Journal of Engineering Mechanics

This paper presents two methods to find the elastica of a bar or a beam of given span length, but unknown arc length. The beam is subjected to a moment at a hinged end that can slide freely over another support. In the first method the differential equation based on large-deflection theory is formulated and solved by using elliptic integrals. The method yields an exact closed-form solution. The critical or maximum applied moment the beam can resist is also obtained by this formulation. Further, the well-known small displacement solution can be obtained from the degeneration of the exact solution by considering small rotations. The second method is based on a variational formulation, which involves the bending strain energy and work done by the end moment. The finite-element discretization of span length instead of bar length is used to solve the problem. Numerical comparisons are given and results from the finite-element method show good agreement with the elliptic integrals solutions.

In many cases, small-scale modeling requires the scaling up of the gravitational acceleration. Yet this requirement sets a technical problem, and unless the use of a centrifuge is available, it is not fulfilled. Consequently there is a distortion in the extrapolated results of the small-scale model, which lacks scaling of gravity. So far, the extent of the effect of gravity scaling on the extrapolated results has been speculated. A quantitative way to evaluate this effect is suggested here. An expression for the distortion in the extrapolation of a measured model variable is developed, based on similitude requirements. This expression depends on the geometrical scaling factor, and on the ratio of a variable measured model value to the value of its gravitational component. It shows that for geometrical scaling factors of 10 and 50, the distortion is less than 10% when the gravitational component of the variable is less than 1% and ∼0.2%, respectively.

The directional-simulation procedure to estimate the zero-time failure probability and the outcrossing rate for structural systems is extended to structural frames subject to loads modeled as mixed Poisson pulse processes. The problem is formulated in the space of the load processes. The structural system resistance is represented by probabilistically defined region boundaries obtained from the presumed (known) limit state functions for the structure. The theory is applied to a simple rigid framed structural system acted on by two discrete load processes. The results obtained are compared with those derived from a consideration of bounds on the outcrossing rate for mixed sparse Poisson processes. A comparison with results published in the literature is also given. It is shown that there may be considerable differences. A detailed discussion of the reasons for these differences closes this paper.

This paper explores the theory of reactive porous media in the modeling of thermochemomechanical couplings of concrete at early ages. The formulation is based upon thermodynamics of open porous media composed of a skeleton and several fluid phases saturating the porous space. It accounts explicitly for the hydration of cement by considering the thermodynamic imbalance between the chemical constitutents in the constitutive modeling at the macrolevel of material description. In particular, the diffusion of water through the layers of hydrates is considered as the dominant mechanism of the hydration with respect to the kinetics of two apparent phenomena: aging and autogeneous shrinkage—the first related to the formation of hardened cement gel, the latter induced by capillary effects related to the formation of menisci due to water consumption through hydration. The intrinsic relations concerning heat generation, aging, and autogeneous shrinkage are so derived. Furthermore, it allows to make precise the decoupling hypothesis in order to clarify the linkages between different aging models: solidification theory and maturity models. In particular, it is shown that hydration degree, autogeneous shrinkage, and maturity are equivalent state variables, provided that stress and temperature evolutions do not effect the thermodynamic imbalance of hydration.

An insight is given into the recovery length phenomenon in axially preloaded multilayered spiral strands. Recovery length is defined as the length measured from the fractured end of the wire, in which the wire will be able to carry its appropriate share of the axial load. Numerical results on realistic spiral strand constructions suggest that the recovery length in various layers is a weak function of the mean axial load on the cable. The lay angle has been found to be the primary parameter determining the magnitude of the recovery length of various layers in multilayered spiral strands and, hence, a straightforward method for determining variations of recovery length with lay angle in any layer of any spiral strand construction aimed at practicing engineers has been proposed. Using such estimates of recovery length, a minimum length of test specimens (for axial fatigue loading) equal to about 10 lay lengths is recommended for spiral strands.

