Uniform Lateral Load Research Articles

Nonlinear in-plane thermomechanical stability of shallow sandwich micro-arches including strain gradient tensors

The microstructural-dependent nonlinear in-plane stability characteristics of functionally graded (FG) sandwich shallow micro-arches subjected to a uniformly distributed lateral load in conjunction with a temperature rise are investigated in the current study. In this regard, the third-order shear flexible arch formulations are established within the framework of the modified strain gradient continuum mechanics. The considered sandwich micro-arches are made of nanocomposites reinforced with graphene nanofillers based upon various FG lamination patterns. The Chebyshev–Gauss–Lobatto type of gridding scheme together with the pseudo arc-length continuation technique are employed to employ a numerical solution strategy for tracing the size-dependent lateral load–deflection and lateral load–axial load nonlinear stability plots. It is observed that by adding a rise in the temperature to the applied uniform lateral load, the first bifurcation lateral load enhances, while the second one reduces. Also, it is dedicated that there is a unique value of the applied uniform lateral load corresponding to which the axial resultant load as well as the induced lateral deflection in the micro-arch are the same for all values of the temperature rise. Moreover, it is revealed that by increasing the value of the rise in the temperature, the size dependency in the value of the upper limit lateral load becomes less prominent, while it enhances in the value of the lower limit lateral load.

DETERMINING THE OPTIMUM LOCATION OF TWO-FLEXIBLE OUTRIGGER SYSTEMS IN TALL BUILDINGS USING ENERGY METHOD

Construction of tall buildings has been rapidly increasing worldwide, introducing new challenges that demand rigorous engineering. Structural and nonstructural damage to tall buildings can be minimized by implementing appropriate lateral resisting systems, such as the outrigger and belt-truss system. The location of outrigger and belt-truss systems plays a critical role in the behavior, structural integrity, safety, and overall construction cost of tall buildings subjected to lateral loads; thus, they should be selected carefully. This research develops a framework that can determine the optimum location of two flexible outrigger and belt-truss systems in skyscrapers subjected to uniform lateral loading. To achieve this goal, an energy method is applied to maximize the outrigger and belt-truss system’s strain energy. In this approach, the framed tube and effect of outrigger and belt-truss systems on shear core are modeled as a cantilevered hollow section beam with orthotropic plates and rotational springs placed at outrigger and belt-truss location respectively. The optimal location is determined where the rotational spring absorbs the most amount of energy; and this is accomplished by setting the first derivative of the energy equation with respect to the spring’s location, as measured from the structure’s base, to zero. The practical graph developed in this research can aid engineers during the preliminary design of tall buildings for quick calculation of the optimum locations of outrigger and belt-truss systems.

Thermo-Electro-Mechanical Analysis of Micropolar FGP Cylindrical Shell Covered with Piezoelectric Actuator Layers

An investigation is performed in this paper to analyze the nonlinear thermo-electro-mechanical response of long sandwich cylindrical shells with functionally graded porous (FGP) core and thin piezoelectric actuator layers. The FGP core of the sandwich shell is assumed to be temperature- and microstructure-dependent. It is assumed that the sandwich shell is subjected to uniform lateral pressure loading in a thermo-electrical environment. The equilibrium equations of the shell with infinite length are established with the aid of the virtual displacement principle and von Kármán kinematic assumptions. The governing equations are obtained in terms of displacement components based on the first-order shear deformation model of shallow cylindrical shells and the modified couple stress theory. These nonlinear differential equations are analytically solved for a sandwich shell having both the simply-supported and clamped–clamped edge conditions by employing a two-step perturbation technique. Analytical closed-form solutions are determined as a relationship including the load parameter and the mid-span deflection. The comparison examples are made with the existing results in the literature for a simple functionally graded shell, where good agreement is obtained. It is shown that the nonlinear response of the sandwich shell is highly dependent upon the temperature variation, power law index, porosity coefficient, couple stress parameter, piezoelectric layers, and geometrical parameters of the shell.

