Journal of Engineering Mechanics

A torque may be classified as semitangential or quasitangential, according to the way in which it is generated. Both types of torques may cause a torsionally loaded bar to buckle at certain critical values. This paper investigates the instability of an initially straight but pretwisted bar subjected to a semi‐ or quasi‐tangential torque. The governing differential equations of a bar in the buckled state are derived using a global coordinate system, but are transformed to the local principal axes of each cross section for the convenience of solution. The characteristic equations of the boundary value problems are classified into three types, i.e., the transcendental, the periodic, and the discrete types. In the case studies, the effect of pretwist is demonstrated to be significant on the critical loads of a torsionally loaded bar.

An analytical method for investigating the effect of a stiffening beam on coupled shear walls is presented. Closed‐form solutions to the problem based on the continuous medium technique are obtained with the position of the stiffening beam placed somewhere along the structural height as a variable. The results of analysis for a typical structure demonstrate that great beneficial effects on the structural behavior can be achieved by installing a stiffening beam at about 0.2 to 0.5 of the structural height in the coupled shear walls, depending on whether the condition for the minimum value of the laminar shear, the base moment, or the top deflection is to be made.

The mechanical behavior of granular material is greatly influenced by packing geometry. A stress‐strain theory for small deformations of granular media made of equal‐sized particles arranged systematically is developed based on micro‐mechanical considerations. Stress, treated as a continuum field variable, is defined for a representative cell of the packing instead of an infinitesimally small point as in continuum materials. The overall macroscopic stress‐strain relationship is derived from the use of principle of energy conservation. The force‐deformation relationship at the contact between two particles is assumed to follow Mindlin's theory. However, this assumption is not a restriction of the proposed stress‐strain theory. The derived stress‐strain relationship is compared to experimental results and the existing solutions.

Previous studies on the buckling of an elastic strut with discrete flexible transverse supports indicate that a sufficient support stiffness may be found such that the flexible supports would act as rigid supports for a hinged‐end strut. In the present work, a comprehensive study of the buckling and postbuckling behavior of both hinged‐end and fixed‐end struts is carried out. It is revealed that the fixed‐end struts behaves differently from the hinged‐end struts and a clear‐cut suffcient support stiffness cannot be defined from the result of a buckling analysis. A postbuckling analysis indicates that there is a region of support stiffness, in which the postbuckling behavior of the strut is unstable. Therefbre, a sufficient support stiffness may be defined as one that would lead to a stable postbuckling behavior. With this new concept a single support stiffness value is suggested for the design of struts with fixed‐end, hinged‐end, or partially constrained end‐conditions.

The geometric relations required for an embedded finite element representation of generally curved reinforcing bars or prestressing tendons are developed. For practical reasons, the reinforcing layers are described in global coordinates, independently of the finite element mesh. An inverse mapping procedure is developed to transform global coordinates of points on the reinforcement layer into local natural coordinates in the parent element. The strain field in the layer is discussed, including a bond slip model. The principle of virtual work is used to derive the various element matrices. The procedure is successfully tested, using both regular and irregular meshes, on three test problems: a uniform strain field, and two versions of a quarter ring under external pressure.

The characteristic length of a heterogeneous brittle material such as concrete represents a material property that governs the minimum possible width of a zone of strain‐softening damage in nonlocal continuum formulations or the minimum possible spacing of cracks in discrete fracture models. This length is determined experimentally. The basic idea is to compare the response of two types of specimens, one in which the tensile softening damage remains distributed and one in which it localizes. The latter type of specimen is an edge‐notched tensile fracture specimen, and the former type of specimen is of the same shape but without notches. Localization of softening damage is prevented by gluing to the specimen surface a layer of parallel thin‐steel rods and using a cross section of a minimum possible thickness that can be cast with a given aggregate. The characteristic length l is the ratio of the fracture energy (i.e., the energy dissipated per unit area, dimension $N/m\text{.}$) to the energy dissipated per unit volume (dimension $N/m^2\text{.}$) Evaluation of these energies from the present tests of concrete yields $l\simeq 2.7$ times the maximum aggregate size.

