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The shear performance of T-shaped reinforced concrete (RC) deep beams with openings and subjected to several loading types was numerically investigated; and compared with existing experimental results. The studied parameters included flange dimensions, shear span-to-depth ratio, concrete strength, size and location of openings, VL and HZ stirrups ratios and loading type. In addition, top and bottom loaded deep beams were investigated. Increasing the flange depth by 50% and 100% increases the initial cracking load by 10% and 14% and the ultimate shear capacity by 16% and 22% respectively. The opening size controlled the appearance of the first diagonal crack load. Decreasing the opening size enhanced the first cracking load. Decreasing (a/d) by 16.7% and 41.7% increased the cracking load by 17% and 131% and the ultimate shear capacity by 13% and 115% respectively. Finally, the shear capacities for 71 test results have been calculated using an existing strut-and-tie model (STM). The comparison showed that the STM model performs well in predicting the ultimate shear capacity. The overall average value of the ratio between NLFE and predicted strengths is 1.157.

By conducting the direct shear test on a sample with a stepped structural plane and selecting representative samples for the cyclic shear test under fixed normal stress, the effects of the number (N) of the stepped structural plane, the top length (l1) of the stepped plane and the height (h) of the stepped structural plane on the shearing characteristics and damage morphologies of the specimens were studied. Test results show that: The shear strength of the stepped structural plane and the deterioration index of shear strength are affected by the stress concentration at the corners of the structural plane, the length of the rock bridge, the area and the aspect ratio of structural plane and the ability to resist edge failure of the specimen. When the value of l1 and h is fixed, as N raises from 1 to 5, the shear strength reaches the minimum value at N = 5. Shear failure is transformed into direct shear failure. In the specimen with single stepped structural plane, when the value of h is fixed, as l1 from 10 to 50 mm, the frictional sliding force between the crack surfaces will decrease firstly and then increases with the growth of number of diagonal crack. In the double stepped structural plane specimen, when the value of h is fixed, as l1 from 10 to 50 mm, the shear strength and c increases first then decreases. When the value of l1 is fixed, as h from 10 to 25 mm, the shear strength reaches the maximum value at h = 20 mm. The deterioration index of shear strength was inversely proportional to the number of cyclic shears, which is in turn proportional to N, h, and l1.

Deep beams are used in various applications in reinforced concrete (R.C.) structures. There have been continuous efforts to enhance and improve the performance of these crucial elements in (R.C.) structures by using several strengthening techniques such as using the carbon fiber-reinforced polymer (CFRP). However, by exploring the literature, none of the previously conducted experimental tests have studied the propagation of cracks beneath the (CFRP) sheets. In this research, the propagation of the first diagonal crack, which takes place beneath the (CFRP), is investigated by modeling sixteen (R.C.) deep beams with different opening sizes. Two shear span/depth ratios (a/h) are studied numerically using the finite element analysis tool (ABAQUS). All models are validated using the concrete damage plasticity (CDP) model, and their results are found similar to the experimental results obtained by other authors. Results show that the Finite Element models catch the real behavior of the (R.C.) deep beams. In addition, the (CFRP) sheets are found to enhance the failure load capacity as well as the flexural crack remarkably. Moreover, the (CFRP) increases the load required to cause the first diagonal crack for models with (a/h) equals 0.9, while there is a slight change in this load for models with (a/h) equals 1.1.

This paper experimentally studied the shear behavior of corroded post-tensioned prestressed concrete beams with full grouting. The effects of insufficient grouting in shear span on the shear behavior were also investigated. Eight beams were fabricated and divided into two groups: four beams with full grouting and four beams with insufficient grouting. Three beams in each group were subjected to accelerated corrosion. All beams were tested to failure in four-point loading. Experimental data on shear cracking, load-deflection response, shear strength and failure modes were presented. Results showed that strand corrosion accelerated the formation and propagation of diagonal crack. Insufficient grouting decreased the number of diagonal cracks. Strand corrosion degraded the post-cracking stiffness and shear strength. Insufficient grouting aggravated the propagation of diagonal crack and the degradation of post-cracking stiffness. The shear strength of corroded beam with 31.7% corrosion loss decreased by 15.44% as compared to that of the uncorroded beam. Strand corrosion loss less than 31.7% did not change the shear compression failure mode in fully grouted beams. The failure modes of locally ungrouted beams changed from shear compression failure to rupture of wires as the corrosion loss exceeded 39.6%.

This paper will examine in detail a posttensioned concrete (PTC) girder bridge with dapped-end connections, with a re-entrant corner diagonal crack that is typical of these types of bridge...

