Journal of Engineering Mechanics

Probability density functions, mean crossing rates, and other descriptors are developed for the quasi‐static and dynamic responses of offshore platforms to wave forces. It is assumed that offshore platforms can be modeled by simple oscillators, the wave particle velocity is a stationary differentiable Gaussian process, Morison's equation can be applied, and wave forces are perfectly correlated spatially. Results show that both the quasi‐static response and the dynamic response of offshore platforms to wave forces are generally underestimated if the drag force is linearized. Estimates are developed for probabilistic characterictics of these responses based on the crossing theory of random processes and time‐discretization of the wave force process. Simulation studies indicate that these estimates are satisfactory.

The approximation of the Pierson‐Moskowitz (P‐M) wave spectrum as the output of digital filters to white noise excitation is considered. It is shown that the mathematical peculiarity of this spectrum is the source of the numerical difficulties encountered in approximating it by autoregressive (AR) models. Further, it is shown that a reasonably accurate initial AR approximation leads to quite efficient autoregressive moving average (ARMA) models. This is accomplished by employing two new techniques. Numerical data are given in a dimensionless form so that they are applicable to a variety of structural dynamics applications.

An incremental type of stress‐strain relationship is proposed for simulating the hysteretic response of concrete, subjected to biaxial cyclic loading. The behavior of concrete is represented by an infinite number of rheological elastic‐plastic type of elements connected in parallel. The strain at elastic limit and maximum plastic strain values of each element are assumed to be stochastically distributed. It is possible to simulate with sufficient accuracy, the strain softening, the path dependency and the hysteretic response using this model. The model is computationally efficient and the relatively few parameters needed can be calibrated from the monotonic, uniaxial response and from the biaxial failure envelope. Shear stresses and rotation of loading axes cannot yet be handled with this model.

An experimental study utilizing 4‐point bending SENB specimens was carried out to determine the effect of fatigue on the fracture toughness of plain concrete. In addition to fourteen static tests of beams with a midspan precast notch, nine specimens with an initial precast notch of a depth to height ratio of $l/d=0.20$ were fatigued until a certain crack length was reached. Crack growth was successfully monitored by the CMOD compliance measurements. Independent surface crack length measurements by a hand‐held scope and observations of the crack front with the use of a fluorescent dye‐penetrant injected into the notch root were also performed. The fracture toughness, $G_{\mathrm{IC}}\text{,}$ under fatigue appears to be higher than under static loading and shows an increasing trend with increasing crack length and number of loading cycles. The observed behavior is most likely related to the presence of a microcracking zone that evolves with fatigue.

Most research studies on inelastic material behavior of steel structures under earthquake ground motions are concentrated on general uniaxial cyclic loading conditions. Very limited attention has been given to the responses of structures subjected to multiaxial and nonproportional loading conditions. This study is concerned with the observations of experimental behaviors of structural steel subjected to biaxial nonproportional loading conditions. Six annealed A‐36 steel tubular specimens were tested under constant strain rate and room temperature using an MTS axial‐torsional testing system under prescribed strain paths. Results of three of the six tests are reported in this paper (the other three are primarily duplicates). Four important observations on the material characteristics are described and discussed. They are the initial plastic plateaus of structural steel under biaxial loading, the hardening behavior under multiaxial cyclic and nonproportional loading, the material memorial characteristics, and the effect of nonproportional loading.

The mechanical properties of metals in the inelastic range may generally be described by mathematical relationships. Many such constitutive relationships or plasticity models were formulated based on limited experimental data and were at best validated by static or uniaxial cyclic loading tests. Very few of the mathematical models have been substantiated by test results under biaxial and nonproportinal loading conditions because experimental information was not available. This is particularly true for structural steel. This paper is concerned with the improvement of a plasticity model of the two‐surface type for structural steel based on experimentally observed features of annealed A‐36 steel specimens tested under biaxial cyclic and nonproportional loading conditions at room temperature. This two surface plasticity model for A‐36 steel is then used to predict numerically the experimental curves covering the entire strain histories of the tests. Excellent correlations are obtained.

Starting from a continuum mechanics basis, the principle of virtual displacements is used for deriving the differential equations of equilibrium for a horizontally curved I‐beam. In the present formulation, the effect of curvature is considered, while the condition of inextensibility, usually adopted in conventional analyses, is not required. The cross‐sectional displacements for the curved I‐beam are derived through employment of Vlasov's thin‐walled beam assumptions. Due to the inclusion of nonlinear strains in the virtual work equation, the instability effects caused by various loads, including the axial force, transverse shears, torque, bending moments, and bimoment are generally taken into account. The solutions are presented and compared with existing ones for two special cases.

This paper concerns a general theory for elastic structures with prescribed deflections and constrained ``taper'' (= rate of spatial change of the cross-sectional area). The proposed theory is applied to minimum weight beams with a linear relationship between the flexural stiffness and the cross-sectional area. This application is then illustrated through an example of a cantilever beam with constrained taper, having a prescribed slope at its free end. As this structure is statically determinate, the ``associated'' displacement field (that is, the Lagrangian for the equilibrium condition) is not employed directly in obtaining the soptimal solution. However, it can be used for checking the validity of the solution through a dual formulation. In this example, the optimal length of the section with constrained taper is given by another Lagrangian. In addition to verifying them through the dual formula, the results are checked by another independent method (differential calculus for an assumed class of solutions). Finally, it is pointed out that in optimizing statically indeterminate elastic structures, the solution can be obtained directly by considering the associated (Pragerian) displacement field.

A general theory is presented for optimizing the layout of elastic structures for a prescribed deflection at a given point. This development is an extension of an earlier layout theory which was derived in the context of optimal plastic design and based on optimality criteria. After comparing the ``classical'' layout theory for low-density, grid-like structures with the ``advanced'' layout theory for elastic continua having a high material volume/feasible volume ratio, general optimality criteria are developed for both non-vanishing (optimal) and vanishing potential members of elastic systems having a prescribed deflection. The above theory is then applied to elastic circular grillages (beam-grids or truss-grids) with a given central deflection. It is shown that a grillage or uniform stiffness has almost 41% higher weight than that of the optimal solution. In light of some recent work the above theory is being applied to the optimization of solid plates.