Shear Strength Equation Research Articles

Influence of Morphology Characteristics on Shear Mechanical Properties of Sawtooth Joints

The interface problem exists widely in building. Joints are interfaces of rock mass structures. To further study the influence of morphological characteristics on the shear mechanical properties of sawtooth joints, this paper prepared rock-like materials based on the similarity principle and carried out direct shear tests of sawtooth joints. The results showed that: (1) the peak shear displacement of joints first increases and then decreases with increasing normal stress, but the normal trend of stress during turning is different under different sawtooth angles. When the sawtooth angle of the joints is small, the decrease in shear stress between shear strength and residual shear strength is not obvious, and the rate of decrease is also small. (2) The shear strength of joints is positively correlated with normal stress. Using the Mohr–Coulomb criterion to analyze the shear strength of joints, it was found that the cohesion c and internal friction angle α of joints increased nonlinearly with increasing sawtooth angle, but their increasing trends were different. By introducing the function relation between cohesion, internal friction angle, and sawtooth angle into the classical shear strength equation, an empirical equation for the shear strength of joints was established in consideration of sawtooth angle. (3) There are two modes of shear failure for serrated joints: the “saw-toothed sliding gnawing failure mechanism” (SSG) and the “tensile fracture mechanism” (TFM). In the SSG, the shear failure mode of joints evolves in a slipping–gnawing–complete gnawing mechanism with increasing sawtooth angle and normal stress. The TFM mainly occurs at high sawtooth angles. This study provides a theoretical reference for the prediction and prevention of geological disasters.

Experimental analysis of the cold-formed steel beam-to-column connection using the welded clip-angle

An experimental investigation on the fillet welded clip-angle connection between the cold-formed steel (CFS) beam and column was conducted under four-point bending. The purpose of the study was to investigate the shear strength of the fillet welded clip-angle between the CFS beam and column. To accomplish this objective, a total of 30 experiments with 27 clip-angle configurations and three repeat tests were carried out. The parameters studied include thickness and aspect ratio of the clip-angle. The clip-angles were found to fail in (i) distortional buckling for an aspect ratio (W/D) < 0.8 and (ii) local buckling for an aspect ratio (W/D) ≥ 0.8. The experimental outcomes of the welded clip-angles were summarized and compared with the design strength predictions for screwed and bolted connections in terms of design shear strength equations and behavior of the test specimens. The studies indicate that the welded connections exhibited higher stiffness with respect to the screwed and bolted connections resulting in lower serviceability limit requirements. Based on the test results, a new shear strength design equation for the fillet welded clip-angle is suggested. Further, the reliability analysis is conducted to evaluate the resistance and safety factors for the LRFD, LSD and ASD methods to determine the design shear capacities accordingly. The effectiveness of the proposed design method for the welded clip-angle between CFS beam and column is illustrated with the help of the design example in this paper.

Comparative Assessment of Shear Strength Equations for Reinforced Concrete

Several methods for predicting the one-way shear strength of reinforced concrete beams and one-way slabs are available in the literature. An assessment regarding the accuracy of a selection of one-way shear strength methods for reinforced concrete members is described in this paper. These methods include American Concrete Institute (ACI) 318 procedures in addition to several potential design methods proposed by various researchers. Predictions of these methods are compared with a set of experimental results reported in the literature. The objective is to provide engineers guidance to select the most appropriate shear design method for a given structural application. Almost all methods included in this analysis exhibit satisfactory predictions. The new ACI 318-19 shear design method is the simplest of the methods reviewed, and it gives reasonably accurate predictions for members with or without shear reinforcement.

Disturbed state concept and non-isothermal shear strength model for unsaturated soils

Shear strength of unsaturated soils is an important engineering property that is required for addressing geotechnical problems, the prediction of which remains to be a challenging task for design engineers due to the complex interaction problem. This study presents a new shear strength equation based on the micromechanical model and the disturbed state concept for unsaturated soils. The original point of this study is considering the solid contact area ratio which was neglected in most of the existing equations. Using the proposed model, the non-linear relationship between the matric suction, saturation degree, and the shear strength of unsaturated soils are described. Validation of the shear strength model was verified against the experimental data and several current models on six different types of soils. The results indicate that the proposed model has a good performance in predicting the shear strength of unsaturated soils, and generally is better than other existing models. In response to varying climatic conditions, the analytical model was then extended to consider the effect of temperature on the shear strength of unsaturated soils. The comparison between predicted and measured results was carried out on compacted silt for three different temperatures. The results show that the proposed model is capable of accurately predicting changes in unsaturated shear strength as a function of temperature.