In this work, an experimental investigation on the behavior of reinforced concrete deep beams strengthened by near surface mounted steel bars is presented. Thirteen beams were cast and strengthened by steel bars with different strengthening schemes. The specimens were categorized into three groups according to the shear span over depth (a/d) ratio. Each group contained one unstrengthened beam as a control and other strengthened beams using different strengthening schemes of near surface mounted steel bars. Some parameters that might affect the performance of strengthened deep beams were studied, such as bar spacings, bar sizes, and their inclinations. All beams were tested under two points loading, adopting various shear span over effective depth ratios. The test results showed considerable enhancement in the ultimate capacity of strengthened beams by about 7.35–20.6%. Besides that, ductility and diagonal crack width were improved when more intensive strengthening schemes were adopted.

The results of an experimental and analytical study of the shear behavior of damaged or under-strength concrete beams strengthened with carbon fiber reinforced plastics (CFRP) grid and polymer cement mortar (PCM) shotcrete describes in this paper. The aim of this study is to evaluate shear performances of reinforced concrete beams retrofitted by using PCM shotcrete and CFRP grid. Four concrete beams reinforced internally with steel and externally with both PCM and CFRP grid (longitudinal direction used CR-10 and transversal direction used CR-6) applied to the specimens were tested under three-point bending. The shear failure is initiated by a major diagonal crack within the beam shear span. This diagonal crack extended horizontally at the level of the CFRP grid. Results show that PCM shotcrete with CFRP grid is very effective for shear strengthening. Increases in strength of 140% for PGB over the RCB as control, un-retrofitted beams were noted.

The present article proposed the analytic solution for the stress intensity factor of the symmetric coalescence crack, and then the effect of the crack propagation direction and the geometry characteristics on the stress intensity factor was discussed. The stress intensity factors of the central symmetric cracks, the edge symmetric cracks and the diagonal symmetric cracks were analyzed using the weight function method for various geometry sizes. In addition, we discussed the propagation direction of the coalescence cracks and introduced the dimensionless stress intensity factor to study the effect of the geometry characteristics on the stress intensity factor. Moreover, the theoretical results were verified by a numerical tests applying FLAC 3D. The results show that the stress intensity factor decreased and then remained at an asymptotic value with the increase in the intersection angle. Simultaneously, the magnitudes of the stress intensity factors for the mode-I and mode-II cracks decreased in the order of the diagonal crack, the central crack and the edge crack.

Purpose During service period, due to the overload or other non-load factors, diagonal cracks of the pre-stressed concrete beam are seriously affecting the safety of the bridge structure. The purpose of this paper is to quickly realize the shear bearing capacity and shear stiffness through maximum width of the diagonal cracks and make correct judgments. Design/methodology/approach Through the shear failure test of four test beams, collecting data of diagonal cracks and shear stiffness loss value. According to the deformation curve of the shear stiffness, and combined with the calculation formula of the maximum width of diagonal cracks, the formula for calculating the effective shear stiffness based on the maximum width of diagonal cracks is deduced, then the results are verified by test data. Data regression method is used to establish the effective shear stiffness loss ratio calculation formula, the maximum width of diagonal cracks used as a variable factor, and the accuracy of this formula is verified by comparing the shear failure test results of pre-stressed hollow plates. Findings With the increase in width of the diagonal crack, the loss rate of shear stiffness of the concrete beams is initially fast and then becomes slow. The calculation formulae for shear stiffness based on the maximum width of the diagonal cracks were deduced, and the feasibility and accuracy of the formulae were verified by analysis and calculation of shear test data. Originality/value A method for quickly determine the shear stiffness loss of structures by using maximum width of the diagonal cracks is established, and using this method, engineers can quickly determine effective shear stiffness loss ratio, without complex calculations. So this method not only ensures the safety of human life, but also saves money.

