Distributed Loading Conditions Research Articles

Progressive collapse resistance of precast concrete beam–column assemblies using dry connections under uniformly distributed loading condition

Improving the integrity of precast concrete (PC) frame structures using dry connections is essential for enhancing their robustness against progressive collapse. Therefore, three PC beam–column assemblies using different dry connections specially designed to ensure the connectivity were experimentally examined under progressive collapse scenarios. And a seven-point loading tree device was adopted to simulate the uniformly distributed loading conditions in practical engineering. The connection details were classified as follows: normal top-and-seat angle connection in TSA, strengthened top-and-seat angle connection in STSA, and strengthened top-and-seat angle with high ductility longitudinal reinforcements in the plastic regions in DSTSA. Under small deformations, STSA had the highest first peak load attributable to its strengthened joint connection. TSA obtained a lower load than that of STSA because of the low joint connection stiffness. Meanwhile, DSTSA achieved the lowest load among the three specimens because the smoother surface of the high-ductility reinforcements (compared with that of normal ones) weakened its bond to the concrete. However, under large deformations, the high ductility of the reinforcements ensured the specimen integrity; consequently, the largest final load was achieved in DSTSA. On the contrary, the high joint stiffness and normal reinforcements in STSA hindered the beam end rotation, and the steel angle failed early in TSA. As a result, the two connections failed to ensure the specimen integrity. To further shed light on the resistance mechanisms of beam–column assemblies under the uniformly distributed loading condition, an iteration-based model was developed to calculate the first peak load under the beam and compressive arch actions. The maximum prediction error achieved was 12%. Based on the model, the load contribution from the friction effect of the loading device was identified as 27%. And it was found that during the collapse, increasing reinforcement deformation region that might be induced by slippage between the concrete and reinforcements could lead to a continuous increase in the horizontal reaction force after the specimen reaching the first peak load.

Nonlinear fully coupled thermoelastic transient analysis of axial functionally graded composite panel

In this article, the two-way coupled thermoelastic behavior of axially graded composite plate and doubly-curved (cylindrical, spherical, hyperbolic, and elliptical) panels is examined under conductive-convective boundary and uniformly distributed loading conditions. Here, the material properties of the axial functionally graded panel are computed by employing the power-law-based Voigt’s scheme. The material and geometric nonlinearities are incorporated using the cubic-polynomial-based temperature-dependent constitutive model and higher-order kinematics-based Green-Lagrange strain, respectively. The temperature profile is obtained through thermally nonlinear theory associated with high temperature, which is used to extract the energy equations obtained from the first law of thermodynamics and deformation-dependent entropy relation. The weak forms of motion and heat-transfer equations are derived using Galerkin’s method and further combined into the two-way coupled field equation through 2D-finite element approximation via Lagrangian elements. The transient responses are computed via the Newmark and the Crank-Nicolson schemes, whereas the nonlinear iterations are executed through Picard’s iteration technique. The performance of the fully coupled model for an axially graded (metal/ceramic) structure is verified with analytical, numerical, and experimental results and tested through a variety of numerical illustrations under various sets of conditions.

The effect of core materials on flexural behaviour of sandwich panels with basalt FRP facesheets

The flexural behaviour of sandwich panels with basalt fiber-reinforced polymer (BFRP) facesheets was investigated. A total of 10 sandwich panels were subjected to six-point flexural tests to simulate uniformly distributed loading conditions. The variable parameters were the core thickness (30, 50, 60 and 100 mm), core category (polyurethane [PU], extruded polystyrene [XPS], rock-mineral wool [RW]), and hybrid core (PU+RW and XPS+RW). Finally, the shear distribution coefficient of core material for sandwich panels with BFRP facesheets was modified depending on the experimental data. The experimental results showed that an increase in the PU core thickness significantly increased the flexural strength and rigidity of the sandwich panels. For different core materials, the maximum loads of the panels were positive with the shear strength of the core materials. Whereas, XPS+RW hybrid core not only can significantly decreases the costs, but also exhibits the highest bearing capacity and stiffness as compared with the PU+RW hybrid and PU cores.

