Load-deformation Relationship Research Articles

DETAILED EVALUATION OF THE SKELTON CURVE OF BEAMS IN CRUCIFORM UNBONDED PRECAST PRESTRESSED CONCRETE FRAMES

Strength and deflection for beams in cruciform unbonded precast prestressed concrete frames are evaluated using a skeleton curve consisted of four characteristic points (flexural cracking point, tendon’s elastic limit point, ultimate flexural point, safety limit point), based on theoretical approach. The flexural cracking point is evaluated by elasticity theory, and other points are estimated by a macro-model, which well produces the seismic behavior of the target structure. Skeleton curves composed of four characteristic points correspond well to the load-deformation relationship of previous experimental results. Calculated strength and deflection, as well as the tendon strain, show good agreement with the experiments.

An analytical method of axial load distribution of deep groove variable clearance radial ball bearings

Over the past years, researchers have touched each wave successfully and significant advancement have been introduced in the field of ball bearing. But yet some major aspects of ball bearings need to be divulged like operating radial clearance. The performance and life of the ball bearing significantly depend on its operating clearance. To explore this interest 6206 single row deep groove ball bearing with variable radial clearance is considered in this article. The article basically pacts with the load deformation relationship of variable clearance ball bearing subjected to pure axial load. A closed form solution for load shared by balls is developed using mechanics of solids approach of Hertz contact theory. The acquired result show that under pure axial loading the ball with minimum radial clearance will support maximum axial load. Further, the load shared by 0th ball for variable clearance ball and constant clearance ball bearings is compared. The results and other excerpts from the recommended work will help in unveiling the behavior of ball bearings with variable clearance for combined radial, axial, and moment load.

Shear behaviour of vertical inter-module connection with bolts and shear keys for MSCs

Modular steel constructions (MSCs) are increasingly used in mid- to high-rise buildings because of their advantages in higher manufacturing quality, faster on-site installation speed, higher material use efficiency, lower life-cycle cost, as well as some other environment-friendly features. Shear tests of vertical inter-module connections with bolts and shear keys, which play a critical role in the lateral performance of MSCs, were carried out to investigate their shear load-carrying capacities and shear mechanical characteristics. Refined numerical models were established, calibrated against the test results and used to simulate the shear behaviour of vertical inter-module connections. The effects of friction coefficient and axial compression ratio on the shear behaviour were investigated. The connections were shown to exhibit excellent initial shear load-slip behaviour and shear load-carrying capacity under shear load. In terms of initial shear stiffness and slip resistance, the axial compression ratio and friction coefficient were shown to be the critical parameters, while the shear key and high-strength bolt dominated the ultimate shear resistances. Shear processes of vertical inter-module connections in different shear directions were almost consistent, which can be divided into the micro slipping stage, macro slipping stage, bearing stage and failure stage. Through geometrical parameters correlation analysis, a piecewise polynomial simplified shear load-deformation model was proposed for predicting the shear load-deformation relationship. The proposed model was shown to be capable of accurately capturing the shear behaviour of the connection, and is therefore recommended for use in engineering applications and future research on inter-module connections.

Experimental, numerical, and theoretical crushing behaviour of an innovative auxetic structure fabricated through 3D printing

This paper aims to investigate the crushing behaviour and protective performance of an innovative auxetic structure, named the hourglass structure (HGS), under in-plane compressive loads. The HGS was fabricated with a 3D printing method through fused filament fabrication technique. The 3D printed HGS specimens were subjected to a displacement-controlled in-plane quasi-static compressive load. A 3D comprehensive numerical model was developed and calibrated with the experimental results. The calibrated numerical model was used for a parametric study to explore the effects of relative density, functional grading, and crushing velocity on the protective performance of the HGS. Furthermore, a theoretical model was proposed to correlate plateau stress of the HGS with geometric design parameters, effective Poisson’s ratio, and matrix material properties. Verified with a series of numerical analyses of different HGS designs, the proposed theoretical model predicted plateau stress with less than 10% relative error. In addition, experimental, numerical, and theoretical analyses uncovered load–deformation relationship, Poisson’s ratio, crushing mechanism, and energy absorption capacity of the novel auxetic. Overall, the HGS exhibited excellent features for protective engineering applications such as shock mitigation and blast energy absorption.