Predicting shear strength of FRP-reinforced concrete beams using novel synthetic data driven deep learning

Machine learning algorithms have emerged as a powerful technique to predict the engineering properties of composite materials and structures where traditional statistical methods have resulted in poor accuracy and high uncertainty. However, the lack of reliable and comprehensive experimental data hinders developing high-throughput computational models. To mitigate such a limitation, this study deploys the state-of-the-art tabular generative adversarial network (TGAN) to generate synthetic data for training generalized ML models. ‘Train on Synthesized - Test on Real’ approach was used to pioneer a novel framework for predicting the shear capacity of FRP-reinforced concrete beams. Accordingly, the models were trained using 8816 synthesized design data and tested using 304 real experimental data. The TGAN approach exhibited tremendous potential in generating credible data for training robust machine learning models, achievingR2of 0.96 when tested on the entire experimental dataset. Furthermore, a Bayesian optimization was performed on the extensive synthesized data to propose a new predictive shear strength equation. Results demonstrate that the proposed design model attained superior accuracy and vastly outperformed both existing design code provisions and empirical and theoretical models in the literature. The TGAN technique could transcend the lack of available experimental datasets in engineering problems via synthetizing numerous plausible data points to enhance the prediction accuracy and generalization ability of machine learning models.

Effect of Composition on the Compressibility and Shear Strength of Dredged Cohesive Sediment

Progressively, more dredged sediments are being reused for engineering projects. For example, the Marker Wadden is a new wetland constructed in lake Markermeer, the Netherlands, with dredged cohesive sediments originating from the bed of the lake. Such dredged sediments are often dominated by cohesive sediment particles with varying amounts of sand and organic matter. In addition, during and after the construction process, the material consolidates and is often compressed from a very loose state into a significantly denser condition. To assess the mechanical behavior of this material, the compressibility of the Markermeer dredged sediment samples with various sand and organic matter contents was analyzed with incremental loading oedometer tests, whereas the undrained shear strength was studied using the fall cone test. The behavior was theoretically analyzed assuming a fractal structure of the sediment and applying power law constitutive equations for effective stress, hydraulic conductivity, and undrained shear strength. These constitutive equations, usually used at low initial sediment densities, worked well at the relatively high initial densities studied and proved to be a useful tool to identify the transition fines content TFC. The constitutive equations were put in context with indicators traditionally used in soil mechanics. Samples, each with an identical composition of the fines fraction (particles&amp;lt; 63 μm), but with a sand content varying from 9 to 40%, showed the same compressibility and undrained shear strength behavior when considering the sand a filler material. For a natural sand content of 70%, the behavior was dominated by sand. The organic matter oxidation was observed to drastically decrease the compressibility and the shear strength, and even to decrease the amount of sand needed to exhibit sand-dominated behavior, showing the importance of the reactivity or state of organic matter on the TFC.

An analytical model for predicting the shear strength of unsaturated soils

The prediction of shear strength of unsaturated soils remains a significant challenge due to their complex multi-phase nature. In this paper, a review of prior experimental studies is first presented in order to outline important pieces of evidence, limitations and some design considerations. Then, an overview of existing shear strength equations is summarised, with a brief discussion. A micromechanical model with stress equilibrium conditions and multi-phase interaction considerations is presented to provide a new equation for predicting the shear strength of unsaturated soils. The validity of the proposed model is examined using published shear strength data for different soil types. The shear strength predicted by the analytical model was found to be in good agreement with the experimental data and to provide high performance in comparison with existing models. Evaluation of the results using two criteria – the average relative error and the normalised sum of squared error – proved the effectiveness and validity of the proposed equation. Using the proposed model, a non-linear relationship between shear strength, saturation degree, volumetric water content and matric suction was observed.

Analysis of exterior beam-column joints under varying column axial load and code comparisons

This paper presents a finite element (FE) study of beam-column joints subjected to cyclic loading. This study is primarily dependent on investigating the shear behavior of joints under the influence of different column axial load ratios. Wherefore, a total range of the column axial load ratios, whether in tension or compression has been considered. This paper proposes a two-dimensional (2D) FE model that considers material non-linearity. The proposed FE model was verified with experimental results from literature that tested varying column axial load ratios and different failure modes. The examination among experiential and numerical outcomes demonstrated that the FE model can reenact the conduct of beam-column joints and can catch the different failure modes with acceptable accuracy. A parametric study was established using the proposed FE model and strut-and-tie (ST) model of Pauletta to assess the Eurocode joint shear strength equations. For this purpose, four specimens were designed according to Eurocode recommendations while two other specimens were designed to satisfy all of the Eurocode recommendations except for the required joint confinement. An interaction diagram was introduced for each specimen to express the behavior under varying column axial load ratios. The results of the comparison between Eurocode, FE model, and ST model showed some differences in calculating the joint shear strength capacity, especially under column tension loads. Furthermore, this paper proposed new design equations based on Eurocode equations taking into account the column axial load effect. These proposed equations worked to increase the accuracy in calculating the joint shear strength capacity. Proposed equations were compared to the FE model results and other experimental results available in the literature. The comparison showed that the differences with the FE model decreased and that the proposed equations had better accuracy at different tension and compression loads than the Eurocode.

