Diagonal Shear Cracks Research Articles

Rapid crack-based assessment of deep beams based on a single crack measurement

Deep beams in concrete infrastructure often exhibit wide diagonal shear cracks that extend from the supports to concentrated loads. A key problem in these cases is to assess the residual capacity against shear failure across such cracks. This problem can be solved by establishing a relationship between the opening of the crack and the residual capacity, expressed in percentage of the shear strength. The current study establishes such a relationship that requires minimal input information. The input consists of only three on-site measurements: the depth of the critical loading zone (CLZ) determined by the diagonal crack; the angle of the crack in the CLZ; and a single crack measurement: the vertical crack displacement in the vicinity of the CLZ. The physical basis of the proposed crack-based assessment (CBA) is established with the help of a targeted test and advanced modelling. It is shown that only three input parameters and two simple closed-form equations are sufficient to accurately evaluate the residual capacity of diagonally cracked deep beams with various properties. Furthermore, in the presence of loading and unloading cycles, the proposed CBA reveals how close the member has come to shear failure throughout its entire service life. These properties render the CBA not only suitable for rapid assessment, but also for long-term monitoring of deep beams with diagonal cracks.

Mesoscopic simulations of a fracture process in reinforced concrete beam in bending using a 2D coupled DEM/micro-CT approach

In this study, a complex fracture process in a short rectangular concrete (RC) beam reinforced by one longitudinal bar (without vertical reinforcement) and subjected to quasi-static three-point bending was numerically explored in 2D conditions. A critical diagonal shear crack in the beam caused it to fail during the experiment. The numerical simulations were conducted with a classical particle discrete element method (DEM). A three-phase concrete description (aggregate, mortar, and interfacial transitional zones (ITZs) around aggregates) accounted for the concrete heterogeneity. In mesoscopic DEM calculations based on a 2D X-ray CT scan, the actual shape and placement of aggregate particles in concrete were taken for granted. In the study, the steel bar with ribs was replicated. ITZ was also assumed between the bar and mortar. Without imposing any bond-slip law, a geometrical bar/concrete interface condition was explicitly considered. The focus was on the force–deflection diagram, fracture process, contact forces, and stresses along the bar. A good level of agreement about the evolution of the vertical force versus the deflection and failure mechanism was attained between DEM analyses and in-house laboratory tests despite simplified 2D conditions. A strong effect of concrete mesostructure on the crack pattern was found.

Impact characterization of coral aggregate reinforced concrete beam: A 3D numerical study

Coral aggregate concrete (CAC), an innovative construction material, utilizes abundant marine resources, including coral aggregates and seawater. In the realm of reef engineering, CAC is widely used in structural elements such as reinforced beams and columns. This paper presents a three-dimensional (3D) mesoscale model to assess the impact behavior of coral aggregate reinforced concrete beams (CARCB), incorporating the heterogeneity characteristics of CAC and the explicit simulation of reinforcement components. The 3D mesoscale modelling approach developed in this paper was validated by previous experimental data of CARCB, and used for extensive parametric studies evaluating effects such as concrete strength grade, reinforcement ratio, and impact velocity on the static and dynamic bending behaviors of CARCB. Finally, based on the mesoscopic cracking process and damage patterns of CARCB under static and dynamic loads, this study illustrates the corresponding macroscopic mechanical behaviors and failure mechanisms. Results indicate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Results demonstrate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Specifically, local bending failures and symmetrical diagonal shear cracks were evident in the CARCBs subjected to dynamic loads, closely resembling those in ordinary concrete beams. With increasing concrete strength grades (C30 to C60) and reinforcement ratios (0.9 %–1.7 %), a significant reduction in the mid-span ultimate deflection of CARCB is observed, indicating enhanced impact resistance. Additionally, as the impact velocity increases from 1 m/s to 50 m/s, the mid-span ultimate deflection of CARCB is magnified by a factor of approximately 200, indicating intensified dynamic damage to CARCB with increasing impact velocities.

