Central Concentrated Load Research Articles

Behaviour of reinforced concrete two-way slabs using steel bars milled from scrap metals

This paper investigated two-way concrete slabs reinforced with steel bars milled from scrap metals. The slabs were simply supported on all four sides and tested under a central concentrated load. The average experimental failure loads for monotonic and cyclic loading were 32.8 kN and 26.7 kN, respectively. In addition, the experimental failure loads averaged 127% and 98% of the theoretical punching shear strength of the two-way reinforced concrete section under monotonic and cyclic loads, respectively. Collapse of the slabs always occurred through a combination of the crushing of the concrete after flexural cracks propagated extensively, and punching shear. Finally, a recommendation based on the analysis of the results for the design of two-way slabs using steel bars milled from scrap metals is proposed.

Lateral–distortional buckling of I-beams and the extrapolation techniques

Various extrapolation techniques are utilized for predicting the critical buckling load of structural members undergoing lateral buckling. For the application of these methods it is only necessary to have data relating load to a deformation characteristic. In order to obtain an experimental comparison of the Southwell, Modified, and Massey Plot methods, these have been applied on lateral deflections and web transverse strains of four full-scale simply supported I-beams subjected to a central concentrated load with an effective lateral brace at the midspan of the top flange, undergoing inelastic lateral–distortional buckling. Although there is some scatter due to the application of various deformation variables and extrapolation techniques, the agreement between the extrapolated and the maximum test loads is generally good. The smallest discrepancy is found in the case of the Modified Plot. Moreover, in addition to demonstrating direct coupling between the lateral deflections and the web transverse strains representing web distortion, it is also shown that good predictions are provided by applying the Meck Plot on these deformation variables.

Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load

This paper investigates the non-linear in-plane buckling of pin-ended shallow circular arches with elastic end rotational restraints under a central concentrated load. A virtual work method is used to establish both the non-linear equilibrium equations and the buckling equilibrium equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling loads are obtained. It is found that the effects of the stiffness of the end rotational restraints on the buckling loads, and on the buckling and postbuckling behaviour of arches, are significant. The buckling loads increase with an increase of the stiffness of the rotational restraints. The values of the arch slenderness that delineate its snap-through and bifurcation buckling modes, and that define the conditions of buckling and of no buckling for the arch, increase with an increase of the stiffness of the rotational end restraints.

Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells

Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.

Babadua reinforced concrete two-way slabs subjected to concentrated loading

This work investigated the flexural strength and deformation of 14 two-way concrete slabs that were reinforced in two directions with babadua (botanical: thalia geniculata) bars. The slabs were simply supported on all four sides and tested under a central concentrated load. Ten of the specimens were tested monotonically while the remaining four were subjected to cyclic loading prior to failure. The span-to-effective depth ratios of the slabs ranged from 13.2 to 26.2. Cracking loads of the reinforced concrete slabs averaged 42% of the failure loads predicted for the un-reinforced concrete sections. Experimental failure loads were found to average approximately 170% of the theoretically predicted values. Also the experimental failure loads averaged 148% and 198% of the theoretical punching shear strength of the un-reinforced concrete section under monotonic and cyclic loads, respectively. The slabs exhibited high stiffness against deformation prior to collapse through crushing of concrete.

Analysis of clamped unsymmetric cross-ply rectangular plates by superposition of simple exact double Fourier series solutions

Based on the idea developed in an earlier work on orthotropic rectangular plates [Compos. Struct. 63 (2004) 63], it is shown here that exact double Fourier series solutions can be easily obtained for simply supported rectangular unsymmetrically laminated cross-ply plates subjected to various edge forces and moments, and that these can be superposed to yield a simple solution for the title problem considered difficult hitherto. Numerical results, based on the summation of the infinite series without truncation using MATLAB, are presented for a set of symmetric and antisymmetric cross-ply laminates under uniform and central concentrated loads.

Steel Member Strength by Inelastic Lateral Buckling

This paper develops a simple advanced method of designing steel members against out-of-plane failure, in which reduced elastic moduli are used in an out-of-plane buckling analysis to model the effects of high moment, residual stresses and geometrical imperfections on yielding. The reduced moduli are derived from the basic beam and column strength curves of the Australian steel code AS4100 in 1998. The strengths predicted for simply supported beams in uniform bending are exactly the same as those of AS4100, while those for simply supported columns are extremely close. The strengths predicted for simply supported beam-columns with equal and opposite end moments are a little higher than the less conservative predictions of AS4100, and are very close to the basic beam and column strengths when these are plotted against a consistent generalized slenderness. The strengths predicted for simply supported beams under double curvature bending are somewhat less than those of the AS4100 method of design by buckling analysis, while those for beams with central concentrated loads acting at or away from the centroid are very close, and those for end restrained beams under uniform bending and for sway columns are generally a little higher. While the method has been developed from and compared with the Australian code AS4100, it may be modified for any other modern code for the design of steel structures. It may be more widely applied to two-dimensional frames with in-plane loading, as part of a simple method of advanced analysis in which separate assessments are made of the in-plane and out-of plane strengths.