Experimental study on bonding behaviour of interface between UHPC and concrete substrate

The aim of this study is to investigate the effect of substrate surface roughness, fibre type, and water-to-binder ratio on the bond behaviour between ultra-high-performance concrete (UHPC) and normal-strength concrete (NSC). In addition, the suitability of different methods for evaluating the surface roughness using a sand-filling method, the height, number, and area of exposed coarse aggregates, and capillary absorption was verified. The results indicated that surface roughness was the most critical factor, followed by the water-to-binder ratio, and finally, the steel fibre type on influencing the bond strength. These methods for evaluating the surface roughness showed good consistency. The bond strength enhancement was mainly attributed to the compact transition zone of UHPC–NSC and the dowel effect of the steel fibres on the substrate surface recess. Based on the experimental bond strength values, an UHPC–NSC shear strength equation was derived, considering the repair surface roughness, and other research data verified the applicability of the proposed equation. Moreover, the NSC area fraction on the UHPC overlay side and the damage index of the composite specimen after debonding had a good linear relationship with the interface performance.

Analysis of influencing factors on shear behavior of the reinforced concrete deep beams

A database including 833 specimens on reinforced concrete (RC) deep beams with shear failure is presented in this paper. Comprehensive influences of web reinforcement ratio, shear span-to-depth ratio, depth-to-width ratio, and compressive strength of concrete on the shear behavior of deep beams are discussed. It is found that the normalized shear strength of deep beams decreases with an increase of the shear span-to-depth ratio and this trend is affected significantly by the concrete strength, depth-to-width ratio, and web reinforcement ratio. Besides, the restrictions on minimum web reinforcement and minimum sectional size are investigated. It is found that the restrictions on minimum web reinforcement and the minimum sectional size are significantly affected by the web reinforcement ratio and are closely related to the reinforcement strength and concrete strength. However, the effect of the strength ratio of concrete to shear reinforcements on the limit of the amount of web reinforcements has been ignored in current codes. The characteristic value of web reinforcement, considering the web reinforcement ratio and the strength ratio of concrete to shear reinforcements, is proposed. For the horizontal and vertical reinforcements, the minimum characteristic values of 0.54 and 0.25 are suggested as the restrictions on the minimum amount of web reinforcement, respectively. The maximum characteristic values of 1.5 and 1.7 are proposed as the restriction on the minimum sectional size. Moreover, an equation for the ultimate shear strength of deep beams corresponding to the minimum sectional size is also suggested. Compared with the relevant provisions of the current codes, the suggestions on minimum web reinforcement requirements and minimum sectional restrictions are better.

Simplified Equations for Shear Strength of Composite Concrete-Filled Steel Tubes

Shear strength of filled composite members, namely, circular or rectangular concrete-filled steel tubes (CFST) have been investigated in past research. Results established the relative contributions of the steel tube and concrete infill to the total shear strength and showed that the concrete contribution depends on the development of a compression strut in the concrete infill when shear-span values are low. While experimental results and numerical models are available in the literature, simple equations that empirically encompass this behavior are preferable for design purposes. This paper provides an overview of the technical approach that has been followed to propose such equations for consideration and possible implementation in future editions of design specifications. The shear strength obtained using the proposed equation is compared with the shear test database from the existing literature and found to be safe; it accurately captures the contribution of the steel tube to the total shear strength and conservatively approximates that of the concrete.

Generalized Interface Shear Strength Equation for Recycled Materials Reinforced with Geogrids

In this research, large direct shear tests were conducted to evaluate the interface shear strength between reclaimed asphalt pavement (RAP) and kenaf geogrid (RAP–geogrid) and to also assess their viability as an environmentally friendly base course material. The influence of factors such as the gradation of RAP particles and aperture sizes of geogrid (D) on interface shear strength of the RAP–geogrid interface was evaluated under different normal stresses. A critical analysis was conducted on the present and previous test data on geogrids reinforced recycled materials. The D/FD, in which FD is the recycled materials’ particle content finer than the aperture of geogrid, was proposed as a prime parameter governing the interface shear strength. A generalized equation was proposed for predicting the interface shear strength of the form: α = a(D/FD) + b, where α is the interface shear strength coefficient, which is the ratio of the interface shear strength to the shear strength of recycled material, and a and b are constants. The constant values of a and b were found to be dependent upon types of recycled material, irrespective of types of geogrids. A stepwise procedure to determine variable a, which is required for analysis and design of geogrids reinforced recycled materials in roads with various gradations was also suggested.

