Shear Formula Research Articles

Modified Easley formula for elastic critical global shear buckling stress of corrugated steel webs considering real boundary conditions

The real juncture between corrugated steel webs (CSWs) and flanges follows a multi-segmented line, distinct from that of flat steel webs. Classic methods may yield significant deviations in predicting the elastic global shear buckling capacity of CSWs of various scales due to their failure to consider real boundary constraints. Therefore, a universally applicable formula for calculating the elastic critical global shear buckling stress of CSWs, which accounts for real boundary conditions, is proposed. This formula is pertinent to both large-scale engineering CSWs and small-scale testing CSWs. This study commenced with a comprehensive reassessment of the elastic global shear buckling calculation method. Subsequently, the influence of geometric parameter ratios on the elastic critical global buckling stress was examined. The primary parameter was identified and employed to improve the global buckling coefficient. The proposed calculation method was validated using different corrugation configurations, including 1000-type, 1200-type, 1600-type, 1800-type, and 2000-type CSWs, as well as other CSWs used in experimental settings. These results were compared with those obtained from other reference methods. Findings indicate that the accuracy of the classic theoretical method is affected by variations in both boundary conditions and geometric dimensions due to the constraint effect of real boundary conditions. Under the real boundary conditions, the elastic critical global shear buckling stress of CSWs with simply supported boundary conditions is close to that of CSWs with consolidated boundary conditions. The ratio of web height to corrugation depth primarily affects the elastic global shear buckling capacity, which decreases as the ratio increases. The Easley formula can be modified based on the web height to corrugation depth ratio. Comparisons of numerous numerical and theoretical results reveal that the proposed calculation method exhibits commendable computational precision. In comparison to alternative formulas, the proposed method demonstrates enhanced consistency for calculating CSWs with varying geometric dimensions and boundary conditions, thereby demonstrating its favorable applicability. These conclusions provide valuable reference for the shear design of CSWs.

Numerical Simulation Analysis of the Bending Performance of T-Beams Strengthened with Ultra-High-Performance Concrete Based on the CDP Model

Numerical Simulation Analysis of the Bending Performance of T-Beams Strengthened with Ultra-High-Performance Concrete Based on the CDP Model

Machine learning base models to predict the punching shear capacity of posttensioned UHPC flat slabs

The aim of this research is to present correction factors for the punching shear formulas of ACI-318 and EC2 design codes to adopt the punching capacity of post tensioned ultra-high-performance concrete (PT-UHPC) flat slabs. To achieve that goal, the results of previously tested PT-UHPC flat slabs were used to validate the developed finite element method (FEM) model in terms of punching shear capacity. Then, a parametric study was conducted using the validated FEM to generate two databases, each database included concrete compressive strength, strands layout, shear reinforcement capacity and the aspect ratio of the column besides the correction factor (the ratio between the FEM punching capacity and the design code punching capacity). The first considered design code in the first database was ACI-318 and in the second database was EC2. Finally, there different “Machine Learning” (ML) techniques manly “Genetic programming” (GP), “Artificial Neural Network” (ANN) and “Evolutionary Polynomial Regression” (EPR) were applied on the two generated databases to predict the correction factors as functions of the considered parameters. The results of the study indicated that all the developed (ML) models showed almost the same level of accuracy in terms of the punching ultimate load (about 96%) and the ACI-318 correction factor depends mainly on the concrete compressive strength and aspect ratio of the column, while the EC2 correction factor depends mainly on the concrete compressive strength and the shear reinforcement capacity.

Probabilistic code-based shear capacity model for I-shaped steel reinforced concrete (SRC) beams

A code-based probabilistic prediction model is developed for structural design and reliability analysis of the shear capacity of shear-critical steel reinforced concrete (SRC) beams. First, an experimental database of 83 shear tests was compiled from the literature, including steel-reinforced normal-strength concrete, steel-reinforced high-strength concrete, and steel reinforced lightweight aggregate concrete. Then, three deterministic formulations from the most commonly-used specifications JGJ, AIJ, and ACI-AISC were presented and compared against the database. Based on the different shear mechanism and formula considerations in the code-based deterministic models, this study developed 12 probabilistic models that account for both epistemic and aleatory uncertainty to examine the impact of concrete strength, shear span ratio, number of parameters, and their interactions. The Bayesian theory and Markov Chain Monte Carlo (MCMC) simulation method were utilized to calibrate the models by generating posterior distributions of the model parameters and the standard deviation (SD) of the model error. Optimal model selection hinges upon balancing precision and intricacy. An analysis was then conducted to evaluate the accuracy of the selected model, and the probabilistic model was applied to estimate the shear reliability of a SRC beam. Results demonstrate that the model objectively represents the probabilistic properties of the shear capacity of SRC beams and has the capability to conduct reliability analysis.