A discrete-time analysis of seismic site amplification in layered media for vertically propagating shear waves is presented. The discrete-time approach not only is simpler and more accurate than the previously suggested frequency-domain techniques but also provides better physical insight into the problem. The discrete-time domain equations of wave propagation can be derived by using the upgoing and downgoing waves as auxiliary variables, and require only three parameters for each layer: the reflection coefficient at the bottom of the layer, the travel time of waves in the layer, and the damping. The discrete-time formulation results in simple analytical models for site amplification. When compared with the previous ones, these new models have important advantages: (1) They use the physical parameters of the site; (2) for a single soil layer over bedrock subjected to vertically propagating waves, the model is exact; (3) amplitudes and phase characteristics of the site are accounted for in the models; (4) the models can incorporate multiple reflections in the layer; and (5) the models result in simple time-domain filters for simulating ground motions. They also provide convenient tools to develop random vibration models, generate site-specific response spectra, and identify site characteristics from recorded motions.

The imperfection sensitivity of ring-stiffened anisotropic composite cylindrical shells under hydrostatic pressure is investigated using an asymptotic procedure. To this end, a finite-element formulation based on three-dimensional elasticity is developed. The displacement functions take the form of “exact” trigonometric functions along the circumferential direction and p -version-type hierarchic polynomial sets in the other two orthogonal directions. The buckling problem is explored in depth as a preliminary. Convergence studies on the critical pressures and the imperfection-sensitivity parameter are presented. Currently available results on critical pressures based on higher-order shear-deformation theory are cited for comparison. Fluid pressure loading is emphasized in contrast to the centrally directed loading. Comparisons of the maximum pressures as given by full-blown nonlinear analysis is presented. The imperfection sensitivities of several anisotropic and orthotropic laminate configurations are compared. The stiffened shells are investigated for their response in the “local” and “overall” buckling models separately. It is believed that the present approach is a very effective alternative to full-blown nonlinear analysis and can prove to be a powerful tool in preliminary design.

The objective of this study is to investigate effects of both free surface fluctuation (i.e. wave intermittency) and the nonlinearity of wave kinematics on total wave forces and on the dynamic responses of offshore structures. The random wave considered herein is restricted to unidirectional, deep-water ocean waves. Monte Carlo simulations and time-domain techniques are employed so that all nonlinear phenomena can be accurately included. Numerical comparisons are carried out for total wave forces and structural responses according to either linear or second-order random wave theory and by either including or excluding surface fluctuation. The study finds that under a weakly nonlinear, deep-water wave condition, both surface fluctuation and kinematic nonlinearity can be omitted. However, for a relatively strong nonlinear wave condition, both free-surface intermittency effect and nonlinearity of wave kinematics are important.

An experimental study on granular materials in triaxial extension at confining pressures from 0.25 to 68 MPa is presented. Drained and undrained tests were performed utilizing cylindrical specimens. Strain localization was repeatedly encountered in the form of specimen necking. The strain localization was determined to initiate very early in the test. The cause of the strain localization was determined to be the inherent instability in the axisymmetric extension test, which allows stresses, and therefore deformations, to concentrate at the weakest part of the specimen. This instability is a result of the inward radial strains experienced during the extension test. The effect is to lower the measured failure stresses and strains resulting in the conclusion that the conventional extension test is unreliable for determining soil strength in extension. A method was developed to enforce uniform strains in triaxial extension tests on cylindrical specimens by the use of small metal plates separated by lubricated latex membranes. Using this method a series of uniform-strain tests were performed. Detailed comparisons between strain-localized and uniform-strain tests are presented.

A procedure is described for evaluating the buckling load of weightless prismatic columns with uncertain rotational spring elements. The uncertainty in the spring elements is expressed in terms of a nonprobabilistic convex model. An ellipsoidal bound is used that defines the uncertainty in terms of a size parameter and the deviations of the spring constants from their nominal values. The size parameter represents the size of the ellipsoid and is analogous to the standard deviation magnitude in probabilistic analyses. The semiaxes of the ellipsoid are the deviations of the spring constants from their nominal values and they determine the shape of the ellipsoid. A first-order analysis shows that the reduction in the buckling load when uncertainty in the spring stiffnesses is present, is a linear function of the size parameter and a nonlinear function of the semiaxes of the uncertainty ellipsoid. For columns for which more than one buckling mode is possible, different reductions in the value of the buckling load result in each mode for the same uncertainty in the spring element stiffnesses.