There are a significant number of historic masonry buildings and monuments in seismic areas all over the world that need to be retrofitted. Conventional methods of seismic rehabilitation conflict with the appearance of the masonry element and cannot be employed in the case of monumental buildings where the facade and finishing are decorative or where the exposed masonry defines the character of the structure. Centercore strengthening method has been developed in recent decades and is used in various projects of seismic rehabilitation. However, due to the lack of sufficient experimental and numerical investigation, there is no analytical model to predict the behavior of masonry components retrofitted using this technique. In this research, the material properties of conventional brick masonry used for the construction of Iranian historic buildings and monuments were obtained through base material tests. Afterward, two masonry walls were tested under reversed cyclic in-plane loading. The results showed that centercore method improved the cyclic in-plane behavior of the specimens including ultimate lateral strength and energy dissipation. Moreover, based on flexure theory an analytical model is proposed for prediction of ultimate lateral capacity of masonry walls and piers strengthened by centercore technique, associated with rocking and toe-crushing mechanisms. In addition, regarding dowel action of reinforcing bars and using “Beams on elastic foundation analogy”, a simple formula is proposed to predict the dowel action capacity of centercore rebar and hence, the diagonal crack strength of the retrofitted wall. Comparing the values calculated by the proposed models with available experimental data, showed that the proposed models accurately predicted the ultimate lateral capacity of the specimens.

This paper presents an experimental study on diagonal crack width estimation of Shear-Strengthened Pre-damaged Beams with CFRP strips (SSPBCs). Several parameters including pre-damaged degree, shear-span ratio and CFRP strips spacing are considered. The crack formation of shear-strengthened undamaged or low pre-damaged beams with CFRP strips is caused by reaching the ultimate tensile strain of concrete while that of shear-strengthened high pre-damaged beams with CFRP strips is due to the relative slip between stirrups and concrete. The development rate of diagonal crack increases as shear-span ratio, CFRP strips spacing or pre-damaged degree increases. The increase in CFRP strips spacing, pre-damaged degree or the decrease in shear-span ratio enhances the number of diagonal crack. The diagonal crack width of SSPBC increases as shear-span ratio, CFRP strips spacing or pre-damaged degree increases. When the normal service load ( P 1 = 120 kN ) is applied, the diagonal crack width of shear-strengthened pre-damaged beam SA3-A2 with shear-span ratio of 3.49 is 1.45 times than that of shear-strengthened pre-damaged beam SA2-A2 with shear-span ratio of 2.17. The diagonal crack width of shear-strengthened beam SA2-A2 with 150 mm CFRP strips spacing is 0.22 mm while that of shear-strengthened beam SA2-B2 with 100 mm CFRP strips spacing is 0.16 mm. The diagonal crack width of shear-strengthened high pre-damaged beam SA3-A3 is 40% higher than that of shear-strengthened undamaged beam SA3-A1. The ultimate strain of CFRP strips increases as CFRP strips spacing or shear-span ratio increases while the impact of pre-damaged degree on ultimate strain of CFRP strips is not distinct. On the basis of ordinary RC beams diagonal-crack-width model, a simple model for predicting the maximum diagonal crack width of SSPBCs is suggested considering the impact of pre-damaged degree, and the estimated values agree well with test data.

Shear strength is a widely investigated parameter for reinforced concrete structures. The corrosion of reinforcement results in shear strength reduction. Corrosion has become one of the main deterioration factors in reinforced concrete beam. This paper proposes a shear strength model for beams with inclined bars based on a limit equilibrium method. The proposed model can be applied to both corroded and uncorroded reinforced concrete beams. Besides the tensile strength of longitudinal steel bars, the shear capacity provided by the concrete on the top of the diagonal crack, the tensile force of the shear steel at the diagonal crack, the degradation of the cross-sectional area and strength of the reinforcements induced by corrosion are all considered. An experimental work on two groups accelerated corroded beams was performed. Good agreements were found between the proposed theoretical predictions and experimental observations.

The objective of this paper is to study the shear behavior of reinforced concrete (RC) beams cast with lava light weight aggregate (LWA). Six shear deficient beams were designed, constructed and cast with Normal weight concrete (NWC) and lightweight concrete (LWC). All the normal weight concrete (NWC) and light weight concrete (LWC) beam specimens were tested under one point loading, however LWC specimens were tested after 28 and 56 days. Load versus mid-span deflection response along with the failure modes was recorded until the failure of the specimens. The experimental results shows that all beam failed due diagonal crack and the specimens tested at 56 days achieved comparable shear strength to that of NWC beams. In-addition, the shear strength reduction factor was in the range of 0.78-0.94.

The test results on eight two-span deep beams made of self-compacting concrete (SCC) are presented and discussed in this paper. The main parameters investigated were the shear span-to-depth ratio, and the amount and configuration of steel reinforcement. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the other block resting on the other two supports. Both concrete compressive strength and web reinforcement had a major effect in controlling the shear capacity of the beams tested. For the shear span-to-depth ratio considered, the vertical web reinforcement had more influence on the shear capacity of the specimens than the horizontal web reinforcement. The shear provisions of the ACI 318M-11 are unconservative for most of the beams tested. Comparisons of test results with the strut-and-tie model (STM) suggested by ACI 318M-11, EC2 and CSA23.4-04 showed that the predictions are reasonable for continuous deep beams made with low and medium compressive strength. Although the equation suggested by ACI 318M-11 is very simple, its prediction is more accurate than the STM suggested by different design codes.

