Ultimate strength of eccentrically loaded steel plates and box sections

A finite element method is applied to compute the elastic-plastic post-buckling behavior of initially deflected and eccentrically loaded steel plates and box sections. Comparisons with available theoretical and experimental results reveal that the present finite element analysis gives extremely accurate results even with small numbers of elements. Based on an extensive numerical study, an empirical formula is proposed to predict the ultimate strength of steel plates as well as steel box sections with various supporting conditions.     

Seismic analysis of asymmetric building-foundation systems

A method of analysis for the earthquake response of three-dimensional multi-storey asymmetric buildings founded on a flexible foundation is presented. The building-foundation system considered in this study is a linear N-storey asymmetric building on a rigid footing resting on the surface of a linear elastic half-space. The whole system has 3N + 5 displacement degrees of freedom. The governing equations are developed considering the motions of each floor and the motions of the whole system. The governing equations of the floors are first uncoupled in terms of footing displacements using the mode superposition method. Substitution of structural deformations, in combination with the dynamic soil-structure interaction force-displacement relationships proposed by Veletsos and Verbic [ASCE J. Engng Mech. Div. 100, 189–201 (1974)]and Veletsos and Nair [ASCE J. Geotechn. Engng Div. 100, 225–246 (1974)]into the governing equations of the whole system results in five integro-differential equations for footing displacements, which are then solved by numerical step-by-step time-history analysis. A 10-storey asymmetric building on soft soil was subjected to an artificially generated earthquake excitation in order to obtain the soil-structure interaction and eccentricity effects. The results show that soft soil conditions increase the lateral deflections, but reduce the twists, storey shears, and torques. Increasing eccentricity increases the twists and torques, but does not modify the lateral deflections at the centre of mass, and the total storey shears.     

Corner supported equilateral triangular plates

The objective of this study is to investigate the bending of a uniformly loaded isotropic equilateral triangular plate supported at the corners. The proposed approximate solution is obtained under the assumption that the total bending moment along each side of the triangle vanishes. The analytical results predicted by the proposed solution are compared with measurements taken on a steel plate model. In general, analytical and experimental values of deflections and stress resultants are in satisfactory agreement. The analytical results are presented in charts for use in the analysis and design of such structures.     

Improper integrals for infinite elements in vibration of half spaces

In vibration of elastic and viscoelastic multilayered half spaces, the far field of each half space is discretized into infinite elements. Far-field displacement functions of three fundamental problems are used as the shape functions of appropriate infinite element nodal lines. Each fundamental problem solution is obtained as a linear combination of discrete waves. As a result, the mass and stiffness matrices of infinite elements involve improper integrals, which are evaluated by three schemes proposed herein. Different schemes are good for different ranges of the complex argument of the integrals.     

Seismic response to a prescribed seismogram of a body embedded in a multilayered half space

While the actual problem is composed of an active fault surface, a soil site and a body embedded at that site; the proposed method provides an alternative smaller linear problem by replacing the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. The Green's function for each of three fundamental problems of isotropic elastic and viscoelastic spaces undergoing harmonic vibration is derived. Infinite elements are adopted in the far field, and finite elements in the near field. The three fundamental problem solutions are used as the shape functions of infinite element nodal lines. The three concentrated orthogonal force components at the focal point are determined in such a way that the Fourier transforms of the three orthogonal acceleration components measured at a seismograph station are checked. For seismic analysis of a finite embedded body, consider the differential between the actual system and the seismic free field, which is the embedding half space without any embedment and being excited by the fictitious focal point forces. All along the analysis has been carried out in the frequency domain. An appropriate inverse Fourier transform algorithm will properly yield all results as time functions.     

Waves generated from fictitious focal points to match seismograms recorded

The ground domain is separated into a near field and a far field. The near field encompassing the fictitious focal point is discretized into finite elements. The far field is discretized into infinite elements. The shape functions of these infinite elements are in closed forms and with explicit compositions of constituent waves. The harmonic vibration analysis yields the Fourier transform of any constituent wave in terms of the amplitudes of the three orthogonal force components applied at the focal point, thus in terms of the Fourier transforms of the accelerations in three orthogonal directions recorded at a seismograph station. An appropriate inverse Fourier transform algorithm yields the transient constituent waves. All seismic waves at any points, inside the ground and on the ground surface, can be evaluated. The results can be more refined in case of the availability of simultaneous records at more seismograph stations. In case of two stations, we assume two fictitious focal points. Numerical examples of real site responses are presented by using one single focal point and two simultaneous focal points.