Effects of Fixed Edge Conditions on the Load Resistance of Single Glass Lites

The load resistance (LR) of glass lites is determined in the United States by use of standards based on a probabilistic model of glass breakage. These standards generally restrict design to rectangular glass lites continuously supported along one, two, three, or four sides. In addition, these standards treat single glass lites as simply supported flat rectangular plates. Historically, rigid window frames supported single glass lites holding them in place with neoprene or similar gasket material. This attachment method approximated simply supported edges that rotate about an axis parallel to the simply supported edges, deform in the plane of the glass lite, and do not deflect out-of-plane. Advances in structural silicone make it possible to produce rectangular single flat glass lites with edge fixity somewhere between that of simply supported edges and fully fixed edges. The authors applied the glass failure prediction model (GFPM) to a nonlinear finite-element model developed previously by the authors to determine the probability of breakage for selected single glass lite geometries with fully fixed edges under uniform lateral loads. The paper presents comparisons between results of analyses of lites with fixed edges with analyses of lites with simply supported edges. The comparisons indicate that not all single glass lite geometries benefit from fully fixing edges, but the benefits of doing so appear to increase as lite aspect ratio (AR) increases. The comparisons bracket benefits that can accrue from the partial fixity provided by structural silicone supports. The actual degree of fixity provided by structural silicone can only be determined experimentally, which lies outside the scope of this paper.

Comparisons of Performance of Building Using Bright New And Old Rusted Rebar

Reinforced cement concrete structure are the most common structures in India. The strength of structure depends mainly on two components i.e. concrete and steel rebar. One of the main constituent i.e. steel, changes its strength along with the changes in property of steel rebar irrespective of the types of steel, mainly due to rusting of iron i.e. formation of iron oxide by the reaction of iron and oxygen in the presence of water or air moisture. In the present study, experimental investigation has been done as to find the property of steel for the bright new rebar as well as for the old rusted rebar of a particular brand of steel rebar. The experimental result showed that the new bright rebar has ~ 50% higher yielding strength as compared to the old rusted rebar strength. The ductility of new bright rebar is having ~125% higher than the old rusted rebar. The material property of steel extracted from the experiment has been incorporated in Finite Element modelling of a particular building using SAP 2000. The building has been designed under the gravity load as well as uniform lateral load. The performance of building is found out through push over analysis in terms of load vs displacement. The ultimate strength of building using new rebar is around 60% higher than the strength of building with old rebar. The displacement capacity of building also differs significantly i.e. building with new rebar is having ~60% higher than building with old rebar’s. Overall, the steel rebars need to be protected from corrosion for the construction of structures.

Calculations of additional axial force and coupling ratio for coupled shear walls

The additional axial forces (AAFs) in walls and coupling ratio (CR) of coupled shear wall (CSW) systems have significant effects on the local behaviors of the individual walls and the overall structural performance, respectively. A new analytical approach to obtaining AAF and CR for three different types of lateral loads has been proposed to avoid complex numerical simulations or time-consuming analyses. Firstly, a differential equation with respect to AAF was established using a concise expression of the external moment; AAF calculation method considering triangular, uniform, and top concentrated lateral loads was developed. Secondly, CR calculation formulas for three different types of lateral loads were derived based on the formulas of AAF and applied to simplify the formulas of calculating top lateral deflection of CSWs. Thirdly, the calculation method of AAF, CR and the simplified formulas of top lateral deflection were validated by conducting numerical simulations using ABAQUS and OpenSees. Finally, the advantages of the proposed methods as well as the impact of lateral load types and nonlinearities, etc. were discussed. It was found that AAF and CR could be efficiently calculated by the proposed approach for CSWs including asymmetric ones subjected to three typical lateral loads, and the relative errors compared with numerical simulation are less than 10%. Besides, different types of lateral loads affect the distributions of AAFs and the values of CR.

Computational Study of Non-Porous Auxetic Plates with Diamond Shape Inclusions

Creating non-porous structures that offer auxetic behavior can have a variety of industrial applications, especially when the porosity impairs the functionality of the auxetic structures. This study presents the design and finite element analysis of architected bi-material auxetic plates consisting of repeating unit cells that comprise rigid rotary units and soft inclusions. The change in the design parameters of unit cells produces a variety of mechanical properties, such as different levels of Poisson’s ratio and stiffness for the architected plates that can result in specific static or dynamic responses. The natural frequencies and deflection under uniform lateral loading of the architected plates with clamped boundary conditions were investigated. Furthermore, the effectiveness of the homogenization technique based on the mechanical properties obtained from finite element analysis in predicting the dynamic and static response of the architected plate was also studied.