Recommendation on block shear strength equation of double shear four-bolted connection in cold-formed mild carbon steel

In this study, experimental research was performed to investigate the structural behaviors such as the ultimate strength and fracture mode of double shear four-bolted connection fabricated with cold-formed mild carbon steel. It shows that bolted connections failed by either block shear fracture or net-section fracture at test end. Finite element (FE) analysis model was developed to replicate experimental response. After successful verification, it was employed for further analysis such as stress and strain distributions that could not be seen through the physical testing. Three paths on the plate model of bolted connection were established to investigate the critical shear plane and the shear stress distribution on the critical shear plane at ultimate state. A modified block shear fracture strength equation of the bolted connection was proposed considering the shear stress factor (average of ultimate shear stress and yield shear stress) at the critical shear failure plane (midway of gross shear section and net shear section; effective shear plane), and block shear fracture strengths by test and analysis results were compared with those by the suggested equation. It is concluded that the proposed equation is able to provide more accurate prediction in determining block shear strength of double shear four-bolted connection with mild carbon steel.

ASSESSMENT OF NOMINAL SHEAR STRENGTH OF REINFORCED CONCRETE COLUMN

: SNI 2847-2019 and ACI 318-19 have regulated the use of materials in the design for shear strength. This study presents an evaluation of nominal shear strength in Reinforced Concrete (RC) column from SNI 2847-2019 and ACI 318-19 by variants of the RC columns experimental database. RC column variants consist of normal strength and high strength RC column with a total of 162 specimens. Furthermore, the database also provides a variety of shear span to depth ratio and axial-load ratio. In this study, the calculation was carried out the mean and the coefficient of variation of measured to calculated strength ratio which is according to SNI, ACI, and other experimental models. Both SNI 2847-2019 and ACI 318-19 have 2 different (concrete nominal shear strength) equations. The calculation results show that the equation is more conservative in both SNI and ACI compared to other nominal shear strength equations. Overall, the combination of both normal strength and high strength RC columns, the calculation using ACI 318-19 with the first nominal shear strength equation can be said to be more conservative than any other calculations models. This study also shows that by using the ACI 318-19 model in the second equation which is used the size effect modification factor , the results do not have a significant effect because the value is close to 1.

Investigating the reliability of shear strength equations in TS500 and ACI318-19

Lateral loads (e.g., wind and earthquake loads) lead to shear forces as well as the axial loads and moments on the structural members. Although reinforced concrete (RC) columns are commonly assumed as slender members and are not expected to represent shear dominant response characteristics, experimental studies have shown that even slender columns have shear responses. Hence, in seismic design, the shear strength of columns must be accurately predicted to prevent shear failure of columns. Validation of Requirements for Design and Construction of RC structures (TS500) for shear strength calculation of RC columns by a broad range of test data has been neglected in the literature. In this study, 57 test results of rectangular RC columns were collected from available laboratory tests to verify the shear strength calculation approach in TS500. Additionally, a statistical comparison of results obtained from TS500 with Building Code Requirements for Structural Concrete (ACI318-19) has been studied in this study. Maximum shear strength of RC columns obtained from the previously studied test data was compared with shear strengths calculated according to TS 500 as well as with the results obtained from ACI318-19. Comparisons are scrutinized in terms of shear-span-to-depth ratios, reinforcing ratios, material properties, and stirrup spacing as well as axial load ratios applied on top of the columns. Investigation of existing design equations reveals a significant difference in prediction. This study will be extended by adding further test results from the literature to provide crucial comments about the shear strength calculation of RC columns in TS500.

Shear tests of engineered cementitious composites: Mechanical behavior and toughness evaluation

AbstractMechanical behavior of engineered cementitious composites (ECC) under direct shear is investigated by the double‐shear tests. The main test variables are the volume ratio (0%, 1%, 1.5%, 2%) of polyvinyl alcohol fiber and strength grade of ECC. The failure mode, load‐slip response and shear mechanism of ECC under direct shear are analyzed and discussed, respectively. The test results indicate that the failure mode, direct shear strength, shear slip and ductility (toughness) are influenced and been improved significantly by the incorporation of fibers. With the compressive strength of ECC increases, the direct shear strength increases but the post‐peak ductility decreases considerably. The shear mechanisms of ECC is analyzed according to the failure mode. Based on the typical load‐slip curve of ECC under direct shear, a set of size independent toughness indices including the equivalent shear strength and two toughness indices are recommended for evaluating the shear toughness of ECC.