Softened membrane model for shear of ultra-high-performance concrete (SMM-UHPC)

Understanding the shear behavior of Ultra-High-Performance (UHPC) is crucial to prevent undesired responses that could be induced by diagonal shear cracks. Hence, the ability of analytical models to predict shear responses of UHPC members is of paramount importance, which is addressed in this paper by the Softened Membrane Model (SMM). Since the SMM is a two-dimensional shear modeling framework developed for reinforced concrete, a parametric investigation was conducted to assess its suitability for UHPC, namely SMM-UHPC. Through this assessment, a softening coefficient for the biaxial behavior of UHPC was developed and new constitutive laws were integrated in SMM. Comparisons with shear panel tests were used to evaluate the accuracy of SMM-UHPC and quantify the significance of key model parameters. Sensitivity analyses showed that the decomposition between biaxial and uniaxial strain fields, which is used in SMM to capture the Poisson effect, has a negligible influence on UHPC shear. Combining experimental and analytical data, the tensile localization strain was identified to be of most significance for predicting the shear stress-strain response of UHPC.

Experimental investigation on influence of vertical stirrup legs to shear failure behavior in RC beams

Conventional close stirrup has been widely used in RC beams to avoid shear failure behavior but the effect of internal vertical stirrup legs on the shear strength and the initiation of three-dimensional diagonal shear crack in RC beams is still debatable. In this study, three-dimensional crack evaluation was conducted to determine the shear failure mechanism of RC beams with different (two, three and four) vertical stirrup legs across beam width, with almost same stirrup contribution in design equation, using three-point loading test. The load displacement relationship, surface crack initiation and propagation, internal cracking patterns in cross section, vertical stirrup leg strain and concrete strain relationships, shear resistance components were discussed in detail. It was concluded that the presence of two equally spaced internal vertical stirrup legs with conventional close stirrup restricts the initiation and propagation of internal cracks to side surfaces of tested RC beams and influenced the shear strength.

Strengthening reinforced concrete bridge piers against heavy vehicle collisions with ultra-high performance concrete collars: A finite element analysis study

This paper investigates the effectiveness of ultra-high performance concrete (UHPC) collars in strengthening reinforced concrete (RC) bridge piers against heavy tractor-trailer collisions through finite element (FE) analysis. First, validated FE models of UHPC and a heavy tractor-trailer were provided. Then, FE analyses were conducted to evaluate the strengthening performance of the UHPC collar. The effectiveness of UHPC collar was compared with conventional RC collar, and the effects of varying UHPC collar thickness, height, and collar reinforcement were investigated. The results showed that the most severe damage observed on bridge piers due to heavy vehicle collisions primarily occurred below a height of approximately 2000 mm, manifested as diagonal shear cracks and plastic hinges. Therefore, the recommended minimum collar height is 2000 mm. The comparison between UHPC collar and RC collar strengthening demonstrated the superior effectiveness of UHPC collars. A 130-mm UHPC collar exhibited a similar strengthening effect as an 180-mm RC collar. Among the three investigated parameters of UHPC collar thickness, height, and collar reinforcement, the study found that collar thickness had the most significant influence on the effectiveness of the UHPC collar in terms of damage pattern, energy absorption, and maximum deflection. While collar height primarily influenced deflection, a larger collar height was beneficial in reducing pier deflection at the end of the strengthened segment. Adding a small amount of collar reinforcement improved the performance of piers; however, this improvement was limited. The findings of this study address the lack of research on using UHPC for strengthening full-scale bridge piers against heavy tractor-trailer collisions and provide valuable references for future designs with similar applications.

Plastic Hinge Length for Flanged Reinforced Concrete Shear Walls with Asymmetric Sections

ABSTRACT This research investigates the determination method, spreading mechanism and influencing factors of the plastic hinge length for asymmetrical flanged walls using the finite element method. The plastic hinge length of flanged walls under flange-in-compression loading is generally greater than that under flange-in-tension loading. Based on the results, simple equations for predicting the plastic hinge length of flanged walls and which consider the contributions of the moment gradient, diagonal shear cracks, and strain penetration are proposed. Through comparison with the existing equations and design codes, the predicted plastic hinge lengths obtained from the proposed equations accord better with the test results.