A fictitious pile method for interaction factor of two laterally loaded piles in multilayered isotropic soils

An efficient fictitious pile method based on elasticity theory is presented for the analysis of interaction factor of two laterally loaded piles embedded in non-homogeneous soils. The problem is decomposed into two systems, namely the two fictitious piles acted upon by (partial) external loading, and an extended multilayered soil continuum acted upon by a system of pile-soil interaction forces at imaginary positions of the piles. The behavior/responses of the multilayered isotropic soils are analyzed through a computationally effective transfer matrix solution procedure. A Fredholm integral equation of the second kind is then deduced for the load-deformation relationship of a two-pile group system, by considering the equilibrium of the pile-soil interaction forces and the displacement compatibility between the fictitious pile and the extended soil. Comparison of the results calculated by the present fictitious pile method for displacement interaction factor between two piles embedded in multilayered isotropic soils has shown good agreement with the previous ones obtained by using the more rigorous finite element approach. The parametric numerical study demonstrates that the soft-over-stiff-over-soft soil layers have a profound effect on the pile-to-pile displacement interaction factor for the case of moment loading, which should be carefully considered in the practical design.

Deformation and strain limits for IPB-loaded high strength steel CHS joints

In this study, existing deformation limits are first re-examined to investigate if they can be rationally extended to high strength steel circular hollow section (CHS) joints that are subjected to in-plane bending (IPB) moment. It is pointed out that existing deformation limits, which have been developed and validated primarily for mild steel joints, need to be modified when high strength steels are involved. By noting that the ductility of IPB-loaded joints can be significantly reduced with the use of high strength steel, a new deformation limit is proposed which allows less deformation to less ductile high strength steel joints. The deformation limit, proposed in terms of joint rotation angle, is validated both numerically and experimentally. In addition, a recently proposed strain limit criterion is also discussed. To provide a guide for obtaining converged strain from finite element (FE) analysis, mesh sensitivity study is comprehensively conducted. It is shown that the element size required for the convergence of strain is substantially smaller than that required for obtaining satisfactory global response such as joint load-deformation relationship. By applying a systematic FE modeling strategy, numerical investigation is made to check the feasibility of the 5% strain limit criterion which has recently been advocated by the revised draft of ISO 14346. While the limiting principal strain of 5% is shown to be reasonable for CHS-to-CHS joints loaded by IPB, for longitudinal branch plate-to-CHS joints, a lower limiting strain appears more appropriate.

Ultimate compressive capacity of tapered concrete-filled double skin steel tubular stub columns with large hollow ratio

Recent developments in towers of wind turbine have heightened the need for tapered Concrete-Filled Double Skin Steel Tubular columns with Large Hollow Ratio (LHR-CFDST). It is necessary to further investigate the mechanical behaviour, key parameters' effects and design methods of tapered LHR-CFDST columns. This paper thus presents an analytical study on the tapered LHR-CFDST stub column under axial compression. A comprehensive finite element (FE) modelling is developed and then verified with the experimental data. A parametric study is conducted to reveal the effects of tapered angles, hollow ratios and diameter to thickness ratios of steel tubes. Further analysis is carried out to understand the compressive behaviour in terms of the full-range load-deformation relation, the axial compressive force distribution and the limitation of steel tube's diameter to thickness ratio. A simplified method for predicting the ultimate compressive capacity of tapered LHR-CFDST stub columns is proposed and the prediction agrees well with the test data.