Elasto-plastic buckling and postbuckling of arches subjected to a central load

This paper presented a rational finite curved beam-element model for 3D nonlinear elasto-plastic analysis of arches. The finite element model incorporates the effects of large twist rotations of the cross-section and has consistent sampling scheme of sampling points over the cross-section and so it can perform the elastic and elasto-plastic flexural–torsional buckling and postbuckling analysis of arches in combined bending and compression actions. Elastic and elasto-plastic flexural–torsional buckling and postbuckling behaviour of arches that are subjected to a central concentrated load has been investigated using the rational finite element model. It has been found that the slenderness, included angle, and the torsional parameter of an arch play important roles in the elastic and elasto-plastic buckling. In addition, the number of the inflexion points is important for the elastic and elasto-plastic buckling of fixed arch. Yielding is a significant factor for the elasto-plastic buckling and postbuckling behaviour. When the included angle of a stocky arch is not large, its elasto-plastic buckling load is much lower than its elastic buckling load. When the included angle a stocky arch is large, the end support condition plays an important role in the buckling and postbuckling behaviour of the arch. The elasto-plastic buckling load of a stocky pin-ended arch with a large included angle is equal to its elastic counterpart. The elasto-plastic buckling load of a stocky fixed arches with a large included angle is lower than its elastic counterpart. For a slender arch, its elasto-plastic buckling load is also equal to its elastic buckling load. In general, the elasto-plastic postbuckling load carrying capacity of an arch decreases when the arch continues to deform while its elastic postbuckling load carrying capacity can increase. For slender shallow arches, the elastic postbuckling response is stiffer because of the relaxation of axial load and moment distribution.

The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load

The response of an elastic beam on a two-dimensional tensionless Pasternak foundation that is subjected to a central concentrated harmonic load is investigated. The tensionless character of the foundation results in the creation of lift-off regions between the beam and the foundation. Since the contact regions are not known in advance, the problem appears as a nonlinear one, and the calculation of the roots of a nonlinear equation is needed to obtain contact lengths of the beam. The governing equations obtained for the contact and lift-off regions are solved by using the trigonometric-hyperbolic functions. Several numerical examples are provided to show the effects of the foundation stiffness parameters and the frequency parameter on the lift-off regions and the vertical displacements of the beam. It is concluded that more than one contact length may arise in the solution for a fixed frequency parameter, and this parameter may cause to interchange the contact and lift-off regions.

In-Plane Elastic Stability of Arches under a Central Concentrated Load

This paper is concerned with the in-plane elastic stability of arches with a symmetric cross section and subjected to a central concentrated load. The classical methods of predicting elastic buckling loads consider bifurcation from a prebuckling equilibrium path to an orthogonal buckling path. The prebuckling equilibrium path of an arch involves both axial and transverse deformations and so the arch is subjected to both axial compression and bending in the prebuckling stage. In addition, the prebuckling behavior of an arch may become nonlinear. The bending and nonlinearity are not considered in prebuckling analysis of classical methods. A virtual work formulation is used to establish both the nonlinear equilibrium conditions and the buckling equilibrium equations for shallow arches. Analytical solutions for antisymmetric bifurcation buckling and symmetric snap-through buckling loads of shallow arches subjected to this loading regime are obtained. Approximations for the symmetric buckling load of shallow arches and nonshallow fixed arches and for the antisymmetric buckling load of nonshallow pin-ended arches, and criteria that delineate shallow and nonshallow arches are proposed. Comparisons with finite element results demonstrate that the solutions and approximations are accurate. It is found that the existence of antisymmetric bifurcation buckling loads is not a sufficient condition for antisymmetric bifurcation buckling to take place.

Punching Shear Strength of Simply Supported Ferrocement Slabs

The results of punching shear tests on 31 square ferrocement slabs are reported in this paper. The slabs were simply supported on all four sides and tested under a central concentrated load. The parameters investigated include the width of square loaded area w, mortar strength f′c, volume fraction of reinforcement Vf, depth of slab h, and the effective span l. All slabs failed first in punching without total separation, and then exhibited a second peak in the load-deflection history. Both cracking load and punching shear load increased with an increase in w, Vf, f′c, or h, but decreased as l is increased. The critical perimeter for punching shear failure was found to be located at a distance of 1.5h from the edge of the loading plate. Based on the present test data as well as those available in the literature, an equation has been proposed for predicting the punching shear strength of ferrocement.