Primary national codes and standards for reinforced concrete (RC) members and structures specify a limit value of stirrup yield strength. The salient reason for this restriction is to control diagonal crack widths, which lead to shear tension failure. The influence of a high yield strength of stirrups on the failure mode of such members is thus of great concern. To investigate this issue, 12 RC beam specimens incorporating stirrups with high yield strength were tested. The test variables employed in the study were three levels of stirrup spacing and four levels of stirrup yield strength. Assessment of the test results was conducted by analysing the variation of both spacing and number of diagonal cracks due to an increment in the total amount of stirrups. An evaluation of diagonal crack width measured under the service load level was also performed. The test results showed that the diagonal crack width under the service load level is affected by the yield strength of the stirrups and the stirrup spacing. In addition, the number of diagonal cracks increased and the spacing of the cracks reduced as the amount of stirrups was increased. Overall, the average diagonal crack width of all the specimens incorporating high yield strength stirrups was less than the 0·41 mm recommended in ACI 224R-01.

An appraisal of crimped and hooked-end steel fibres as minimum shear reinforcement in reinforced concrete beams made with two concrete grades is presented. Beams conventionally detailed with minimum shear reinforcement were used as control specimens. The fibre reinforced beams also showed varying degrees of multiple cracking at peak loads. The shear strength of the fibre reinforced beams though lower than those of the conventionally detailed beams were higher than a lower bound value recommended in the literature as well as predictions from ACI 318. Effect of concrete grade on normalised shear strength was insignificant. Between the two deformed fibre types, depending upon the aspect ratio, the beams reinforced with the hooked-end fibres had up to 38% higher shear strengths than those containing the crimped fibres. The validity of the ACI 318 flexural performance criteria for deformed fibres proposed to be used as minimum shear reinforcement has been examined and a simple mechanics-based shear strength model for fibre reinforced concrete has been proposed. The proposed model together with seven shear strength models selected from the literature have been evaluated for their predictive efficacy.

Based on the tests among 45 group specimens of five mixes under true tri-axial compressive stress, the characteristics of strain–stress curve, the impact of the stress path and the failure criterion of the plastic concrete were illustrated. The results indicated that the stress - strain curves can be generally divided into four segments, the initial segment was equipped with significantly elastic characteristics, while the last segment indicated severely plastic deformation had occurred. Specimen failure pattern was similar to that of axial compression specimen when the levels of the second and third principal stress were smaller. Otherwise, specimen failure pattern looked like eight diagonal crack. Principal stresses, cohesive forces and angles were influenced dramatically by different stress paths. Based on 93 group test data, three formulas with four parameters, three parameters and two parameters are put forward to express the failure criterion of plastic concrete under true tri-axial compression.

In this study, an experimental study is performed to investigate the effects of section height ( h ), ratio of shear span to effective depth ( a / d ) and compressive strength of concrete ( f c ' ) parameters on diagonal cracking and crack width behavior of RC deep beams after making comprehensive literature research. Effect of shear reinforcement on this behavior is also investigated. Eleven different RC deep beam specimens with or without shear reinforcement are tested under a 3-point loading with a simple support condition. Firstly, the test results reveal that the load carrying capacity of the specimens increases with an increase in section height. Very minor increments in mid-displacements are determined as well. Small increments are experienced in crack widths as h increases. Secondly, an increase in the shear strength of the tested members is obtained as a / d decreases. A small decrease in displacement values is observed with a brittle behavior as well. Moreover, diagonal crack widths increase along with an increment in a / d ratio. Thirdly, an increment of f ck makes a significant contribution to the shear strength of RC deep beams. However, it results in a decrease in maximum diagonal crack widths. Lastly, shear reinforcement makes a very significant contribution to shear strength due to confining struts.