Mechanical characteristics of H-shaped shear panel damper fabricated by SPHC steel according to stiffener reinforcement and stud support installation

In this study, cyclic loading tests were conducted at a constant deformation amplitude to investigate the mechanical characteristics of an H-shaped shear panel damper (HSPD)1HSPD: H-shaped shear panel damper; FE: Finite element.1 fabricated with the use of SHPC steel. Two experimental conditions were established according to the test parameters for the damper unit and damper system (damper supported by studs). For each experimental condition, two types of HSPDs were applied according to the presence or absence of stiffener reinforcement. The experimental results of the damper supported by studs showed that the elastoplastic behavior of the damper part was similar to that of the damper unit. Additionally, it was shown that the stud maintained its elastic state until the end of the test. Furthermore, it was found that when the damper was reinforced with a stiffener, the plastic deformation capacity of the damper was improved significantly compared with the case in which the stiffener was not reinforced. The effect of the stiffener reinforcement was also investigated based on nonlinear finite element analysis. The plastic strain distribution of the HSPD panel was evaluated based on the analyzed results that tracked the load–deformation relationship of the experimental results. As a result, the HSPD panel part was segmented by the stiffener and the width-to-thickness ratio was reduced so that the distribution of the plastic deformation values in the panel was relatively stable, and the deformation in the out-of-plane direction could be suppressed. The results showed that the shear buckling for the same shear deformation could be delayed according to the effect of the width-to-thickness ratio of the panel which was reduced by the reinforcement of the stiffener.

Geometrically nonlinear electro-thermo-static analysis of piezoelectric/CNT/GPL/fibre/polymer sandwich panels with double curvature resting on elastic foundation

Evaluation of the electro-thermo-static behaviour of the shell panels of double curvature using an analytical method is carried out in this paper. The proposed panels are made of a hybrid composite, and considered to be rested on the Winkler-Pasternak elastic foundation. The hybrid composite shell contains two thin piezoelectric sheets at its bottom and top surfaces, and some plies made of carbon fibres and polymeric resin which is reinforced by the randomly oriented nanocomposites. The employed nanocomposites for some layers are carbon nanotubes (CNTs) and for some other are graphene nanoplatelets (GPLs). The governing nonlinear system of differential equations of orthotropic doubly-curved shell panels are developed based on the first-order transverse shear deformation theory (FSDT) which incorporates moderately thick and also thin shells. The Gauss Quadrature method is applied to obtain the forces and moments due to the thermo-electrical loads, and the Galerkin method is employed to solve the developed system of equations which leads to a closed-form load-deformation relationship (equilibrium path of the shell). The novelty of the present study can be expressed in the solution and employed hybrid composite materials. First, by employing the proposed closed-form solution no time consuming computations are required. On the other hand, the effects of the piezoelectric and two different nanocomposite materials on the thermo-electro-mechanical nonlinear static behaviour of the hybrid composite shells can be evaluated. The accuracy of the present method is validated by comparing the achieved results for the some benchmark problems with those are existent in the literature. The impacts of various electro-thermo-mechanical and geometrical characteristics of the proposed shells on their equilibrium paths are also considered by carrying out an extended parametric study.

Numerical Analysis of Shallow Foundations with Varying Loading and Soil Conditions

The load–deformation relationship under the footing is essential for foundation design. Shallow foundations are subjected to changes in hydrological conditions such as rainfall and drought, affecting their saturation level and conditions. The actual load–settlement response for design and reconstructions is determined experimentally, numerically, or utilizing both approaches. Ssettlement computation is performed through large-scale physical modeling or extensive laboratory testing. It is expensive, labor intensive, and time consuming. This study is carried out to determine the effect of different saturation degrees and loading conditions on settlement shallow foundations using numerical modeling in Plaxis 2D, Bentley Systems, Exton, Pennsylvania, US. Plastic was used for dry soil calculation, while fully coupled flow deformation was used for partially saturated soil. Pore pressure and deformation changes were computed in fully coupled deformation. The Mohr–Columb model was used in the simulation, and model parameters were calculated from experimental results. The study results show that the degree of saturation is more critical to soil settlement than loading conditions. When a 200 KPa load was applied at the center of the footing, settlement was recored as 28.81 mm, which was less than 42.96 mm in the case of the full-depth shale layer; therefore, settlement was reduced by 30% in the underlying limestone rock layer. Regarding settlement under various degrees of saturation (DOS), settlment is increased by an increased degree of saturation, which increases pore pressure and decreases the shear strength of the soil. Settlement was observed as 0.69 mm at 0% saturation, 1.93 mm at 40% saturation, 2.21 mm at 50% saturation, 2.77 mm at 70% saturation, and 2.84 mm at 90% saturation of soil.