ANALYTICAL SOLUTION FOR NONLINEAR INTERACTION OF EULER BEAM RESTING ON A TENSIONLESS SOIL

The nonlinear interaction between an elastic Euler beam and a tensionless soil foundation is studied. Exact analytical solutions of the challenging problem are rather complicated. The basic obstacle is imposing compatibility conditions at lift-off points. These points are determined as a part of the solution although being needed to get the solution itself. In the current work, solutions are derived using the approximate Rayleigh-Ritz method. The principal of vanishing variation of potential energy is adopted. The solution is approximated using a set of suitable trial functions. Lift-off points are identified through an iterative procedure and compatibility conditions are satisfied implicitly. Results are presented for various cases, including clamped support and free end condition. Various distributed loading conditions are analyzed. Exact solutions are revised briefly. Accurate high order approximate analytical solutions are obtained using MAXIMA symbolic manipulator. The convergence of approximate solutions towards the exact solutions is verified. For each case detailed results of deflection, bending moment and shear are presented.

Deformation measurement based on high resolution distributed optical fiber sensing and conjugated beam method

Structural deformation is in general an effective indicator of unforeseen damage accumulation. It is difficult to monitor deformation distribution by traditional single point measurement methods. Based on a high strain sensing resolution technique of optical frequency domain reflectometry (OFDR), this paper presents a hybrid method for structural deformation measurement. The main advantage is the explicit relationship between structural deformation and monitored strain data thus the calculation process can be conducted free from load identification and stiffness measurement. The accuracy of this method is investigated via both theoretical and experimental study. In lab experiments, simple support beam with fix supports and spring supports was designed. Compared with classical double integration method, the accuracy of the conjugated beam method (CBM) improved 5%. In concentrated and uniform distributed load conditions, the average relative error ranges from 4% to 7%. Furthermore, the average relative errors for several points are no more than 3% in complex load conditions.

Stress analysis of generally asymmetric non-prismatic beams subject to arbitrary loads

Non-prismatic beams are widely employed in several engineering fields, e.g., wind turbines, rotor blades, aircraft wings, and arched bridges. While analytical solutions for variable cross-section beams are desirable, a model describing all stress components for beams with general variation of their cross-section under generalised loading remains an open and important problem to solve. To partly address this issue, we propose an analytical solution for stress recovery of untwisted, asymmetric, non-prismatic beams with smooth and continuous taper shape under general loading, considering plane stress conditions for isotropic materials undergoing small strains. The methodology follows Jourawski’s formulation, including the effect of asymmetric variable cross-section, with internal forces as known variables. We confirm the non-triviality of the stress field of non-prismatic beams, i.e., the dependency on all internal forces and beam geometry to shear and transverse stress distributions. As a particular novelty, the new formulation for transverse direct stress includes internal forces derivatives, resulting in greater accuracy than state-of-the-art models for distributed loading conditions. Also, closed-form solutions are introduced for non-prismatic and linearly tapered, generally asymmetric beams, both with rectangular cross-sections. For validation purposes, we consider three different practical beam models: a symmetric and an asymmetric, both linearly tapered, and an arched beam. The results, checked against commercial finite element analysis, show that the proposed model predicts the stress-field of non-prismatic beams under distributed loads with good levels of accuracy. Traction-free boundary condition requirements are naturally satisfied on the beam surfaces.

Analysis of Pure Bending Vertical Deflection of Improved Composite Box Girders with Corrugated Steel Webs

Steel bottom plates are applied as replacements for the concrete bottom plates in order to reduce the dead weight of the composite box girders with corrugated steel webs and steel bottom plates (CSWSB). Due to the change in the material, the previous analytical calculation methods of vertical deflection of composite box girders with corrugated steel webs (CSWs) cannot be directly applied to the improved composite box girders. The shear lag warpage displacement function was derived based on the shear deformation laws of the upper flange and the bottom plates of the improved composite box girders. The equations for the calculation of the shear deformation and the additional deflection due to the shear lag of continuous and simply supported composite box girders with CSWSB under concentrated and uniformly distribution loads were derived by considering the double effects of the shear lag and the shear deformations of the top and the bottom plates with different elastic moduli. The analytical solutions of the vertical deflection of the improved composite box girders include the theory of the bending deflection of elementary beams, shear deformation of CSWs, and the additional deflection caused by the shear lag. Based on the theoretical derivation, an analytical solution method was established and the obtained vertical deflection analytical solutions were compared with the finite element method (FEM) calculation results and the experimental values. The analytical equations of vertical deflection under the two supporting conditions and the two load cases have verified the analyses and the comparisons. Further, the additional deflections due to the shear lag and the shear deformation are found to be less than 2% and 34% of the total deflection values, respectively. Moreover, under uniform distributed load conditions, the deflection value was found to be higher than that of the under concentrated load condition. It was also found that the ratio of the deflection caused by the shear lag or the shear deformation to the total deflection decreased gradually with the increase in the span width ratio. When the value of the span width ratio of a single box and single chamber composite box girder with CSWSB was equal to or greater than 8, the deflections caused by the shear lag and the shear deformation could be ignored.