Nonlinear response of laminated cylindrical panels

The geometric nonlinear responses of laminated composite cylindrical panels subjected to (i) axial compression and (ii) central concentrated load are investigated in this work. The parameters considered are: number of layers, symmetric/antisymmetric laminate constructions, cross-ply/angle-ply fibre orientation, boundary conditions and central angle of panel. An eight-node degenerated layered shell element with an efficient explicit through-thickness integration scheme is employed. It has been observed that the cylindrical panels under axial compression exhibit stable post-buckling paths and the number of layers in the laminate for a given total thickness has considerable influence on the load–deflection behaviour. The strength of shallow panels with longitudinal edges hinged, curved edges free and subjected to a central concentrated load is controlled by the limit point load, whereas for deep panels with other parameters remaining the same, the strength is controlled by the bifurcation load. The boundary conditions have significant influence on the load-carrying capacity. The panels with longitudinal edges hinged and curved edges free should be avoided in construction, as they undergo either limit point or bifurcation failure at very low load levels compared with other edge conditions.

Behavior of Two-Way RC Slabs Externally Bonded with Steel Plate

Although a great deal of research has been carried out in recent years on the use of plate bonding for strengthening reinforced concrete (RC) structures, so far this work has generally been limited to RC beams and one-way slabs, with little work on two-way slabs. This paper presents the results of a recent study on the behavior and strength of two-way square RC slabs bonded with a steel plate. Experimental load-deflection curves, failure modes, and strengths of plated slabs under a central concentrated load are first reported. These results show that debonding failures are unlikely in these plated slabs, contrary to the case of plated beams, and there are significant strength gains due to the bonded steel plate as a result of a modified yield line pattern. Yield line analyses are then described for these slabs, and the results are found to match experimental results closely. The yield line method is thus suitable for practical use to determine the strength of these plated slabs.

Fracture Behaviour of FRP Composite Laminates with an Embedded Elliptical Delamination at the Interface

This study deals with the delamination initiation from an existing embed ded elliptical delamination at the interface of FRP composite laminates. A full 3D FE anal ysis has been performed to calculate the interlaminar stresses at the interface responsible for delamination. Concept of fracture mechanics has been used to calculate the components of strain energy release rates at the interface. An elliptical delamination has been simulated to be present at the interface of two sublaminates each consisting of several plies and the laminate has been subjected to a central concentrated transverse loading. Effects of impor tant factors like fiber orientation of the adjacent layers, laminate thickness and the aspect ratio of the elliptical delamination on strain energy release rate components have been stud ied. It has been observed that the strain energy release rates vary along the delamination front showing an anisotropic delamination. The magnitudes of strain energy release rate components depend upon the fiber orientation of the adjacent layers, laminate thickness and the aspect ratio of the delamination present at the interface.

Experimental investigation of the role of reinforcement in the strength of concrete deck slabs

To study systematically the role of each layer of steel reinforcement in conventionally reinforced deck slabs of girder bridges, a full-scale model was built of a 175 mm thick concrete deck slab on two steel girders with a center-to-center spacing of 2.0 m. The 12 m long deck slab was conceptually divided into four 3 m long segments, identified as segments A, B, C, and D. Segment A contained isotropic steel reinforcement in two layers, conforming to the requirements of the Ontario Highway Bridge Design Code (OHBDC). Segment B contained only the bottom layer of steel reinforcement. Segment C contained only the bottom transverse steel bars. Segment D contained only bottom transverse glass fibre reinforced polymer (GFRP) bars having the same axial stiffness, but 8.6 times the axial tensile strength, as those of the steel bars in segment C. Each segment of the deck slab was tested to failure under a central concentrated load, simulating the dual tire footprint of 250 × 500 mm dimension of a typical commercial vehicle. All segments failed in the punching shear mode. The failure loads for the four segments were found to be 808, 792, 882, and 756 kN, respectively; these failure loads are similar in magnitude to that of a 175 mm thick steel-free deck slab with steel straps having nearly the same cross-sectional area per metre length of the slab as those of the bottom transverse steel bars in the first three segments. The tests on the four segments of the full-scale model have confirmed that (i) only the bottom transverse reinforcement influences the load carrying capacity of a reinforced concrete deck slab and (ii) the stiffness of the bottom transverse reinforcement, rather than its strength, is of paramount importance.Key words: arching, deck slab, FRP, shake down, slab-on-girder bridge.

Axisymmetric shells and plates on tensionless elastic foundations

This paper first describes a finite element method for the large deflection analysis of axisymmetric shells and plates on a nonlinear tensionless elastic foundation. Through the use of discrete data points, any form of nonlinear elastic foundation behaviour can be easily modelled. The analysis is then validated by comparison with existing results for circular plates and beams as the only existing results for shells on tensionless foundations are found to be in error. Following this verification, the analysis is applied to investigate the behaviour of shallow spherical shells subject to a central concentrated load on tensionless linear elastic foundations. A number of insightful conclusions regarding the behaviour of such structure-foundation systems are drawn. The numerical results for shells are believed to be the first correct results, which may be useful in benchmarking results from other sources in the future.