Micromechanics of granulated rubber–soil mixtures as a cost-effective substitute for geotechnical fillings

Rubber–soil mixtures (RSM), formed by mixing two types of granules with vastly different mechanical properties, has the potential for serving as a cost-effective substitute for geotechnical fillings. Its micromechanical behavior at a microscopic scale, however, is not yet well understood. In this study, a numerical model of granulated RSM under biaxial compression conditions is established based on the discrete element theory and two-dimensional particle flow code. Microparameters of a particular RSM are studied and calibrated by comparison with triaxial consolidated drained shear tests. The volumetric fraction of sand is assigned as the index of the mixture, and the deviatoric stress–axial strain curves of RSM with different sand fractions are analyzed. Particle rotation, average coordination number, force chain structure, and energy dissipation with axial strains are further investigated to better understand the microscopic mechanisms of RSM. The main findings of the study include: (1) Rubber particles are highly deformable and fill the voids more easily than stiffer sand particles. This contributes to the high friction of sand–rubber interfaces, which delays or even inhibits the relative motion and tumbling of sand particles; (2) The force chains of sand particles are either braced from buckling until large axial strains by rubber particles occupying the intergranular voids or distributed by increased rubber–rubber contacts depending on the rubber content; and (3) RSM with a rubber volumetric content of 30–40% are optimal in that the force chain increases monotonically with axial strain with a stable load-deformation relationship. In addition, the sensitivity analysis of the effect of microparameters on the macroscopic behavior of RSM is presented, which can provide theoretical support for exploring the mechanical properties of similar mixed granular materials subjected to external loading.

Novel Ductile Enhancement in the Structural Characteristics of External Beam Column Joint with Potassium-Activated Green Concrete Technology

Ductility and energy dissipation capacity of the beam column joints are the two prominent characteristics which govern the stability of the entire structure constructed in the seismic prone areas. In this paper, the effect of potassium-activated geopolymer concrete in the exterior beam column joint application is investigated under low frequency cyclic loading. Numerical analysis has been done by using the finite element software Abaqus and compared with the experimental work. From the load deformation relationship, parametric studies are carried out in the aspects of ductility, stiffness degradation, energy dissipation capacity, drift ratio and cracking pattern. The use of potassium-activated geopolymer technology in the exterior beam column joint application resulted in the improved ductility, energy dissipation capacity with superior ultimate load carrying capacity of 1.05% over conventional cement reinforced concrete beam column joints with special confining reinforcement confirmed by IS 13920 due to the enormous polymerization activated by high molecular potassium ions. There is an improved energy dissipation capacity of 2.78% of potassium-based geopolymer specimen resulting in lesser number of non-structural cracks and 11.26% more deformation under 11.96% enlarged drift ratio than the conventional reinforced concrete specimen. From the observed results, it is clearly noted that the implementation of potassium-activated green polymer technology in the beam column joints possessed enhanced ductility characteristics to protect the structure susceptible to seismic environment and resulted in innovative, economical and sustainable mode of seismic-resistant building construction.

Numerical-based analytical model of double-layer steel-LHDCC sandwich composites under punching loads

This study conducts numerical analyses on a newly developed double-layer steel-lightweight high ductility cement composite (LHDCC)-steel sandwich panel under concentrated punching load. Energy absorption ability serves as an important criterion in evaluating the performance of the protective sandwich structures. One critical factor related to energy absorption ability is the stiffness or the deformation capacity of the structure. The present study first develops a procedure to establish a FE model of the double-layer SCS panel. The Concrete Damage Plasticity (CDP) model is adopted to simulate the behavior of LHDCC, with a compressive stress–strain relation represented by a statistically stochastic damage constitutive model. The FE model is validated through comparisons with the test results of 2 single-layer SCS panels and 8 double-layer SCS panels. A series of parametric studies are then performed to check the influences of concrete height, shear span, steel plate thickness, shear connector spacing, loading patch size, concrete strength and steel plate strength on the stiffness and load resistance of the panel. Finally, the paper develops a simplified analytical model to predict the stiffnesses at both elastic and plastic stages, and proposes an idealized load–displacement model to reproduce the load-deformation relation for the double-layer SCS panels. The comparisons with the test and FE results validate the accuracy of the analytical model.