Evaluation of Mechanical Characteristics of High-Strength Reinforced Concrete Columns with Hexagonal Chicken Wire Mesh Under Cyclic Loading

Recently, new materials and methods have been implemented to improve the performance of reinforced concrete columns. This paper studies experimentally the behavior of reinforced high-strength columns, with additional internal confinement using hexagonal chicken wire mesh (HCWM) to enhance ductility, energy absorption, and ultimate strength and reduce the brittleness of traditional columns. Eight double-ended one-third-scale columns with different volumetric ratios of transverse rebar have been constructed and loaded under the uniform axial compression and lateral cyclic loads. Different volumetric ratios of transverse rebar were provided based on special, intermediate, and ordinary moment frames specifications of ACI 318–14 (named SD, ID, and OD, respectively). The specimens were confined by transverse rebars and HCWM and the results were compared with reference specimens with traditional transverse ties. Experimental findings demonstrated that HCWM specimens exhibited better performance compared to their control specimens concerning crack control efficiency, load capacity, ductility, energy dissipation, and failure modes. Implementation of HCWM increased the ultimate deformation, ductility, and energy absorption of OD specimens up to 21%, 50%, and 175%, respectively, compared to their control specimen. Confinement of the concrete columns by HCWM increased the ultimate strength of OD and ID specimens up to 15% and 22% under the cyclic load, but has a negligible effect on SD columns due to enough ratio of transverse and longitudinal rebars in SD specimens. As a result, confinement of specimens by HCWM could be regarded as a simple and effective method to improve the seismic characteristics of RC columns, particularly those members constructed with a minimal number of transverse rebars.

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

Material R-factors of buildings with irregularity

R-factor (Response reduction factor) is an important design consideration in seismic design of structures, which is assumed to consider energy dissipation of structures by means of ductility. So, proper estimation of R-factor is required for seismic design of structures which will account for ductile deformation so that suitable detailing of reinforcement can be done. In case of irregular structures, where the torsion effect is the predominant factor, accurate estimation of R-factor is even more difficult. Therefore, in the present study, an attempt has been taken to determine R-factor for plan irregular buildings. A G +7 storied building is considered and irregularity effect has been incorporated by C and L-shaped configuration. The design of the buildings has been done following Indian Standards. Modeling and analysis have been done using SAP2000. Plastic hinges have been considered to represent material nonlinearity. Mander’s confinement model has been considered. Nonlinear Static (Pushover) following FEMA 440 methods with uniform lateral load variations has been done. Initial tangent stiffness has been followed in equal area method during bi-linearization of pushover curve. It can be stated that apart from material strength and geometrical configuration, performance requirement of the buildings is the most important factor for selection of R-factor.

Comparison of seismic and gravity progressive collapse in dual systems with special steel moment-resisting frames and braces

Progressive collapse studies generally assess the performance of the structure under gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the nonlinear static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

Laboratory and numerical investigations of the effect of geometric parameters on the buckling capacity of thin-walled composite cylindrical shells under external pressure loading.

Buckling is one of the important issues in determining the mechanical behavior of cylindrical shells, especially composite shells. What makes the buckling matter important in composite cylindrical shells is the complexity of the behavior of these structures under the influence of a variety of special loads such as buckling under external pressure load. Uniform lateral loading in tanks occurs when tanks are in the state of liquid discharge. Moreover, if special contrivances such as the drainage valves do not work or properly, then buckling phenomenon and will cause an overall failure in the tank. In this research, the air suction system is used in order to apply external pressure and study the buckling behavior of specimens. As the buckling occurs, tiny cracks are created with a mild sound in the shell wall and in the extreme stage the loading process stops when it collapses. In this paper, the effect of geometric parameters, such as the R/t and L/R of a composite tank under external pressure, on buckling behavior is investigated. Obtained results are compared with software and theoretical results. The results showed in specimen of the same length, by increasing the geometric parameter R / t, the buckling capacity of the shells decreases and the number of buckling modes increases and by increasing the geometric parameter L / R, the buckling capacity of the shells increases and the number of buckling modes decreases.