Comparative Study of Beam Theories on the Effect of Span-Depth Ratio for Symmetric and Un-symmetric Loadings

In the present work, a comparative study is done between Shear-indeformable (Euler-Bernoulli) model and Shear-deformable (Timoshenko) model for two different types of beams (simply supported and fixed beam) under uniformly distributed loading condition and analysed for different Span-Depth ratio (L/D). For un-symmetric loading, a simply supported beam subjected to external point moment is also analysed for different L/D ratios to check the behaviour of beam. Transverse Displacement is taken as a yardstick. Shape functions for Euler-Bernoulli and Timoshenko beam models are developed in MATLAB software by using the Finite Element Method for calculating deflection at different points on the beam. It was observed that for large L/D ratio, the deflections are same for both the beam theory models but as L/D ratio decreases, the deflections for both the beam theories vary from each other. For small L/D ratio, Timoshenko beam model gives more accurate results, since the Timoshenko beam theory is a higher order beam theory than the Euler-Bernoulli beam theory, it is known to be superior in predicting the response of the deep beam.

Experimental Study on Progressive Collapse of 3D Steel Frames under Concentrated and Uniformly Distributed Loading Conditions

AbstractStructures are expected to be robust enough to avoid widespread local failure caused by extreme loading events, so that the complete or disproportional collapse of buildings can be averted....

Design and structural analysis of different piezoelectric tile materials subjected to varied loading conditions

Piezoelectric tiles can be used to generate electricity but its sturdiness to withstand any applied load is a major concern. The material should withstand all types of loadings. Therefore, the focus of this study is to analyze the withstanding ability of the piezo tile by considering different piezo tile materials tested under different loading conditions. Two materials namely, structural steel and carbon fiber is selected as tile materials which is subjected to uniform distributed load and non-uniform distributed load conditions. Finite element method is chosen to carry out the analysis using commercial finite element code ANSYS. The static structural properties namely, total deformation, equivalent (von-misses) stress and equivalent elastic strain is compared for both these materials tested at different loading conditions. Based on the parameters, the structural steel is observed to the apt material for fabrication of piezo tile used for tapping power from footsteps.

Static and Dynamic Responses of Reinforced Concrete Structures under Sudden Column Removal Scenario Subjected to Distributed Loading

In this paper, static and dynamic experiments on reinforced concrete beam-column frames under single-column-removal scenario applying a multipoint loading method were conducted. One of the objectives was to investigate structural behavior compared with the single-point loading method, which has been popularly used in previous studies. By equally applying point loads at four locations of the double-span beam structure, the test setup successfully simulated the uniformly distributed loading condition, which is generally applicable for gravity loads in practice. Compared with the previously conducted static tests based on concentrated loading method, structural response from the static tests under multipoint loading condition differed not only on load-bearing capacity but also on failure sequence and displacement profile. On the basis of the test results, the analytical relationship between behaviors of the two loading methods was developed and verified. Compared with the static tests, the dynamic tests highlighted dynamic effects created by the column loss event and confirmed the structural behavior and failure modes observed in the static environment. The dynamic tests also verified the correctness and conservatism of the dynamic assessment framework using a previously proposed energy-based approach. Most important, both the static and the dynamic tests of structures under distributed loads showed less development of catenary action against progressive collapse compared with concentrated loading tests.

Development and Validation of Experimental Setup for Flexural Formula of Cantilever Beam Using NI-LabVIEW

Measurement of stress is a vital part of the design parameters of any component. Keeping this in mind, the flexural formula used to calculate stresses developed in a beam, has been validated experimentally, theoretically and analytically. In this paper, experimental setup for stress measurement using NI LabVIEW has been presented. The strain gauges used for measurement of deflection of a beam subjected to different point and uniformly distributed loading conditions, were interfaced with the LabVIEW software using NI 9219 Module. A simulation model was developed in ANSYS and the results obtained were compared with experimental and theoretical values. The final results were analysed and thus, the flexural formula for cantilever beam was successfully validated.

