Journal of Engineering Mechanics

Recent studies on the validity of some variational methods applied to stability problems in soil mechanics point out the existence of some important errors in their statement. These errors seem to be due to the lack of a rigorous mathematical analysis that assures the existence of an absolute minimum of the suggested functionals. Such analysis will usually involve considerations of the second variation of these functionals. Therefore, it will frequently lead to serious difficulties; indeed, it may be unfeasible in many cases. In this work, the limit analysis theorems are proposed to define “security” or “load” functionals to be optimized. This methodology assures the existence of a lower or upper bound of the suggested functional depending on which theorem is applied, provided that the mathematical conditions assumed for the validity of limit theorems are satisfied. Moreover, both the functional and the solution based on it have a coherent physical meaning. As a consequence, it is possible to reduce the problem to the analysis of the first variation of the functional. This methodology seems to be applicable to any stability problem in soil mechanics. In particular, it is applied to a slope stability problem by defining a security functional, based on the upper bound theorem. A system of equations, therefore, is obtained from the vanishing of its first variation.

Reliability is estimated for chain and ductile‐parallel systems subjected to random loads in terms of the reliability of their members assumed to have random, equally‐correlated strength. This probabilistic model of strength permits a simple determination of system reliability and the development of practical measures for the reliability of various structures based on a second‐moment or full‐distribution characterization of the random loads and strength. The model is used to find conservative estimates for the reliability of simple structural systems such as portal frames and statically determinate trusses. These estimates do not require that the loads and strength be Gaussian variables.

A method is presented for the identification of dynamic properties such as energy dissipation, permanent deformation and strength deterioration of damaged structures. In this method, the forms of load‐deformation relationships are time variant. Its application to the identification of the inter story hysteretic behavior of high rise buildings is obtained through the use of a lumped mass model. Any errors associated with this identification are dealt with the use of a least squares estimation technique. The proposed method is formulated in detail. It is then applied to identify the inter‐story hysteresis behavior of two one‐tenth scale and 10‐story reinforced concrete structures which were subjected to repeated earthquake loads in the laboratory.

A method of stochastic finite element analysis is developed for solving a variety of engineering mechanics problems in which physical properties exhibit one‐dimensional spatial random variation. The method is illustrated by evaluating the second‐order statistics of the deflection of a beam whose rigidity varies randomly along its axis. A key component of the approach is a new treatment of the correlation structure of the random material property in terms of the variance function and its principal parameter, the scale of fluctuation. The methodology permits efficient evaluation of the matrix of covariances between local spatial averages associated with pairs of finite elements. Numerical results are presented for a cantilever beam, with deformation controlled by shear, subjected to a concentrated force at its free end or to a uniformly distributed load.

A simple, computationally efficient procedure is presented with which the steady‐state response of a discrete linear system to a periodic excitation may be computed from an analysis of its transient response over a single cycle of the excitation. The procedure also is adapted to the solution of the inverse problem, i.e., to evaluate the transient response of the system from knowledge of its steady‐state response to a periodic extension of the excitation. The procedures are introduced by reference to single degree of freedom systems. They are then extended to multi‐degree of freedom systems for which the modal superposition method of analysis is applicable, and are illustrated by a series of simple examples. Both undamped and viscously damped systems are considered.

Crack propagation in concrete is associated with a nonlinear zone around the crack‐tip. The size of this fracture process zone length may be large depending upon the size of the aggregates and the geometry of the specimen. A theoretical model to predict the extent of this nonlinear zone and a method to include the effects of this nonlinearity in predicting the fracture resistance of concrete are described. The model is based on some simple and approximate extensions of the concepts of linear elastic fracture mechanics. The model is successfully used to analyze the results of the experiments on double cantilever, double torsion and the notched‐beam specimens.

An accurate and unified finite element description is presented, in both stiffness and flexibility formats, of the response of planar elastic beams subject to terminal loads. The stability and bowing functions are inter‐related, their descriptions accounting for the effects of axial deformability and a measure of the shear deformation effects. A perturbation technique is used to solve the non‐linear governing equations. The solutions so derived are cast in four distinct forms: (1) Deformation; (2) incremental; (3) perturbation; and (4) asymptotic forms of structural analysis. A brief comparison between related formulations presented in the literature is included.

Intending to achieve optimum finite element modeling of column supported cooling towers for seismic response studies according to the distributions of dominating bending and membrane stresses and intending to model the vulnerable shell‐column region using discrete column elements and quadrilateral shell elements, a set of elements is adopted, modified or extended. The set includes: (1) A 16 d.o.f. column element; (2) a 48 d.o.f. doubly curved quadrilateral general shell element; (3) a 42 d.o.f. doubly curved general‐membrane transition element; (4) a 21 d.o.f. and 39 d.o.f. doubly curved triangular membrane filler elements; and (5) a 28 d.o.f. doubly curved quadrilateral membrane element. Examples are given to evaluate a single type, combined types, and the whole set of elements with results in good agreement with alternative solutions. These elements may be used for accurate and efficient free vibration analysis of column supported cooling towers. The modeling may be used in seismic response analysis of cooling towers for obtaining detail stress distribution in the vulnerable shell‐column region. This model may be extended to include material nonlinearity in the shell‐column region for the seismic response studies.

The governing differential equation of linear, elastic, thin, circular plate of uniform thickness, subjected to uniformly distributed load and resting on Winkler-Pasternak type foundation is solved using ``Chebyshev Polynomials''. Analysis is carried out using Lenczos' technique, both for simply supported and clamped plates. Numerical results thus obtained by perturbing the differential equation for plates without foundation are compared and are found to be in good agreement with the available results. The effect of foundation on central deflection of the plate is shown in the form of graphs.

This note presents the results of an analytical study on the growth of plane turbulent plumes in coflowing streams. Similarity analysis of the integrated continuity, momentum, and buoyancy conservation equations has shown the velocity scale (with reference to the coflowing stream) remains constant with the axial distance x whereas the length scale grows linearly with x and the density defect scale varies inversely with x. Regarding the characteristic coefficients involved in these three expressions, if one of them is obtained experimentally, the other two can be evaluated using the expressions developed in this note.

This paper presents a simple analytical method for the calculation of the trajectories of jets in weak crossflows. Assuming a general similarity of the jet, a simple convection relation with no experimental coefficients is derived using the integral momentum, energy, and moment of momentum equations. The present analysis is concerned with plane jets.