Many researchers have performed experimental and theoretical studies on the shear behavior of steel fiber reinforced concrete (SFRC) beams with conventional reinforcement, few studies involve the shear behavior of SFRC beams with high-strength reinforcement. In this paper, the shear test of eleven beams with high-strength reinforcement was carried out, including eight SFRC beams and three reinforced concrete (RC) beams. The load-deflection curve, concrete strain, stirrup strain, diagonal crack width, failure mode and shear bearing capacity of the beams were investigated. The test results show that steel fiber increases the stiffness, ultimate load and failure deformation of the beams, but the increase effect of steel fiber decreases with the increase of stirrup ratio. After the diagonal crack appears, steel fiber reduces the concrete strains of the diagonal section, stirrup strains and diagonal crack width. In addition, steel fiber reduces crack height and increases crack number. Finally, the experimental values of the shear capacities were compared with the values calculated by CECS38:2004 and ACI544.4R, and the equation of shear capacity in CECS38:2004 was modified to effectively predict the shear capacities of SFRC beams with high-strength reinforcement.

The purpose of this study was to quantify the amount of steel fibers needed to supplement the minimum distributed side face reinforcement requirement for deep beams. The ability of steel fibers to supplant conventional reinforcement was quantified in terms of the serviceability performance or maximum diagonal crack width measured during testing. To achieve the goal of this study, the research plan included the fabrication and testing of nine 300 mm wide by 460 mm deep specimens with a shear span-to-depth ratio of 1.8. Experimental variables included the volumetric percentage of steel fibers and transverse web reinforcement. The diagonal crack widths for specimens were compared with one another and this relationship was used to quantify their serviceability performance. Upon completion of the proposed study, the authors observed that the serviceability performance of deep beams reinforced solely with fibers was equivalent to beams reinforced solely with conventional web reinforcement. The performance of beams reinforced with a combination of steel fibers and conventional reinforcement was further improved. These results provide preliminary support for replacing conventional web reinforcement in deep beams with steel fibers.

The deflection of reinforced concrete (RC) beams with low span-effective depth ratios can be attributed equally to shear and flexural deformations. Although truss models can be used to evaluate shear deformation, their prediction accuracy is strongly dependent on how the diagonal crack angle is estimated. This paper presents the results from an experimental test of nine RC beams that failed in shear and had low span-effective depth ratios (i.e., a / h 0 3 ). It then proposes a multi-angle truss model for predicting ultimate shear deformation while considering the effect of the bending moment variation along the span on diagonal crack angles. An empirical formula is also presented to predict the shear stiffness degradation of RC beams up to the ultimate state through regression analyses. Numerical results show that the proposed multi-angle truss model can be used to predict the shear deformation of RC beams with low span-effective depth ratios with reasonable accuracy.

An experimental and numerical program to investigate the behavior of intermediate crack (IC) debonding failure and the bond-slip relationship between the fiber-reinforced polymer (FRP) plat...

This research presents an experimental study related to the shear behavior of simply supported reinforced concrete beams reinforced with Glass Fiber Reinforced Polymer (GFRP) bars. Four concrete beams reinforced with GFRP bars and four control concrete beams reinforced with steel bars were tested until failure. In order to realize the occurrence of shear failure, all tested beams were designed with longitudinal reinforcement only and without shear reinforcement. The test variables used in this study were the concrete strength, f'c, and longitudinal reinforcement ratio, ρ. The crack patterns, location of the diagonal crack and angle of the diagonal crack were also observed during the test. The shear design equations obtained from the codes and references were used to evaluate the data obtained from the test. Finally, based on the data obtained from experimental and theoretical analysis, comments and recommendation on the shear strength equations were suggested.

In the paper, the method of a numerical simulation concerning diagonal crack propagation in concrete beams was presented. Two beams reinforced longitudinally but without shear reinforcement were considered during the Finite Element Method analysis. In particular, a nonlinear method was used to simulate the crack evaluation in the beams. The analysis was performed using the commercial program ANSYS. In the numerical simulation, the limit surface for concrete described by Willam and Warnke was applied to model the failure of concrete. To solve the FEM-system of equations, the Newton-Raphson method was used. As the results of FEM calculations, the trajectories of total stains and numerical images of smeared cracks were obtained for two analyzed beams: the slender beam S5 of leff = 1.8 m and the short beam S3k of leff = 1.1 m. The applied method allowed to generate both flexural vertical cracks and diagonal cracks in the shear regions. Some differences in the evaluation of crack patterns in the beams were observed. The greater number of flexural vertical cracks which penetrated deeper in the beam S5 caused the lower stiffness and the greater deformation in the beam S5 compared to the short beam S3k. Numerical results were compared with the experimental data from the early tests performed by Słowik [3]. The numerical simulation yielded very similar results as the experiments and it confirmed that the character of failure process altered according to the effective length of the member. The proposed numerical procedure was successfully verified and it can be suitable for numerical analyses of diagonal crack propagation in concrete beams.