Numerical assessment of punching shear strength of eccentrically loaded footings with nonconventional shear reinforcement

Rapid increase rate of using flat slabs and flat foundations is noticed in different reinforced concrete projects. These concrete elements have many features in their concrete casting and reinforcement placement, but on the other side, the non-ductile punching shear failure around the supporting columns is the main issue. Many experimental and statistical studies have been focused on assessing the punching shear capacity of centric flat plate elements. Due to the size effect and fracture mechanics, the behavior of a thick flat foundation is not typical of the behavior of the thin elements, as the shear crack inclination angles with thick elements are steeper than those in thin flat plates. The difference in behavior is increased with eccentric loadings. Construction imperfections and/or limited foundation space are the main reasons for these eccentricities. This puts limitations on using some previously developed punching shear formulas when dealing with thick footing elements. This numerical study investigates the behavior of both centric and eccentric loaded flat thick footings without and with shear reinforcement. This study showed a good prediction for the punching shear strength of footings with different eccentricity levels compared to the reference case studies. The results demonstrate that higher eccentric levels significantly reduce the strength of footings without shear reinforcement. However, the footing deformation capacity was improved. Parametric studies utilizing the validated developed numerical models have been conducted to assess the efficiency of two nonconventional shear reinforcements; U and S-shaped. Both options significantly increased the footing punching shear strength and improved the deformation capacity. In addition, the S-shaped reinforcing option showed its efficiency in limiting the strength reduction to 8% compared to 17% for footing without shear reinforcement under load eccentricity less than 1/9 of the footing length. Moreover, the arrangement of the S-shaped reinforcement can govern the behavior of the footings under different load conditions. The results of providing two identical amounts of S-shaped reinforcement showed that one closely spaced row is more efficient under centric loading while two rows are more suitable under eccentric loading.

Optimizing I-Beam by Using Shape Generator Tool

Today, there are many different types of shaped steel with different characteristics, designed to meet the different needs of modern buildings. The most common is H-shaped steels, I-shaped steels and V-shaped steel. Shaped steel is hard and durable, with high tensile strength, and can withstand strong vibrations. When subjected to harsh conditions due to the impact of chemicals, the temperature should be kept suitable for industry and construction. Beams are designed for strength, so that they can resist the internal shear and moment developed along their length. To design a beam in this way requires the application of shear and flexure formulas, provided the material is homogeneous and exhibits linear elastic behavior. Although some beams may also be subjected to axial force, the effects of this force are often neglected in design, since it is generally much smaller than the stress developed by shear and bending. To optimize the design of the I-beam, the CAD model was developed in Inventor Professional 2019, and we used the Shape Generator module to determine the best design. In addition, these models also employ finite element analysis to determine whether the designs created are safe. This research also aims to assess long-standing traditional structures.

A new shear formula for tapered beamlike solids undergoing large displacements

In many engineering applications it is often necessary to determine the flow of shear stresses in the cross-sections of beamlike bodies. Taking a cue from Jourawski's well-known formula, several scholars have proposed expressions for evaluating the shear stresses in non-prismatic linear elastic beams, where longitudinal variations in the size and shape of the cross-sections produces complex stress fields. In the present paper, a new shear formula, derived using a mechanical model developed in a previous work, is presented for tapered beams subject to even large displacements and small strains. Numerical examples and comparisons with results obtained using other formulas in the literature and non-linear 3D-FEM simulations show how the new formula constitutes an important generalization of the previous ones and is able to provide particularly accurate results.

