Journal of Engineering Mechanics

For creep analysis of large structural systems, the linear aging integral‐type creep law needs to be converted to a rate‐type form which consists of a system of first‐order linear differential equations with age‐dependent coefficients. The system may be visualized by the Kelvin chain model with age‐dependent elastic moduli and viscosities. In the existing formulation, the independent variable is actual time. It is shown that, by using as the independent variable a certain reduced time which increases with time at a gradually declining rate, one reduces the number of differential equations needed to describe creep within the given time range, thereby making numerical structural analysis more efficient. An algorithm for identifying the material parameters from given creep data, based on minimization of a sum of squared deviations, is also presented. Thermodynamic restrictions on the material coefficients are analyzed. Finally, the capability of closely approximating available creep data is demonstrated.

A method of analysis is presented for free vertical vibration of suspension bridges. The method takes into account the effects of shear deformation and rotary inertia, and uses a linearized theory which maintains small amplitudes of vibration. The formulation of the problem is based on the Timoshenko beam theory, and the differential equations of motion and the associated boundary conditions are derived by applying Hamilton's principle. The analysis is conducted by using general solutions for the fourth order differential equation of motion. The objective of the study is to determine a sufficient number of natural frequencies and mode shapes, and to enable an accurate vibration analysis for higher modes. A detailed numerical example, which includes the various boundary conditions of the stiffening girders and the elasticity of the towers, is shown to illustrate the applicability of the analysis and to investigate the dynamic characteristics of vertical vibrating suspension bridges.

The problem of deriving approximations for multinormal integrals is examined using results of asymptotic analysis. The boundary of the integration domain given by $g\left(\underset{\text{¯}}{x}\right)=0$ is simplified by replacing $g\left(\underset{\text{¯}}{x}\right)$ by its Taylor expansion at the points on the boundary with minimal distance to the origin. Two approximations which are obtained by using a linear or quadratic Taylor expansion are compared. It is shown that, applying a quadratic Taylor expansion, an asymptotic approximation for multinormal integrals can be obtained, whereas using linear approximations large relative errors may occur.

The effect of follower forces and weight on the stability of elastic rods is studied using the 2‐mode Galerkin method. Stability boundaries are presented to show how various combinations of the loads lead to divergence or flutter instability. Results are presented for pinned‐pinned rods, clamped‐free rods and free‐free rods. The free‐free rod corresponds to a flexible missile with distributed follower forces due to drag and weight‐like forces due to thrust. It is shown that a good choice of mass distribution can eliminate flutter instability for all practical loading situations.

A theory is developed to predict the static response of a wire rope with complex cross sections. The solutions of the nonlinear equations of equilibrium are linearized, and the results are applied to a $6\times 19$ Seale rope with an independent wire rope core. The linearization permits a considerable simplification in the theory so that the results can readily be applied to other types of cross sections. Expressions are presented for the stresses in the rope, and the maximum tensile stress is also determined. A load‐deformation curve of a Seale rope is obtained experimentally, and the results are compared with the theory.

A practical structural analysis of suspension bridges by the stiffness matrix method is presented. This analysis is based on deflection theory. In this method all live loads are applied at arbitrary points and locations along a stiffening girder or truss because of the inclusion of the load terms derived by means of the Laplace transformation. Therefore, it is possible to reduce the number of division elements. Horizontal cable tension can be determined by integral of Green's function with respect to deflection. Irrespective of the number of division elements, the magnitude of horizontal cable tension can be obtained precisely. The method is applicable to an analysis of suspension bridges with any number of spans and variable cross sections. The validity of the stiffness matrix method proposed herein is examined and checked by numerical calculations. This stiffness matrix method can be developed and extended to a three‐dimensional analysis of suspension bridges.

This paper examines the problem related to the unilateral interaction between two smoothly precompressed isotropic elastic halfspaces which is caused by the wedging action of a rigid circular inclusion of finite thickness located at the interface. The unilateral nature of the contact leads to the development of a zone of separation between the halfspace regions. This paper discusses a mathematical treatment of the problem and develops an approximate estimate for the radius of the zone of separation. Numerical results presented in the paper illustrate the manner in which the extent of the zone of separation is influenced by the precompression stress and the geometry of the embedded disk inclusion.

The rectilinear motion and the conditions of reattachment and separation of a rigid body, in friction contact with another body are considered. A graphical representation of the motion is indicated, and analytical expressions for the velocities and displacements are derived. The existence of limiting values of velocity and displacement is shown for a special class of periodic ground motions which include harmonic motions. Also, the equations of motion and the conditions of reattachment and separation of a two degrees of freedom model of a sliding structure and foundation are derived. The numerical integration of the response of this system is carried out, as well as a parametric study showing the effect of different values of the mass ratio, coefficient of friction and amplitude of the ground acceleration. Use of results of the parametric study, concerning amount of slippage, resonance frequency ratios, minimum allowable frequency for sticked mode, etc. in the design for structural base isolation is indicated.

The extension of Morison's equation to allow for structural motion in predicting the hydrodynamic force on offshore steel jacket platforms may be based on two different hypotheses: (1) The relative velocity model which replaces the fluid velocity by the relative velocity between the fluid and the structure; and (2) the independent flow fields model which considers the flow to be a superposition of two unrelated flows, one due to the wave‐current action on a rigid cylinder, and the other due to the structural motion in still water. An iterative computational procedure that combines time domain and frequency domain analysis techniques is developed to solve the nonlinear governing equations for both models. Comparison studies are carried out for seastates ranging from the drag dominant through the inertia dominant regimes. Results indicate that the independent flow fields model always predicts a higher structural velocity response, the difference increasing with wave height. There is negligible difference for the inertia dominant range. At intermediate seastates, which are of primary concern for fatigue analysis, the relative velocity model appears to overestimate the damping. Consequently, its use in fatigue life prediction may be questioned. For typical offshore platforms, the applicability of the independent flow fields model diminishes as the seastate approaches extreme values.

A plate element in plane stress state is simulated by a network obtained from a regular octagon in which all the diagonals are bars. Simple formulas govern the general nonlinear anisotropic behavior of the model. In order to calibrate the model on an initially isotropic material, all the bars are provided with uniaxial stress‐strain laws analogous to experimental ones. The proposed network model is compared with experimental data and rules of plasticity with respect to the following five items: (1) Poisson ratio for nonlinear elastic behavior and for uniaxial loading in plastic state; (2) proportional monotonic loadings with various ratios ${\sigma }_y/{\sigma }_x$ and $\tau =0$ in the cases of an aluminum alloy and a type of concrete; (3) initial yield curve and ultimate strength envelope on the plane ${\sigma }_x-{\sigma }_y;$ (4) study of the hardening rule of the model on the ${\sigma }_x-{\sigma }_y$ plane, distortion of the yield curve and formation of a corner on it; and (5) exact validity of the normality rule for the network model.

Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios $(h/d)$ ranging from 1‐3 are treated. A simple constitutive model of the concrete is employed, which accounts for the strain hardening and softening in the pre‐ and postfailure regions, respectively. When $h/d=2\text{,}$ the failure mode is found to consist of undisturbed end cones and the occurrence of strain softening, especially in the outer region of the cylinder middle. For shorter cylinders the strain softening is more pronounced along the surface of the cylinder middle, whereas longer cylinders exhibit a more uniform distribution of strain softening. The failure modes for force and displacement controlled tests are found to be similar. If long cylinders are to provide the true uniaxial strength the use of geometrically matched loading plates seems to be advantageous. Finally, it is observed that for variations of the element size within limits otherwise required to obtain a realistic analysis, the results are insensitive to the element size.