Structural retrofitting of RC slabs using bamboo fibre laminate: Flexural performance and crack patterns

Enhancing the durability of structural elements is a viable approach to promote sustainability in civil engineering. Research has shown that well-maintained slabs outperform degraded ones, which deteriorate rapidly due to insufficient upkeep. The occurrence of cracking and deformation in slabs subjected to sustained loads significantly impacts their functionality. However, the implementation of appropriate retrofitting techniques utilizing locally available materials can effectively minimize deflection and crack propagation while also improving flexural capacity. This particular study aimed to evaluate the flexural performance of slabs that were retrofitted using bamboo fibre laminate (BFL). Also, the study investigated two alternative replacement methods alongside the conventional mix; one involved replacing all fine aggregates with ceramic fine aggregate and the other involved a complete replacement of coarse aggregates with ceramic coarse aggregate. These mixes were represented in both the retrofitted and non-retrofitted samples. The retrofitting process included using the combined external bonding and near surface-mounted method. Twelve slab samples were made, with six being non-retrofitted and the other six retrofitted with BFL. Each of the samples had dimensions of 300 mm × 300 mm × 50 mm for reinforced concrete (RC) slabs. The slabs were tested employing the three point-bending system, and the retrofitted slabs with the conventional mix exhibited the highest ultimate failure load and flexural strength (62.1 kN), which compared to the non-retrofitted slabs of the same mix was a 60.76% increase. Additionally, the study did a thorough analysis of the presence of flexural and diagonal shear cracks, as well as the occurrence of debonding between BFL and the slabs. Non-destructive tests were also conducted on the slab samples to further confirm accurate results. These findings offer helpful insights into the development and application of a sustainable retrofitting material that can remarkably improve RC slabs.

Shear strengthening of RC beams with U-wrapped FRCM composites: assessment of current design guidelines

Fabric-reinforced cementitious matrix (FRCM) composites have been widely used in the past two decades as externally bonded (EB) reinforcement of existing concrete structures. They represent an effective solution for the flexural, shear, and torsional strengthening of reinforced concrete (RC) members. Shear strengthening with EB FRCM can be performed by either side bonding, U-wrapping, or full-wrapping the reinforcement around the cross-section of beams and columns. The FRCM can have a continuous or discontinuous layout, and the textile can be applied with different inclination angles with respect to the beam longitudinal axis. The contribution provided by the EB FRCM to the member shear strength is usually computed by an extension of the Mörsch truss model, which assumes the formation of a main diagonal shear crack. This approach is followed by both the Italian CNR-DT 215 (2018) and the American ACI 549.4R (2020) design guidelines, which provide similar formulations but rely on different hypotheses. In this paper, the accuracy of these formulations to determine the shear strength of U-wrapped FRCM-strengthened RC beams is assessed against a database of RC beams collected from the literature. Comparison between experimental results and analytical predictions allowed to identify the main features of the design models considered.

Unbonded Pre-Tensioned CF-Laminates Mechanically Anchored to HSC Beams as a Sustainable Repair Solution for Detachment of Bonded CF-Laminates

The present article outlines a Finite Element Model (FEM) that was created and validated by comparing it to prior experimental investigations to estimate the flexural performance of HSC beams strengthened with exterior bonded, unbonded, and unbonded pre-tensioned Carbon Fibre Reinforced Polymer (CFRP) sheets in several patterns. Nonlinear analysis was performed on three-point-loaded beams using ANSYS software, incorporating the constitutive characteristics of various components (concrete, CFRP, and steel). The comparison of FE-models and experimental data, namely for load-deflection curves, crack patterns, and failure modes, revealed that the developed numerical FE-models and experimental outcomes are in good accord. There has been numerous prior research on the behavior of beams strengthened with externally bonded CFRP sheets, but few on those reinforced with externally unbonded CFRP laminates, and even fewer on HSC beams reinforced with externally unbonded pre-tensioned CFRP laminates. Therefore, the major contribution of this article is to investigate the flexural behavior of HSC beams strengthened utilizing externally unbonded pre-tensioned CFRP laminates. The analysis revealed that the bending performance of RC-beams strengthened using external unbonded pre-tensioned CFRP-laminates is quite similar to that of bonded CFRP-strengthened beams, indicating a high potential for tackling the durability issues caused by detachment of bonded CFRP-strips in such structural elements. The existence of a fully wrapped CF sheet forced the beam to develop diagonal shear cracks in the region between the wrapped CF sheet and beam supports while also enhancing the flexural cracked zone at mid-span to change from smeared to discrete fractures. The flexural fractures spread over a deeper and wider area of the beam as a result of the incorporation of a half-wrap CF laminate. Externally unbonded CFRP-sheets pre-tensioned with 45% of the CFRP ultimate strength utilizing various patterns (straight and U-wrap) performed similarly to bonded CFRP-sheets, with a slight boost in load capacity of around 4.5% and notable reduces in deflection ranging from 9.7% to 16.24%. Using exterior unbonded CFRP laminates to strengthen RC-beams resulted in a flexural capacity increase ranging from 22.3% for NC beams to 71.6% for HSC beams.