Local buckling of thin-walled fibre composite beams under transverse loading

Plate structures are often subjected to differential compression due to nonuniform bending during their service life. In practice, most beams are subjected to transverse loads that create moment gradient; the resulting loading system for such beams is a combination of longitudinal stress gradient with associated shearing and transverse stresses. This paper presents a theoretical view of elastic local instability of anisotropic composite beams which are treated as assemblies of symmetric angle-ply composite plates buckling under nonlinear varying, uniaxial compressive forces. Uniformly distributed load and central concentrated load are two common loading systems acting on simply supported, wide-flange I-section beams. The Galerkin method is applied to the resulting plate equilibrium equations. The present study shows that the buckling load obtained from the proposed approach for composite flanges is greater than that obtained by existing solutions. Results also show that for beams subjected to the uniformly distributed load loading system, local buckling may be initiated in the web, especially for short-span deep beams. However, under the central concentrated load loading system, the compressive flange limits buckling strength.Key words: local buckling, stress gradient, fibre composite, pultruded beam.

Creep behaviour of commercial wood based boards under long-term loading at room conditions in Taiwan

The purpose of this study was to investigate the creep behaviour of commercial wood based boards (sanded and laminated) under long-term loading at room conditions in Taiwan. Ten types of commercial wood based boards were used to test their physical and mechanical properties in this study. Four types of these boards were used for the same test after laminating with red oak (Quercus spp.) veneer or balanced paper. The bending creep was measured at room conditions with central concentrated loading. The values for creep deflection of commercial wood based boards 18 mm thick decreased from 1.06–1.19 mm ti 1.00–1.12 mm after laminating veneer or balanced paper. The relative creep (120 days) of those specimens decreased from 1.71–3.17 to 1.43–2.04 after laminating with veneer or balanced paper in four months’ loading. The creep deflections of specimens increased with increasing loading time. The linear regression function ist/y=a+bt, wheret is time,y is deflection. When theb value is larger, the boards displayed good creep resistance. The residual bending strength of wood based boards after creep test would be retained at about 80–95%, and the residual bending strength between particleboard proved more significant than between fiberboard.

Instability of cylindrical panels under combined static and dynamic loads

This paper presents a numerical study of the dynamic snap-through instability of cylindrical panels subjected to the combined loading of uniform pressure and a central concentrated load. All static and dynamic (sudden step load) combinations of the concentrated load and the uniform pressure are considered. The characteristics of the dynamic instability of the panel are described for the two cases of static pressure with dynamic concentrated load and dynamic pressure with static concentrated load. The critical load curves for both cases are presented. To explain the effects of the initial static loads on the critical dynamic loads, the static and dynamic critical loads corresponding to both static loads or both dynamic loads are also calculated. The Budiansky-Roth criterion is employed in all these studies to determine the critical dynamic loads. The numerical results show that the static critical load curve gives an upper-bound whereas the dynamic critical load curve offers a lower-bound. Both the compound critical load curves lie between the static and dynamic critical load curves.

A flexible rectangular footing on aGibson soil: Required rigidity for full contact

The problem of a rectangular footing or a strip footing resting on a nonhomogeneous elastic half-space is studied in this paper. The medium is assumed to be isotropic with a shear modulus linearly increasing with depth G (z) = G 0+ mz and a constant Poisson's ratio equal to 1/3. An important feature of this model is that either the Winkler foundation or the elastic homogeneous half-space can be made special cases by letting G 0 or m equal zero, respectively some results are presented for these cases. In order to investigate the necessary conditions for a footing to be considered rigid, both rigid and flexible footings have been studied. Central concentrated (column) loading, in addition to the self-weight, is treated-being the most demanding in terms of the zero uplift requirement (under conditions of symmetry in the loading with respect to the plate geometry, imposed for reasons of mathematical feasibility). The contact is assumed to be tensionless. There are three important steps in this formulation. The fundamental solution of the nonhomogeneous half-space is separated into the fundamental solution of the homogeneous half-space and a function related to the nonhomogeneity of the half-space. The latter function is approximated by an analytically tractable expression. The contact region is discretized using an adaptive scheme that accounts for the possible edge and corner singularities. The latter scheme removes the burden of most of the numerical integration. A rigid strip footing and a rigid rectangular footing are treated first to ascertain the convergence of the solution procedure and to provide information requisite for the flexibility study. The title problem is transformed into the solution of three coupled two dimensional singular integral equations. The contact regions are found iteratively since the problem is nonlinear.