Investigations of tensile membrane action in beam-slab systems under progressive collapse subject to different loading configurations and boundary conditions

Although catenary action in beams and tensile membrane action in slabs are generally believed as high-level analyses to mitigate progressive collapse in a reinforced concrete building, previous research studies did not clearly differentiate the contributions of the two mechanisms in combined three-dimensional beam-slab systems. Besides, most of the recent experimental studies on column removal scenarios focused on point load application as it is more difficult to apply the more realistic uniform distributed loads in the laboratory. In this paper, numerical analyses were first employed to investigate the combined effects of beams and slabs under both point load (idealised) and uniform distributed load (more realistic) conditions. The results show that differences between these two loading methods not only affect overall structural capacities, but also influence vertical deflections and failure modes. It is also observed that tensile membrane action in slabs was less sensitive to boundary conditions compared to catenary action in beams. Moreover, catenary action in beams which showed limited development in beam-slab structures can be conservatively neglected. Besides, under uniform distributed loading condition, scenarios with different locations of column removal were numerically investigated, showing that the loss of a penultimate column, rather than a corner column, could be the most critical case, contrary to conventional wisdom. In fact, in a corner-column removal scenario, tensile membrane action can still be partially mobilised owing to the presence of two stiff discontinuous edge beams. This phenomenon was well observed in a beam-slab test conducted in this study.

Analysis of stress concentration in isotropic and orthotropic plates with hole under uniformly distributed loading conditions

The Behaviour of Stress Concentration Factor in rectangular and circular plates of Isotropic (Magnesium alloy) and Orthotropic material (E-glass/Epoxy) under static loading in transverse direction (UDL) has been studied. Aim of this work was to analyse the effect of D/A (From 0.1 to 0.9) and D/t ratio (From 0 to 90) upon Stress Concentration Factor (SCF) for Isotropic and Orthotropic material under given boundary conditions. To solve this problem, Finite Element Method (i.e. FEM Software) ‘ANSYS’ was used. Element length of 2mm was adopted. For design, a quarter rectangular plate and a complete circular plate were considered. Orthotropic material of rectangular plate for given boundary conditions achieved more Stress Concentration Factor than Isotropic Material. In Orthotropic Material, circular plate, Stress concentration was observed less than Rectangular Plate, whereas in Isotropic circular plate, SCF is almost similar to rectangular plate. Material properties of Orthotropic material has vital role for this behaviour when compared with Isotropic material and Geometry of the plate was also a reason to get SCF for Rectangular plate.

Explosion induced dynamic responses of blast wall on FPSO topside: Blast loading application methods

Topside areas on an offshore oil and gas platform are highly susceptible to explosion. A blast wall on these areas plays an important role in preventing explosion damage and must withstand the expected explosion loads. The uniformly distributed loading condition, predicted by Explosion Risk Analyses (ERAs), has been applied in most of the previous analysis methods. However, analysis methods related to load conditions are inaccurate because the blast overpressure around the wall tends to be of low-level in the open area and high-level in the enclosed area. The main objectives of this paper are to study the effects of applying different load applications and compare the dynamic responses of the blast wall. To do so, various kinds of blast pressures were measured by Computational Fluid Dynamics (CFD) simulations on the target area. Nonlinear finite element analyses of the blast wall under two types of identified dynamic loadings were also conducted.

Assessment of recent zig-zag theories for laminated and sandwich structures

Abstract The flexural response of laminated composite and sandwich beams/plates under static distributed loading, classical and non-classical boundary conditions (simply-supported, cantilever and propped-cantilever) and geometric/constitutive heterogeneity of layers is analysed. As structural models, a recently developed equivalent single-layer zig-zag model by the authors, a discrete-layer model and a sublaminate model developed from it in this paper are used. Their contribution is to consider the continuity of the transverse normal stress and its through-thickness gradient at layer interfaces, as prescribed by the elasticity theory in addition to kinematic and transverse shear stress interlayer continuity customary considered in the literature. To this purpose, a piecewise variation of the three displacement components is adopted. The zig-zag amplitude expressions are obtained in closed-form from the enforcement of stress continuity conditions. To be refined without affecting costs, the equivalent single-layer model has variable kinematics and just five unknowns. Instead, sublaminate and discrete-layer models are refined by increasing the number of computational layers and variables. The aim of this paper is to assess whether the equivalent single-layer model having a computational cost comparable to that of classical models can be as accurate ad discrete-layer and sublaminate models. Benchmarks are presented, for which exact elasticity and approximate solutions are available for comparisons in literature. It is illustrated the utility of considering a variable kinematics for obtaining accurate stress predictions from constitutive equations and the transverse normal deformability for keeping equilibrium. The equivalent single-layer model is shown as accurate as discrete-layer and sublaminate models in all cases examined.