Shear design equation and updated fragility functions for partially grouted reinforced masonry shear walls

This paper proposes specific ultimate shear strength expressions for partially-grouted reinforced masonry (PG-RM) shear walls that are bed-joint reinforced (BJR) and made with either multi-perforated clay bricks (MPCLBs) or hollow concrete blocks (HCBs). For each unit type, a set of constant coefficients of an arbitrary mathematical expression is optimized to minimize the error against experimental databases of walls made with the same unit types. Additionally, the assembled databases are employed to calculate lognormal empirical fragility functions, following performance-based earthquake engineering (PBEE) methodologies. For this, two different engineering demand parameters (EDPs) (story drift ratio, SDR, and normalized diagonal shear demand, NDSD) are proposed, and two damage states (DS) (named DS4 for moderate damage and DS5 for severe damage) are investigated. The proposed shear formulae are used in the normalization of calculated NDSD values. Moreover, databases are sorted by a selected design parameter (aspect ratio) to calculate design parameter-sensitive fragility functions.Overall, the results indicate that the proposed expressions are more accurate than the corresponding expressions proposed by the American and Canadian codes when assessing BJR-PG-RM shear walls in terms of the average error and dispersion of relative prediction error. All the fragility curves adjusted to the whole database pass the Lilliefors goodness of fit test (α=5%). Comparing SDR-based curves of walls of a different unit type, DS4 curves present a smaller difference in the median value (θ) than DS5 curves. Additionally, the variations in the θ of NDSD-based curves of walls of different units are smaller than those observed in SDR-based fragility functions, indicating that NDSD represents a less variant EDP to describe the probability of shear damage at DS5 when a proper expression is employed for the normalization. Regarding design parameter-sensitive fragility functions, sorting databases reduces the number of data points used to calculate the functions, which produced two SDR-based and one NDSD-based function to fail the Lilliefors test (α=5%). In general, the θ value of SDR-based curves increases in proportion to the aspect ratio. Additionally, classifying the databases by a design parameter (aspect ratio) corroborated that the proposed expression has acceptable accuracy based on the adjusted NDSD-based DS5 fragility functions. It is highlighted that calculating design parameter-sensitive functions might increase the accuracy of PBEE assessments (e.g., loss estimations) when an EDP insensitive to design parameters normalization (e.g., SDR) is employed.

Deformation capacity evaluation for flat slab seismic design

In flat-slab frames, which are typically designed as secondary seismic structures, the shear failure of the slab around the column (punching failure) is typically the governing failure mode which limits the deformation capacity and can potentially lead to a progressive collapse of the structure. Existing rules to predict the capacity of flat slab frames to resist imposed lateral displacements without losing the capability to bear gravity loads have been derived empirically from the results of cyclic tests on thin members. These rules account explicitly only for the ratio between acting gravity loads and resistance against concentric punching shear (so-called Gravity Shear Ratio). Recent rational models to estimate the deformation capacity of flat slabs show that other parameters can play a major role and predict a significant size effect (reduced deformation for thick slabs). In this paper, a closed-form expression to predict the deformation capacity of internal slab-column connections as a function of the main parameters is derived from the same model that has been used to develop the punching shear formulae for the second generation of Eurocode 2 for concrete structures. This expression is compared to an existing database of isolated internal slab-column connections showing fine accuracy and allowing to resolve the shortcomings of existing rules. In addition, the results of a testing programme on a full-scale flat-slab frame with two stories and 12 columns are described. The differences between measured interstorey drifts and local slab rotations influencing their capacity to resist shear forces are presented and discussed. With respect to the observed deformation capacities, similar values are obtained as in the isolated specimens and the predictions are confirmed for the internal columns, but significant differences are observed between internal, edge and corner slab-column connections. The effects of punching shear reinforcement and of integrity reinforcement (required according to Eurocode 2 to prevent progressive collapse after punching) are also discussed.