Tensile and flexural behaviors of connections between steel beam and concrete-encased-and-filled steel tube column

Concrete-encased-and-filled steel tube (CEFT) columns with a circular tube section can be potentially used for hollow precast concrete (PC) constructions, in which thin PC encasement is used to reduce the lifting weight of a large PC column. In the present study, connection methods were studied for steel beam-CEFT column joints with the thin concrete encasement. Two sets of testing were performed focusing on the local behavior of the connection: 1) monotonic tension test for beam flange-column connections, and 2) cyclic loading test for beam-column joints. In the first test, the local out-of-plane behavior of the flange plate-tube connections and the associated damage mode of the concrete encasement were identified. The load-deformation relationships of the test specimens were evaluated by nonlinear finite element analysis. Based on the results, exterior beam-column joint specimens were designed, and the flexural behavior of the connections was verified under cyclic loading. The joint specimens were strengthened with connection methods such as tension bars, thick steel tube, and vertical continuity plate, inducing the beam failure. In particular, the thick tube and vertical continuity plate were effective in restraining the concrete damage. The tensile and flexural strengths of the test specimens were evaluated using design equations.

Behavior of new types of flange connectors of precast double‐tees

SummaryDouble‐tees are often used as roof and floor systems in commercial buildings and parking garages, and they are often joined with mechanical connectors to form a floor system. The properties of flange‐type connectors directly affects the in‐plane behavior of double‐tee diaphragms; however, most of them have been developed through field experience with undependable capacities, despite such connectors having been extensively applied in practice. Five new types of connectors were constructed, and a total of 15 connector tests were conducted under a variety of loading conditions with both monotonic and cyclic reversing in‐plane shear. The load–deformation relationship, stiffness, energy consumption capacity, and shear capacity of the five new types of mechanical connectors were obtained. The results show that the seismic performance of new types of mechanical connectors deviated from each other by large margins, and they are satisfactory for vertical loading. The test results also show that the pre‐toppings can effectively improve the strength and deformation capacity for all kinds of connectors.

A Proposal for Classification of Wooden Houses Based on Seismic Performance and Calculation Method of Standard Load-Deformation Relationship

A Proposal for Classification of Wooden Houses Based on Seismic Performance and Calculation Method of Standard Load-Deformation Relationship

Numerical analysis of lightweight concrete wall panels having a variation of dimensions and openings that were subjected to static lateral loads

Wall panels are non-structural parts of buildings that are considered dead loads. The mass of wall panels must be reduced to minimize earthquake risk and enhance structural resistance to lighter dead loads. This study used wall panel models that consisted of lightweight foamed concrete materials containing expanded polystyrene. The wall panels used in this study also had a variety of dimensions and reinforcements. The effect of openings on wall panel model performance was also investigated. This study aimed to analyze the performance of lightweight concrete wall panel models under static lateral loads applied until the ultimate condition. It was found that the load-deformation relation performs varying values of stiffness, strength, and ductility depended on the wall panel dimensions, reinforcements, and openings. A wall panel model with a height of 1000 mm that had length of 1500 mm and thickness of 60 mm with wire mesh and without openings achieved the highest ultimate stiffness and strength. The highest ductility was achieved by a wall panel model with openings, without wire mesh, with height, length, and thickness of 1500 mm, 1500 mm, and 40 mm, respectively. Diagrams of the deformations in this paper reflect the compressed and tensioned areas. The lefthand parts of all wall panel models without wire mesh were tensioned and had concentrations of deformation in those areas. The existence of openings also caused increased deformation due to less stiffness in the wall panel models.