A nonlinear finite element procedure for arch dams is described in which the gradual opening and closing of vertical contraction joints and predetermined horizontal cracking planes are considered. A special joint element approximately represents the deformations due to plane sections not remaining plane at each open joint and allows a single shell element discretization in the thickness direction to be used for the dam. Compressive and sliding nonlinearities are not included. Finite element treatments are also used for the water, assumed incompressible, and for the foundation rock, assumed massless, with all degrees of freedom (dof) off the dam condensed out. For efficiency in the computations, the condensed water and foundation matrices are localized in a way which maintains good accuracy. The response of Pacoima Dam to the 1971 San Fernando ground motion recorded on a ridge over one abutment and scaled by two.‐thirds is computed first for water at the intermediate level that existed during the 1971 earthquake and then for full reservoir. In the first analysis, the dam exhibits pronounced opening and separation of the contraction joints, allowing violation of the no‐slip assumption. The presence of a full reservoir greatly increases the dam response, enough to bring some of the other assumptions of the analysis into question. Reducing the ground motion scale to 0.44 with full reservoir drops the response back to a reasonable level, but the contraction joint separations remain.

A stress‐strain relationship for granular soils based on microstructural consideration is presented. Granular medium is considered to be an assembly of particles intersected by a large number of potential sliding planes. Under loading the planes are mobilized and the overall deformation of the soil mass is obtained from the movement of these planes. The movements of these planes are governed by the resolved tractions on these planes. The mechanical properties of these planes can be different in each orientation in order to account for the anisotropy of the granular media. The parameters of each plane is estimated from the overall deformation behavior of fhe soil sample. Procedure for the determination of the model parameters is discussed. Three types of tests are needed for determining the parameters, namely, isotropic compression test, triaxial compression test and triaxial extension test. An example of Ottawa sand in cubical triaxial device is shown to demonstrate the applicability of the model.

This is the first part of an investigation of time variant structural system reliability under multiple loadings. The formulation of the problem in the context of outcrossing of a vector random process of a safe domain is examined. Methods of evaluating reliability of series systems and plastic frames are developed. Emphasis is on use of existing time invariant reliability methods and methods of load combination. Simple and well‐defined loading and structural systems are used to develop basic understanding of the problems. Extensive Monte Carlo simulations are carried out to verify the analytical methods. For the foregoing systems whose reliabilities do not depend on the loading sequence and loading path, a load coincidence analysis in conjunction with an efficient time invariant reliability analysis may give good, conservative estimates of the failure probability.

This is the second part of an investigation of time variant structural system reliability under multiple loadings. The study is concentrated on brittle, redundant systems. The emphasis is on the consideration of load sequence, load path, and progressive failure over time. Currently available methods such as those based on an outcrossing analysis and a load coincidence consideration are critically examined. A new method based on a Markov model is also proposed. Extensive Monte Carlo simulations are carried out to verify the analytical methods. The accuracy and computational effort of each method are examined. The importance of the effect of load path and load sequence is demonstrated by numerical examples of simple parallel bars under tension and trusses with both tension and compression members.

Two curved beam elements are derived for the buckling and nonlinear analyses of horizontally curved I‐beams. Starting from a continuum mechanics basis, the incremental equation of equilibrium is established for a bar in its deformed state using an updated Lagrangian formulation. The curved beam elements presented herein are advantageous in that the effects of curvature and warping are consistently considered. Difference in the performance of each element is primarily due to the use of different shape functions. Numerical examples will be given to illustrate the applicability of the two elements and the inconsistencies of modeling a curved beam with chordwise straight beam elements.

The problem of extreme wind prediction for determination of design wind speed is considered. Drawbacks of the presently used method based on the classical extreme-value theory are pointed out, and a step toward better statistical treatment of data is presented. The new procedure, which is based on estimating the tail of a probability distribution, forms a powerful and flexible class of alternatives to the traditional methods. Here, rather than the annual maxima, all the large values are included in the analysis, regardless of their occurrence time. For the parametric family of distributions involved (which take only three forms, like the classical extreme-value theory), the available estimating methods are described, and an illustrating example is presented using a set of published data. The general advantages of the procedure over the subsample method developed by Gumbel are examined.

The failure criterion for orthotropic materials as wood is presented. Using Tsai and Wu criterion the failure criterion for wood is derived under plane stress conditions ignoring the influence of stress perpendicular to the grain. The failure criterion for wood is given by an ellipse. Tests of mechanical properties of Japanese cedar are carried out, where eight groups of wood transmission poles are used. Tests are performed on 104 small specimens to determine direct compressive, tensile and shearing strengtjh of the test materials. The ultimate tensile strength parallel to the grain of the test specimens are 1.5 to 2.4 times the ultimate compressive strength parallel to the grain. The failure criterion for the test specimens is shown.