In situ damage characterization of CFRP under compression using high-speed optical, infrared and synchrotron X-ray phase-contrast imaging

The strain rate dependency and failure modes of carbon fiber reinforced plastic (CFRP) laminate were investigated under out-of-plane compressive loading. Simultaneous high-speed optical and infrared imaging were used to measure full-field deformation and temperature in the dynamically loaded specimens. The damage initiation and propagation inside the CFRP laminates at high strain rates were characterized using in-situ ultra-fast synchrotron X-ray phase contrast imaging (XPCI). The visually observed damage onset occurs at the strain value of 4.2 ± 0.6% as a transverse shear fracture at the free edge of specimens. The local temperature increases significantly to 185 °C due to damage initiation at high strain rates, while at low strain rates the temperature rise occurs after the final shear band forms. The XPCI and post-failure analysis provide an integrated perspective on the formation of a diagonal shear crack and disintegration of the specimen into two pieces with the fracture of plies in the in-plane transverse direction. Scanning electron microscopic (SEM) study was integrated with XPCI results to append the time scale for the post-mortem failure pattern as well as the length scale for microcracks and filament-level failure.

Predicting the shear behavior of reinforced concrete beams with Fe-Based shape memory alloy stirrups

Existing studies using Fe-based shape memory alloys (SMAs) for shear reinforcement have focused on strengthening aged structures. Studies on using Fe-SMAs as shear reinforcements for new structures have not been reported. Accordingly, this study performed experiments to evaluate the shear behavior of reinforced concrete (RC) beams with Fe-based SMA stirrups. Ten specimens were prepared for the experiments. The activation of the Fe-SMA stirrup, stirrup spacing, and shear span-to-depth ratio were considered as variables. The Fe-SMA stirrups were activated via electrical resistance heating. Activating the Fe-SMA stirrups applied compressive forces to the specimen, reduced the occurrence of diagonal shear cracks, and improved shear stiffness. However, it did not significantly affect the shear strength. The shear contribution of the Fe-SMA stirrup increased with an increase in the shear span-to-depth ratio and amount of shear reinforcement. In addition, the simulation results using the modified compression field theory (MCFT)-based section analysis model were consistent with the experiment results. Therefore, the model can predict the shear behavior of RC beams with Fe-SMA stirrups.

Experimental qualification of seismic strengthening of URM buildings in Nepal

Nepalese buildings are typically constructed using unreinforced masonry (URM) as the lateral load-bearing system. In the 2015 Nepal Gorkha earthquake several URM buildings suffered heavy damage. The limited economic resources available in the country and the challenge of strengthening a large portfolio of buildings highlight the need for low-cost retrofitting techniques. This paper presents a large-scale experimental campaign aimed at quantifying the seismic performance of a typical URM wall when strengthened with splints and bandages. This represents one of the retrofit techniques that are most widely-used in Nepal. A 5 × 3 m URM wall was constructed using 1:6 cement–sand mortar as per the mechanical properties identified by material testing in Nepal. The URM wall was tested under a two-way ramp cyclic loading. Typical crack patterns associated with URM were observed. The wall was subsequently retrofitted with 8 mm rebars as splints and bandages and tested to failure. The results show that the strength of the retrofitted wall is almost twice that of the URM wall. The observed crack damage improved from EMS-98 Grade 2, with horizontal and diagonal shear cracks in the mortar bed, to Grade 1, with hairline cracks on the rendered splints and bandages. Overall, the experiment demonstrated the efficiency of this practical, low-cost retrofitting technique that is tailored to traditional Nepalese URM buildings. This work can be used to advise local stakeholders in the construction industry as well as to act as a benchmark to improve the reliability of fragility functions for URM buildings in Nepal.