The Elastic Constant of Coagulative Viscoelastometry

Clot strength is of utmost clinical significance. The elastic constant of the forming clot is a surrogate of its strength. The elastometric assessment of the forming clot, known as thromboelastography, is therefore of utmost clinical importance. Thromboelastography using a rotational viscoelastometer requires a geometric model to couple the shear deformation of a forming blood clot to its viscoelastic properties. Hartert’s original model idealized the complex geometry of the clot as a single cuboid and predicted a maximal effective shear modulus Gmax=5000 dyn/cm2. Hochleitner et al. recently reviewed this decades-old model, with the aim to refine it by reducing geometric simplifications that made the model more tractable. Hochleitner’s revised model uncouples annular segments and idealizes them as cuboids, thereby obtaining a maximal effective shear modulus of Gmax=4466 dyn/cm2. Hochleitner’s idealizations, while more accurate that Hartert’s, still produces error of at least 52%. Using the actual formula for annular shear from an applied torque, as derived by Ramberg and Miller, obviates several geometric simplifications assumed for analytical tractability and produces an elastic constant of G=2930 dyn/cm2. The clinical importance of precise determination of the formula for transforming clot amplitude to clot strength is underscored by the nonlinear relationship between elastometric amplitude and elastic constant, as the systematic error cannot be linearly rescaled. Thus, clot strength in several clinical scenarios should be based on clot strength as opposed to clot amplitude.

Applicable Formulas for Shear and Thermal Buckling of Perforated Rectangular Panels

The goal of this study is to create semiempirical formulations for predicting thermal and shear buckling loads of perforated rectangular isotropic panels for eight combinations of boundary conditions. The finite element method (FEM) was used to develop and evaluate empirical formulations. In this study, the influences of plate aspect ratios, boundary conditions, and perforation sizes on the buckling strength of perforated panels subjected to shear and thermal loads are investigated. The proposed formulas will enable consistent and reliable computation of the buckling loads for perforated rectangular panels without the need for complex calculations. The results of the empirical equations were found to be reasonably consistent with the outcomes of finite element analysis (FE) and findings from the literature. Various perforation patterns are investigated, ranging from a single circular hole up to 441 circular holes distributed across the plate. The results show that plates with a single central cutout have lower shear buckling loads than plates with multiple holes and an equal total cutout area.

Rubble Stone Masonry Buildings with Cement Mortar: Base Shear Seismic Demand Comparison for Selected Countries Worldwide

Full base shear seismic demand analyses with calculated examples for heavy stone masonry buildings are not present in the literature. To address this shortcoming, analyses and calculations are performed on nominally reinforced rubble stone masonry house and school designs, as typically built in Nepal. The seismic codes are literally applied for countries where the technique is still allowed (Nepal, India, China, Tajikistan, Iran, Croatia), or should be reintroduced based on current practices (Pakistan, Afghanistan, Turkey). First, this paper compares the base shear formulas and the inertia forces distributions of these codes, as well as material densities, seismic weights, seismic zoning, natural periods of vibration, response spectra, importance factors and seismic load combinations. Large differences between approaches and coefficients are observed. Then, by following Equivalent Lateral Force-principles for Ultimate Limit State verifications (10%PE50y), the base shear and story shears are calculated for a design peak ground acceleration of 0.20 g, as well as the effects of critical load combinations on the forces and moments acting on the lateral-resisting elements. It is concluded that Pakistan has the most tolerant code, Nepal represents an average value, whereas India and China are most conservative toward the case study buildings. Overall, it is observed that heavy-masonry-light-floor systems with negligible diaphragm action behave different under seismic motion than most other building typologies. Given the observations in this paper, the applicability of conventional ELF, S-ELF and S-Modal methods for heavy masonry buildings is questionable. The codes however do not introduce modified approaches that address these differences. Possible implications of the exclusion of plinth masonry and large portions of seismic weight need further assessment and validation, for which different (possibly more sophisticated) concepts must be considered, such as the equivalent frame method or distributed mass system. Since Nepal allows stone masonry in areas with higher seismic hazard levels >0.40 g (opposed to India <0.12 and China <0.15 g), their code is taken as the reference and starting point for follow-up research, which aims to verify the seismic demand by performing seismic capacity checks of the masonry piers and spandrels. The paper ends with an appeal for global collaboration under the research project SMARTnet.

Mechanical Characteristics of Steel Shear Keyed Joints in the Construction and Finished States

Joints that represent locations of discontinuity were the prominent factors affecting the overall behavior of precast segmental bridges. In this study, the steel shear key was designed, which was used to transmit the shear stress of the joints. To study the mechanical characteristics of the steel shear keyed joints in the construction and finished states, direct shear experiments and numerical analysis were carried out. The experimental results showed that the steel shear keyed joints had a high bearing capacity and good ductility. Under the action of confining stress, the joints relied on the mechanical occlusion between the steel keys to transmit the shear forces. When the load‐displacement curve entered the horizontal stage, it can still bore large relative deformation, and the bearing capacity did not decrease. In the construction state, the inelastic deformation of the steel shear key should be used to control the design value of the temporary load. In the finished state, the bearing capacity of joints should be controlled by the direct shear strength of the steel shear key, which can be calculated according to the shear formula. The shear strength of the material and size of the steel shear key are the main factors affecting the bearing capacity of steel shear keyed joints.