An investigation on mechanical failure of hip joint using finite element method.

The aim of this work was to study how the stress distributions of the hip joint's components were changed if the activity was switched from walking to stair climbing for three different prostheses types subjected to either concentrated or distributed load. In the scope of the study, three different cemented prostheses, namely, Charnley, Muller, and Hipokrat were used for cemented total hip arthroplasty (THA) reconstruction. The finite element modeling of the hip joint with prosthesis was developed for both hip contact and muscle forces during walking and stair climbing activities. The finite element analyses were then pursued for both concentrated and distributed loading conditions applied statically on these models. Maximum von Mises stresses and strains occurred on the cortical and trabecular layers of bones; prosthesis and cement mantle were determined in order to investigate the mechanical failure of cemented THA reconstruction subjected to the different femoral loading and the activity conditions. This study showed that prosthesis, loading, and activity types had a significant effect on the stresses of components of the hip joint utilized for predicting mechanical failure of the cemented THA reconstruction.

Failure analysis for resistance spot welding in lap-shear specimens

Abstract Based on the elasticity theory and finite element method, this paper aims to explore the failure incidence of resistance spot welding in dual-phase lap-shear specimens. The stress function approach is adopted to derive an analytical solution to a lap-shear specimen containing a spot weld nugget subjected to the uniformly distributed loading condition, which provides a means to exploring the stress distributions near the spot weld nugget. The normalized effective stress obtained indicates that the initial yielding failures likely occur at four specific angles of 38.02°, 141.98°, 218.02°, and 321.98° along the spot weld nugget in the lap-shear plate. In addition, the contours of normalized stress are also plotted in the polar system to understand the surrounding stress distributions, which reveals that the locations of the maximum and minimum values of normalized radial, hoop, and shear stresses are located at angles 0°/180° and 90°/270°, 90°/270° and 0°/180°, 135°/315° and 45°/225°, respectively, as the normalized radial distance r / a goes to infinity. The elasto-plastic finite element analysis (FEA) is also conducted to analyze the initial necking or thinning phenomenon. It is found that the angular locations of the maximum equivalent plastic strain or initial necking failure points are located at four angular intervals for the advanced high strength steel (AHSS) plate with a spot weld nugget. The derived stress distributions allow predicting failure behavior and evaluating damage evolution on many engineering structures jointed with spot welds.

Behaviour of Self-Consolidating Concrete Two Way Slabs Under Uniform Loading

An experimental investigation was conducted to study the strength, behaviour and deflection characteristics of two way slabs made with both self-consolidating concrete (SCC) and conventional concrete (CC). Six concrete slabs were tested to failure under simply supported uniform by distributed loading conditions. The variables were concrete type and macro synthetic fibres ratio (0%, 0.07% and 0.14%). The performance was evaluated based on crack pattern, ultimate load, load-deflection response and failure mode. The results showed that the ultimate strength of SCC slabs was larger than that of their CC counterparts. The results also showed an improvement of the behaviour and strength of slabs by adding the synthetic fibres.

Implementation of Distributed Generation (IDG) algorithm for performance enhancement of distribution feeder under extreme load growth

This paper presents a new algorithm, written in C-language for Implementation of Distributed Generation (IDG) to radial distribution feeder, heavily overloaded with non-uniformly distributed load. Majority of the existing algorithms are designed for distribution feeders with uniformly distributed load, working in single DG scenario. The applicability of these algorithms is restricted because of the unity power factor and high computational work. The methodology proposed in the research paper is capable of functioning under randomly distributed load conditions with low power factor for single DG as well as multi-DG system. The algorithm is based on analytical approach and is implemented to radial distribution network, considering the worse case scenario. The analyses carried out show that the algorithm can be applied to enhance the performance of distribution system in terms of node voltage profile improvement and power loss reduction. The simulation results indicate that IDG is capable of identifying the optimal location and size of DG in any problematic distribution system effectively. The results obtained are verified and are within the international standards limits.