Influence of aggregate source and size on the shear behavior of high strength reinforced concrete deep beams

This paper aims to examine the influence of coarse aggregate characteristics, including toughness and nominal maximum size of aggregate on the RC deep beams’ shear behavior made with and without shear reinforcement. Nine deep beams were prepared with three coarse aggregate types (i.e., limestone, steel slag, and quartzite) having different toughness properties and two nominal maximum aggregate (10 mm and 20 mm) sizes, which were examined under four-point bending. The experimental findings showed that the deep beams exhibited shear failure caused by diagonal shear cracks initiated between the supports and the loading point. Utilizing bigger coarse aggregate size has led to reducing the number of shear cracks. The deep beam stiffness was not impacted by the change in coarse aggregate toughness, aggregate size, or the use of shear reinforcement. For the beams without shear reinforcement, increasing the nominal maximum coarse aggregate size improved the deep beams normalized shear strength. This improvement depended on the coarse aggregate’s toughness with the toughest aggregate (steel slag) showing the greatest improvement. Moreover, using shear reinforcement has contributed to improving the deep beams’ normalized shear strength. The normalized shear strength increased from 6% to 16% compared to deep beams without shear reinforcement.

Shear behaviour of seawater sea-sand coral aggregate concrete beams reinforced with FRP strip stirrups

The preparation of concrete for remote islands or reefs using locally available seawater, sea sand, and coral aggregate can greatly shorten the construction period and mitigate the shortage of river sand and natural gravel resources. This study is the first to experimentally investigate the shear behaviour of seawater sea-sand coral aggregate concrete (SSCAC) beams reinforced with non-corrosive carbon fibre-reinforced polymer (CFRP) strip stirrups. The test parameters included concrete strength, concrete type, and stirrup configuration. The experimental results suggested that CFRP-reinforced SSCAC beams exhibited a brittle shear failure mode because of the sudden CFRP rupture at the bend portions. The ratio of the measured maximum strain to the ultimate tensile strain of the CFRP strip stirrups varied from 36.6% to 47.8%. The critical diagonal shear cracks of SSCAC beams directly penetrated through the coral aggregates and split the aggregates, whereas those in the natural aggregate concrete (NAC) beams bypassed the natural gravel. In this regard, the SSCAC beams exhibited approximately 10% lower shear strength than their NAC counterparts owing to the loss of the aggregate interlocking effect after the occurrence of smooth diagonal shear cracks. The higher the strength grade of SSCAC, the greater the shear strength and service load.

Shear behavior of two-span continuous concrete deep beams reinforced with GFRP bars

To investigate the shear behavior of reinforced concrete (RC) continuous deep beams with glass fiber reinforced polymer (GFRP) bars, four large-scale beams with a constant shear span-to-overall depth ratio of 1.2 and different GFRP shear reinforcement ratios were tested. Digital image correlation technology was used to track the kinematics of diagonal shear cracks in the shear span. It was found that the moment redistribution in the deep beams was very limited. A tie-arch action was confirmed in the tested deep beams with the crack propagation and the strains developed in longitudinal reinforcements. For the beams without GFRP stirrups, the aggregate interlock contribution constituted 46.3% of the total shear resistance. For the beams with GFRP stirrups, however, the shear contribution of aggregate interlock was less significant. As the GFRP shear reinforcement ratio increased from 0% to 0.47%, the failure mode changed from shear compression failure to compression strut failure. As the shear GFRP reinforcement ratio increased from 0.24% to 0.32% and 0.47%, the load-carrying capacity increased by 35.5% and 73.5%, respectively. The minimum required GFRP shear reinforcement in ACI 440.1R-15 was ineffective for the tested GFRP-RC continuous deep beams in terms of shear capacity enhancement and shear crack control. Finally, a database of shear tests on continuous GFRP-RC beams was collected to assess the ability of strut-and-tie methods in three code guidelines.

Shear resistance and structural hardening resistance models for hybrid NSC-UHPC elements

Ultra-high performance concrete (UHPC) is being increasingly used as a thin overlay for deficient normal strength concrete (NSC) structural elements. Compared to reinforced NSC elements, hybrid NSC-UHPC elements have two stages' structural behaviour under high shear load before failure: monolithic action followed by a composite mechanical action. The composite mechanical action gives to hybrid elements a structural hardening capability after the occurrence of a diagonal shear crack and is not yet considered by most design standards. Two analytical models for hybrid elements under shear load are thus proposed to predict the shear resistance V R of the monolithic action and to predict the structural hardening resistance V Rsh of the composite mechanical action. The shear resistance model integrates the UHPC contribution in the estimation of the tensile strain at mid-height cross-section according to the general method of the Canadian code. The structural hardening behaviour is reproduced with a strut-and-tie system with plastic hinges, where the failure is controlled by the crushing of a concrete strut. Predictions of the proposed models are in very good agreement with 31 hybrid elements experimental results retrieved from the literature.