Tensile and shear performance of rotary inter-module connection for modular steel buildings

Because of the advantages of construction speed and efficiency, modular steel buildings (MSBs) have been increasingly used in mid-to high-rise buildings with repetitive units. Different form of connection and mechanical performance of the inter-module connection of MSBs from the traditional structure have always been remained a research hotspot. In this study, the mechanical performance of an innovative rotary inter-module connection was studied mainly through two tensile and two shear resistance tests. Then, the parametric analysis was carried out through the finite element analysis. The critical components of the connection under the tensile load were the corner fitting and the bottom plate of the lower rotating part, whereas, during the shear performance, the top plate of the lower corner fitting played a vital role. The edge yield of the bottom plate of the lower rotating part was used as the basis for deriving the formula of the tensile bearing capacity of the connection. Finally, a simplified calculation model was developed, and the formulas for tensile and shear bearing capacities were derived and verified.

Modelling of Textile Reinforced Concrete in bending and shear with Elastic-Cracked Stress Fields

Textile Reinforced Concrete (TRC) is emerging as a promising alternative to ordinary Reinforced Concrete for the construction of durable, lightweight and more sustainable structures, with a large potential particularly in shells and thin members. Research on the response of TRC in bending and shear as so far been performed on the basis of different approaches: plain section analysis with compatibility conditions for bending and mostly empirical strength formulas for shear. This paper explores a comprehensive approach for modelling the TRC response both for bending and shear on the basis of the Elastic-Cracked Stress Field (ECSF) method. The results of two full-scale flanged members in TRC tested in three-point-bending are presented. The tests are investigated by using Digital Image Correlation and the results are used to validate the assumptions of the ECSF. This approach allows accounting for the peculiarities of the material (notably for the linear-brittle response of the fabric) and leads to consistent results, accurately predicting the structural response in terms of strength and deformation capacity. The method is finally validated with other tests from the scientific literature, showing consistent agreement with a low coefficient of variation.

Shear performance of single-keyed dry joints between reactive power concrete and high strength concrete in push-off tests

Shear key joints are commonly used in constructions of precast concrete segmental bridges. Most researches focused on shear performance of the dry joints with the identical-strength concrete, leaving a research gap on that of composite joints between different concrete segments. This research aims to investigate shear behavior of shear key joint between reactive powder concrete and high strength concrete. Totally 12 specimens of single-keyed dry joint were tested, with the parameters of concrete compressive strength, steel fibers, and confining stress. The experimental results indicated that shear failure was observed, but crushing phenomenon occasionally occurred in composite joints in testing, which was confirmed by stress distribution from numerical simulation. In terms of shear capacity of composite joint, peak shear loads of reactive powder concrete specimens without steel fibers were enhanced by 10%–12% as increasing of concrete compressive strength, while those with steel fibers achieved 22%–25% enhancement. Nevertheless, a slight reduction of normalized shear strength was obtained because of its lower volume fraction of coarse aggregate. In numerical simulation, as increasing the concrete compressive strength of convex part, peak shear load was enhanced, but the increment rate of peak shear load decreased. Shear design formulae underestimated shear capacity of reactive powder concrete specimens with steel fibers, but the models proposed by Buyukozturk and Rombach gave accurate predictions on those without steel fibers.