Large Deflection Analysis of Axially Symmetric Deformation of Prestressed Circular Membranes under Uniform Lateral Loads

In this study, the problem of axisymmetric deformation of peripherally fixed and uniformly laterally loaded circular membranes with arbitrary initial stress is solved analytically. This problem could be called the generalized Föppl–Hencky membrane problem as the case where the initial stress in the membrane is equal to zero is the well-known Föppl–Hencky membrane problem. The problem can be mathematically modeled only in terms of radial coordinate owing to its axial symmetry, and in the present work, it is reformulated by considering an arbitrary initial stress (tensile, compressive, or zero) and by simultaneously improving the out-of-plane equilibrium equation and geometric equation, while the formulation was previously considered to fail to improve the geometric equation. The power-series method is used to solve the reformulated boundary value problem, and a new and more refined analytic solution of the problem is presented. This solution is actually observed to be able to regress into the well-known Hencky solution of zero initial stress, allowing the considered initial stress to be zero. Moreover, the numerical example conducted shows that the obtained power-series solutions for stress and deflection converge very well, and have higher computational accuracy in comparison with the existing solutions.

Research on mechanical behavior of three-layer toughened sandwich glass with trilateral simple support

This paper presents the results of an experimental investigation on the mechanical behavior of three-layer toughened sandwich glass with trilateral simple support under uniform lateral loads. A total of sixty-four specimens with different test parameters are designed and tested to consider the effects of the thickness of single layer, supporting width and loading length. It was observed that the specimens failed with all pieces of cracks combined together as an entire unit rather than to separate into a large number of glass fragments. The cracks occurred only at the lower layer of toughened sandwich glass and extended in a way similar to the spider web. The ultimate bending strength and bending rigidity of the toughened sandwich glass are enhanced as the thickness of single layer, the supporting width, and the loading length increase. Among the above parameters, the thickness of single layer plays a leading role in improving the ultimate bending strength and bending rigidity of toughened sandwich glass. However, the enhancement effect of supporting width on the ultimate bending strength and bending rigidity of toughened sandwich glass is quite limited. Based on elastic thin plate theory, the derived mechanical formulae were presented to evaluate the ultimate bending strength of three-layer toughened sandwich glass with trilateral simple support under uniform lateral load, which was verified to be reasonable and accurate.

Nonlinear thermal stability and snap-through buckling of temperature-dependent geometrically imperfect graded nanobeams on nonlinear elastic foundation

In this research, thermal postbuckling and nonlinear thermal bending of size-dependent functionally graded (FG) perfect/imperfect nanobeams in-contact with a nonlinear elastic foundation and exposed to thermal loading are first scrutinized. The second objective of this research is to investigate snap-through instability in a thermally postbuckled FG nanobeam due to uniform lateral load. The geometrical imperfection of the nanobeam is taken into account. Thermo-mechanical material properties are temperature-dependent and are assumed to vary continuously throughout the nanobeam thickness on the basis of the power-law model. The nonlinear equilibrium equations are derived according to the Euler-Bernoulli beam theory in conjunction with the nonlinear von-Karman assumptions based on the nonlocal elasticity theory. Using Chebyshev polynomial of the first kind, Ritz method is utilized into the principle of virtual displacement to form nonlocal governing equations. Three different methodologies, including direct displacement control approach, Newton-Raphson iterative method, and cylindrical arch-length scheme are utilized to investigate the nonlinear thermal stability curves and snap-through phenomenon through limit points of a thermally postbuckled FG nanobeam. The primary purpose of this research is to explore the influences of the nonlocal parameter, nonlinear elastic foundation coefficients, power-law index, imperfection amplitude as well as the different types of boundary conditions on the nonlinear thermal stability and snap-through phenomenon of the FG nanobeam.

Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads

The present investigation deals with the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads. The structure is resting on a three-parameter elastic foundation containing the Winkler springs, the shear Pasternak layer, and hardening nonlinear springs. The arch is made of a through-the-thickness functionally graded material. Except for Poisson’s ratio, the other properties of the arch are assumed to be temperature and position dependent. Each property is estimated according to the rule of mixtures in terms of the volume fraction of the constituents. The case of uniform temperature rise and uniform radial lateral load is considered. The governing equations of the arch are obtained with the aid of the third-order shear deformation arch theory and the von Karman type of geometrical nonlinearity. The developed coupled and nonlinear equilibrium equations are solved using the two-step perturbation technique for the case of simply supported arches. Closed-form expressions are developed for nonlinear bending equilibrium path of shallow arches under thermal and mechanical loads. Results are provided for different power law indices, geometrical parameters, and the foundation stiffness.