Parametric investigation and economic design of slender steel fibre reinforced concrete beams using shear resisting mechanisms approach

The shear resisting mechanisms (SRM) in slender steel fibre reinforced concrete (SFRC) beam (without stirrups) comprised of four shear resisting mechanisms (uncracked concrete in the compression zone, the dowel action of the longitudinal reinforcement bars, the aggregate interlocking through the aggregates protruding at the critical diagonal shear crack, and the steel fibres bridging the diagonal crack). These shear resisting mechanisms are interrelated to each other and very complex to quantify. However, parametric analysis is one of the methods which can easily be applied and quantify their interconnection. As a result, the parametric analysis has been carried out in this research with the main focus on the effect of influential parameters on shear strength, shear resisting mechanisms, and the interrelationship between them. Thus, the SRM model has been again verified and validated through the results of parametric investigation. Furthermore, the SRM based model has been further modified, and a cost analysis for economic beam design was performed. Finally, design recommendations from the standpoint of practical application have been proposed.

In-plane cyclic behavior of brick walls strengthened with CFRP plates embedded in the horizontal mortar joint

Unreinforced masonry (URM) buildings exhibit significant vulnerability under in-plane seismic loads due to poor tensile strength and integrity. An experiment was carried out to investigate the effectiveness of embedding carbon fiber reinforced polymer (CFRP) plates in the horizontal mortar joint on improving the in-plane seismic performance of URM wall that was prone to fail by diagonal shear failure mode. A total of five half-scale specimens, each measuring 2250 mm × 1500 mm × 240 mm, including two un-strengthened brick walls and three strengthened walls, were tested undergoing pre-compression stress combined with incremental lateral displacement. The CFRP plates were only embedded in the wall on one side in order to reduce the impact on building appearance and different reinforcement ratios were adopted. The failure mode, hysteretic behavior, shear strength, ductility, stiffness degradation and energy dissipation capacity of the specimens were discussed. The results showed that reinforcement can control the initiation and rapid growth of diagonal shear cracks. The strengthened masonry walls exhibited flexural rather than brittle shear failure with good ductility and energy dissipation. The ductility of the strengthened walls increased significantly with the increased reinforcement ratio and there was an optimal reinforcement ratio that maximized the ductility. The strengthened wall with medium reinforcement ratio showed the highest increase in ductility factor of 45.71% compared with the control specimen. The strengthened specimens displayed greater bearing capacity compared with the un-strengthened specimen. The largest increase in the shear strength of the strengthened walls was 10.16%, which indicates the effectiveness of the reinforcement method of used to embed CFRP in the horizontal joint to improve the in-plane seismic performance of URM walls. In addition, the abilities of several analytical models used to predict the shear capacity of the URM and strengthened walls were analyzed.

Experimental investigation of resistance function of RC beam considering membrane effects

Membrane actions commonly exist in reinforced concrete (RC) elements under flexural deformation, which could significantly increase the ultimate flexural load-bearing capacity and potentially influence the damage mode of the RC element. Most design codes only treat membrane actions as a “hidden” safety factor without considering its influence on the resistance functions and failure modes. In this paper, an experimental investigation is conducted to study the membrane actions on the resistance behaviors of restrained RC beams. It is found that compressive membrane effect occurred at early stage of a fully restrained RC beam, which leads to amplified flexural bending resistance capacity. Diagonal shear crack is developed since the designed shear resistance is lower than the amplified flexural bending capacity. Under membrane actions, the damaged beam with shear crack could still carry the imposed load and develop further tensile membrane action until eventual failure. The resistance function of the restrained beam under combined membrane and shear damage is significantly altered as compared to the un-restrained reference beam that failed in flexural bending. A modified theoretical resistance function is proposed to consider both the membrane effects and diagonal shear damage. Comparison with testing data shows that the proposed model could accurately describe the resistance of fully restrained RC beams under combined shear and membrane actions.