Simulation of Crack Propagation in Some Self-Compacting Concrete Structures and Determination of Their Strength and Ductility Performances

A study on the crack propagation, strength and ductility performances of some self-compacting concrete (SCC) structures with and without steel fibers can be made through experiments. But testing is laborious. For large structure like dam, testing is impossible. Sometimes, there could be insufficient laboratory facilities. Under such circumstances, the non-linear analysis of concrete structures became a novel design tool. It employs the power of computer simulation using finite element method (FEM) based software to support the structural engineers. The ATENA software uses smeared crack approach and is based on the Bazant’s crack band theory. The experimental total fracture energies of both SCC and steel fiber reinforced SCC (Steel fibers of length 25mm@ 0.6% by volume of mix) beams of strength M50 determined by RILEM’s work of fracture method, corresponding material properties and tension softening behavior are used as input data in the software. The simulated load-deflection/CMOD curve could be used to access the strength and ductility performances of the structures. The strength is identified by peak load and ductility by extension of tail end of this curve beyond yield load. Hence, this paper presents an appropriate methodology to determine the performances by simulation. Ductility is the desired property required for structures during earthquake. This can be improved by increasing the main steel reinforcement, incorporate fiber reinforced plastic (FRP) and steel tubes to impart it. But this could be uneconomical. In such cases, it is to be investigated that ductility can be improved by incorporating steel fibers of appropriate aspect ratio and volume in the mix. The ductility ratio (μ) determined from the load-deflection/CMOD curves is further used to evaluate the response reduction factor(R) by an empirical formula as established in earlier investigation. The R used in base shear formula of IS 1893(Part-I)-2002 code considers the ductility property of the structures that are subjected to lateral base shear during earthquake. Thus this study is carried out to identify the usefulness of simulation technique which is a new and robust tool to assess these performances of the structures using ATENA software that avoid the tedious testing procedures. This study investigates the influence of steel fibers in SFRSCC structures to improve their strength and ductility performances compared to SCC structures.

Anisotropic inflation with coupled p−forms

We study the cosmology in the presence of arbitrary couplings between p-forms in 4-dimensional space-time for a general action respecting gauge symmetry and parity invariance. The interaction between 0-form (scalar field ϕ) and 3-form fields gives rise to an effective potential Veff(ϕ) for the former after integrating out the contribution of the latter. We explore the dynamics of inflation on an anisotropic cosmological background for a coupled system of 0-, 1-, and 2-forms. In the absence of interactions between 1- and 2-forms, we derive conditions under which the anisotropic shear endowed with nearly constant energy densities of 1- and 2-forms survives during slow-roll inflation for an arbitrary scalar potential Veff(ϕ). If 1- and 2-forms are coupled to each other, we show the existence of a new class of anisotropic inflationary solutions in which the energy density of 2-form is sustained by that of 1-form through their interactions. Our general analytic formulas for the anisotropic shear are also confirmed by the numerical analysis for a concrete inflaton potential.

Development of a modulus of subgrade reaction model to improve slab-base interface bond sensitivity

ABSTRACT In the Pavement ME Design, the modulus of subgrade reaction (k-value) is characterised by the dense liquid or Winkler model, which does not consider the interface bond within the supporting media. In this study, a modified k-value model was developed to take into account the shear interaction between concrete slab and base course. Formulation of the modified k-value model contained four steps: (a) correction of cross anisotropic base modulus; (b) development of a submodel for slab-base equivalent thickness; (c) development of a formula for slab-base interface shear bonding; and (d) determination of k-value using the calculated shear bonding and the deflection patterns of falling weight deflectometer (FWD). A large number of rigid pavement structural and strength properties and the corresponding FWD deflection patterns data were collected from the Long-Term Pavement Performance database and used to calculate the modified k-value. These were compared against the k-values using the existing ‘backcalculated best-fit approach’. The results showed that the modified k-values changed significantly due to the consideration of cross anisotropy and slab-base interface bonding. Finally, an artificial neural network (ANN) approach was employed to predict the modified k-values for the given pavement structures, layer moduli and interface bonding ratios.

Investigation of the Mechanical Behavior of Partially Precast Partially Encased Assembled Composite Beams

In view of the characteristics of a high floor and the heavy load of logistics buildings, a partially prefabricated partially encased assembled composite beam (PPEC) is proposed in order to achieve the low cost construction of such buildings. In this research, the mechanical properties of PPEC beams were studied experimentally. The effects of the concrete strength grade, steel content, shear span ratio, and fabrication methods on the mechanical properties of the PPEC beams were analyzed. The results showed that the proposed structural form of the PPEC beams was generally feasible. Based on the test results, a practical shear formula for PPEC beams was proposed, and the calculated results were in good agreement with the test results.