A semi-analytical investigation on geometric nonlinear and progressive damage behavior of relatively thick laminated plates under lateral pressure and end-shortening

Because of applications of composites in aircraft structures such as skin panels in the wings subjected to lift forces, ultimate strength estimation of these structures is of great importance. In order to more realistically simulate these structures, relatively thick composite plates are analyzed under both end-shortening and lateral pressure loadings using a new simplified and reliable approach. Ultimate strength, progressive damage and geometric nonlinear analyses of such laminates under these loading conditions have not been done yet. Therefore, in the present study, first order shear deformation plate theory is considered with the assumptions of large deflections to perform the geometrically nonlinear and progressive failure analysis of moderately thick composite plates. In order to simulate the lift loads, two different types of lateral pressure distribution have been assumed to be applied on the plates; uniform and sinusoidal lateral pressure loads. The initial failure loads are calculated by means of elastic stress analyses. In this investigation, Hashin failure criteria have been selected for predicting failures. To modify the material properties, two geometric models have been considered to estimate the degradation zone around the failure location; degrading the material in regions of the plies or degrading the entire plies. The load is then increased step by step and for each given load, the stresses are reevaluated to inspect for possible failure. This procedure is repeated for each load increment until the final failure occurs and then ultimate strength is determined. To verify the proposed formulation, obtained results are compared with those calculated by finite element analyses. Plates having a range of thicknesses and with different intensities of pressure load have been analyzed extensively.

Resilience: Theory and metrics – A metal structure as demonstrator

The paper develops a theoretical model and metrics for structural resilience. It addresses the general case of physical systems after they suffer damages due to natural or industrial hazards. They may suffer serious physical damages and may generate also social and economic losses. Depending on the interaction between the sub-systems and individual components, it may be possible for the system to absorb the damage, remain on service and recover. The method addresses the utility functions (resistance), damaging sequences, residual state, post-event capacity, recovery functions and resilience metrics and indicators. It becomes then possible to identify whether a structure is “objectively” resilient or not, under a given set of conditions. A simple metal structure relying on a full support is adopted as demonstrator. The resilience indicator expresses the residual capacity under bending effects of the system, when subject to uniform lateral load and initial damage of the critical cross section (at beam support). Due to plasticity, it is shown that the system can recover and be resilient as long as the damage does not exceed 18.4% of the cross critical section. Subdomains for resilience are also easy to identify in the [hazard, vulnerability, damage] operating space for the case study.

Full scale tests of heat strengthened glass with ceramic frit

The authors tested five full scale samples of nominal 6 mm thick heat strengthened glass to failure under uniform lateral loading. One sample was clear glass, one sample had full coverage ceramic enamel frit, and the other three samples had ceramic enamel frit patterns with different percentages of coverage. In testing the samples with ceramic enamel frit applications, researchers oriented the specimens to place the ceramic enamel frit in tension under lateral loading. The authors found that the samples with ceramic enamel frit displayed considerably lower magnitudes of load resistance than did the clear heat strengthened sample. In addition, the authors noted that every fracture origin they have inspected to date from the 75 specimens with ceramic enamel frit patterns occurred underneath frit. Micrographs of fracture origins indicate that the frit may actually damage the glass surface during the heat strengthening process. This study has significant implications for architectural glass design.

Nonlinear response of nanotube-reinforced composite cylindrical panels subjected to combined loadings and resting on elastic foundations

This paper presents an investigation on the nonlinear behaviors of nanocomposite cylindrical panels subjected to the combined action of uniform lateral pressure and compressive edge loads. The panels may rest on elastic foundations and be in a varying temperature environment. The nanocomposite consists of reinforcing carbon nanotubes either uniformly distributed (UD) or functionally graded (FG) along the thickness direction of the panels. The two cases of nonlinear bending of initially compressed cylindrical panels and postbuckling of initially pressurized cylindrical panels are considered. A high-order shear deformation shell theory in association with von Kármán nonlinear strain–displacement relationships is applied to derive the governing equations for the carbon nanotube reinforced composite (CNTRC) panels. Furthermore, the effects of the panel-foundation interaction and the temperature variation are also included in the analysis and the material properties of CNTRC panels are assumed to be temperature-dependent. Numerical results are presented to illustrate the nonlinear bending responses and the postbuckling behaviors of CNTRC cylindrical panels resting on the Pasternak-type elastic foundations. The present solutions also highlight the effects of the CNT volume fraction, temperature rise, foundation stiffness as well as initial stress on the nonlinear behaviors of CNTRC cylindrical panels.