Progressive Collapse Performance of Steel Beam-to-Column Connections: Critical Review of Experimental Results

Background: The steel beam-to-column connections are vulnerable structural elements when a building loses one or more of its vertical load-carrying components due to abnormal or accidental loading conditions. After a column is destroyed by abnormal loads, the tensile axial force of the beam gradually increased, while the bending moment decreased, and the load-resistance mechanism shifts from a flexural mechanism to a catenary mechanism, with the axial force becoming the prevailing factor. Aims: This paper investigates the progressive collapse performance of steel beam-to-column connections. While undergoing large deformation, the beam-to-column connections are subjected to moment, shear, and tension in conjunction with high ductility demand. Their behavior under monotonic loading depends on the moment-axial tension interaction and greatly affects the progressive collapse resistance of the structure. This paper presents a critical review of experimental tests of different types of steel beam-column joints (flexible, rigid, and semi-rigid) under a central-column-removal scenario. Methods: The experimental results, including load-deformation relationships, failure modes, and catenary effects, are described in detail. The findings are used to evaluate the rotation capacity of different types of steel beam-to-column connections. The results are compared to the acceptance criteria specified by the main progressive collapse guidelines for several beam-to-column connection categories. Results: In simple (flexible) joints, the stiffness and strength at higher drift angles essentially depend on the tensile capacity of the connection that prevents, in some cases, the full development of the catenary mechanism. The connection depth alone does not seem to be an effective parameter to predict the rotational capacity of beam-to-column connections, since different connections with similar values of the connection depth result in very different values of the maximum rotation capacity. In fully rigid and semi-rigid connections, after the column removal, the flexural resistance controls the behavior at the preliminary phase, and the tensile force is almost zero. With increased downward displacement, the axial tensile force also increases, developing a catenary mechanism. Although the stiffness of rigid and semi-rigid connections is higher than flexible connections, both categories result in similar rotation capacity. Conclusion: In all the simple connections herein considered, the plastic rotation capacity obtained by tests was found much higher than the code recommended values that are probably too conservative. On the contrary, for one rigid and two semi-rigid connections, the values of the plastic rotation capacity obtained by tests are lower than the corresponding recommended values. Thus, the suggested acceptance criteria proved to be out of the conservative side.

Research on the multi-shear spring model for circular-section steel piers

The main damage caused by earthquakes to single-column circular-section steel piers is the bulged deformation at the bottom, generated by local instability. The refined shell-based finite element (FE) model can accurately simulate the deformational behavior, but it is still cumbersome and time-consuming to apply to the engineering design currently. Further, the existing simplified methods cannot be used in seismic response analyses under horizontal bidirectional earthquakes. Therefore, this paper uses the multi-shear spring (MSS) mechanical model as the basic model and proposes an MSS calculation model for circular-section steel piers. This model is applicable for horizontal bidirectional seismic response analysis and considers the local instability effect of steel plates. In this study, the load–deformation relationship of the modified Menegotto-Pinto model is employed in all directions as the hysteresis curve equation of the springs. The basic parameters of the corresponding models for different structures are determined according to the calculation results of the refined-shell models. In addition, the Ibarra-Krawinkler degradation rule is employed to simulate the degradation process of structural bearing capacity and stiffness, and the degradation parameters are identified. The pseudostatic and seismic time-history response analyses of steel piers with different width-to-thickness ratios verify that the proposed model has reliable calculation accuracy and greatly improved efficiency. The research in this paper provides a practical calculation method for the seismic response analysis of steel bridge piers.

Finite element modelling of rectangular concrete-filled steel tube stub columns incorporating high strength and ultra-high strength materials under concentric axial compression

This study presents a unified approach to simulate the behavior of rectangular concrete-filled steel stub columns incorporating high strength and ultra-high strength materials subjected to concentric axial compression. The finite element model is developed based on Abaqus software, which is capable of accounting for geometrical nonlinearity, material plasticity, and interaction between multi-physics. The proposed model incorporates the influences of residual stress for welded-box steel sections and initial imperfection. A novel stress-strain relation of confined concrete is proposed to account for the composite action, which might increase the strength and ductility of infilled concrete under multi-axial compressive conditions. Various verification examples are conducted with wide ranges of geometrical and material properties. The simulation results show that the proposed model can accurately predict the ultimate strength, load-deformation relations, and failure mode of the experimental specimens.