete deep beams and costly experimental processes.

Fracture Response of Reinforced Concrete Deep Beams Finite Element Investigation of Strength and Beam Size

This article presents a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The article describes the development of a numerical model that includes several nonlinear processes such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.