In-plane shear strength and damage fragility functions for partially-grouted reinforced masonry walls with bond-beam reinforcement

This paper presents a study on the in-plane shear response of partially-grouted reinforced masonry walls with bond-beam reinforcement. A database of 95 tests on partially-grouted walls made of concrete hollow blocks was compiled from experimental studies reported in the literature to characterize the capacity and damageability of walls subjected to in-plane lateral loading. The database has been used to evaluate the accuracy of existing design shear strength equations for partially-grouted walls. It is concluded that the shear strength expressions in the Masonry Standards Joint Committee (MSJC) code and Canadian standard are unconservative for partially-grouted walls. A modified equation based on the MSJC expression is proposed which better estimates the shear strength of this type of walls. Seismic fragility functions are also derived based on the experimental database to calculate the probability of experiencing moderate and severe damage in a partially-grouted wall for a given story-drift ratio deformation or normalized shear force demand. The resulting fragility functions show that the normalized shear demand is better correlated with the level of damage than the story-drift ratio.

Evaluation of Design Provisions for Horizontal Shear Strength in Composite Precast Concrete Beams with Different Interface Conditions

In a precast concrete (PC) composite beam, the horizontal interface between the PC beam and the cast-in-place (CIP) slab is located either on the compression side or on the tensile side of the cross-section. If the CIP slab is on the compression side, it becomes C-type interface, and if it is on the tensile side, it becomes T-type interface. Tensile cracks in the CIP slab may cause the horizontal shear strength of composite beams to decrease because of the reduced anchorage performance of shear reinforcements as well as the sliding on the interface. Such a tendency can be found from previous test results of specimens having T-type interface. In this study, the results of the push-off test and the beam flexure test were collected and analyzed to evaluate effects on the horizontal shear strength depending on the interface conditions, such as the interface location, surface roughness, concrete compressive strength, and clamping stress by shear connectors. The horizontal shear strength equations of ACI, PCI, AASHTO LRFD, and MC 2010 were evaluated with a database composed of 84 push-off tests and 95 beam tests from previous studies. According to the evaluation, evaluation results show that the design codes predict the horizontal shear strength conservatively for conditions other than the interface location. The horizontal shear strength deviated largely depending on the interface locations. The design codes conservatively estimate the horizontal shear strength for C-type interface, but the horizontal shear strength of T-type interface is overestimated. Based on current studies, it is recommended to use a friction coefficient of 0.7 as MC 2010 when calculating the horizontal shear strength of a composite beam with roughened T-type interface.

COMPARING THE HOEK-BROWN AND MOHR-COULOMB FAILURE CRITERIA IN FEM ANALYSIS

This paper revisits the issue of a potential substitutions of the Hoek-Brown failure model by the standard Mohr-Coulomb model in the stability analysis of rock masses. The derivation of equivalent shear strength parameters of the Mohr-Coulomb proposed by Hoek et al. [1] is addressed with emphases on the suitable range of stresses for which the equivalence of the two failure criteria applies. To that end, a simple numerical analysis of the oedometric test is carried out. It is seen that a correct choice of the upper limit of the minimum compressive principal stress is crucial for the Mohr-Coulomb model to provide predictions comparable to the Hoek-Brown model. This issue is addressed next in the light of the solution of slope stability problem. All the presented results were derived with the help of the GEO5 FEM finite element software [2].

PEAK SHEAR STRENGTH OF H-SHAPED REINFORCED CONCRETE SQUAT WALLS

Flanged RC squat walls are widely used in conventional buildings and nuclear facilities owing to the significant lateral strength and stiffness in both principle directions. The building codes are found to have some problems in predicting the peak shear strength of flanged RC squat walls, such as insufficient parameters and the exclusion of the influence of the flanges. Moreover, calculated values are more discrete than experimental values. In this paper, we established a database of the comprehensive information of 152 flanged RC squat walls. The performance of popular building codes in predicting the peak shear strength of this kind of walls was compared and analyzed. Based on the crack patterns on the web, a model of flanged RC squat walls considering the influence of the flanges was built, based on which the equation for the peak shear strength was deduced. The results reveal that the proposed equation can calculate the peak shear strength of the shear walls in the database with a mean value of 1 and a small variation coefficient. These results can provide guidance for the design of structural walls and the revision of building codes.