Journal of Structural Engineering

In this paper, a truss-core sandwich panel is introduced and its elastic properties are presented. Two thin flat sheets, separated by two inclined plates acting as the core and rigidly jointed at their ends, characterize the sandwich section. This construction form eliminates most of the attendant problems of conventional spot-welded or rivet-fastened sandwich panel construction. Advantages of the truss-core panel are discussed. The 3D sandwich panel is idealized as an equivalent 2D orthotropic thick plate continuum. Equivalent bending, twisting, and transverse shear stiffness are derived, and the influence of the relatively weak shear stiffness on the behavior is discussed. By integrating these elastic stiffness constants into closed-form solution, panel response is calculated. The calculated results, which require significantly less computational effort, agree well with 3D finite-element analysis. Comparisons of stiffnesses and deflections with the corresponding responses of conventional sandwich construction are provided. This study indicates that the truss-core sandwich panel performs better due to its inherently higher flexural resistance per unit weight.

A model to predict the behavior of embedded plates is developed considering plate flexibility, effects of transverse shear in plate, base stiffness (for tensionless base), anchor parameters, and attachment size. The development of the model, including its validation for linear elastic behavior, is presented. Linear behavior revealed influence of plate flexibility, transverse shear effects in plate, anchor stiffness, base stiffness, and attachment size on important design parameters of embedded plates. Subsequent development of a comprehensive model that includes material nonlinearity for prediction of behavior, mode of failure, and capacity of embedded plates is also presented. The model is validated with the available results of experimental and analytical work. Adoption of the model will be of help in obtaining better insight for formulating design guidelines for embedded plates.

Hyperelastic material models are derived from strain energy potentials expressed in terms of strain invariant or principal stretches. For a (nearly) incompressible material, the strain energy density depends on the first and second strain invariant; the third invariant describing a change in volume is equal to one. If the material is not highly confined it may be satisfactory to select an incompressible approach. However, for seismic bearings a highly confined situation does exist, and the compressibility must be included to obtain realistic results. Further, cavitation and associated stiffness reduction in bearings are shown based on experimental observations. In fact, it was noticed that a hydrostatic tensile stress in rubber causes internal rupture and a significant reduction in the bulk modulus. Thus, a hyperelastic formulation based on a variable bulk modulus does suggest a simple approach to realistically represent the mechanics of cavitation in rubbery solids.

A member model divided into subelements along the member axis with end fibers is developed for material and geometrical nonlinear analysis of a space frame structure. The fiber stress-strain relationship is an extended Ramberg-Osgood model. To assume appropriate stiffness on the alternative of fiber loading or unloading, a trial stiffness selection procedure is presented. Analytical increments for an overall frame are set relatively large for application to a frame with many members. Analytical results for a simple truss agreed well with the experimental results and simulated the complicated behavior of a web member, which first buckled slightly, then was unloaded, and finally rebuckled in another mode under a monotonous loading.

Material and geometric nonlinear analysis of the tested models for a large space frame is presented based on the 1D finite-element method. The analytical results have been confirmed to agree sufficiently with the experimental results up to a large deformed state. Members-coupled buckling of continuous chords and complicated collapsed states were simulated well. The analytical results of the partial models have shown that coupled buckling between several continuous chords appears to be asymmetric because of the difference in axial forces allowed by adjacent members. Except for whole bucklinglike phenomena, it is possible to analyze a large and complicated space frame with elastoplastic coupled buckling up to a large deformed state.

In the traditional optimization algorithms, constraints are satisfied within a tolerance defined by a crisp number. In actual engineering practice, constraint evaluation involves many sources of imprecision and approximation. When an optimization algorithm is forced to satisfy the design constraints exactly, it can miss the global optimum solution within the confine of commonly acceptable approximations. Extending the augmented Lagrangian genetic algorithm (GA) of Adeli and Cheng, a fuzzy augmented Lagrangian GA is presented for optimization of steel structures subjected to the constraints of the AISC allowable stress design specifications taking into account the fuzziness in the constraints. The membership function for the fuzzy domain is found by the intersection of the fuzzy membership function for the objective function and the constraints using the max-min procedure of Bellman and Zadeh. Nonlinear quadratic fuzzy membership functions are used for objective function and constraints. The algorithm is applied to two space axial-load structures including a large 37-story structure with 1,310 members. The features and advantages of the new fuzzy GA include acknowledging the imprecision and fuzziness in the code-based design constraints, increased likelihood of obtaining the global optimum solution, improved convergence, and reduced total computer processing time.

In the earthquake resistance design of frame structures, the yielding of all the beams in flexure prior to possible yielding of columns is generally considered to be a preferable mode; this is defined as a beam-hinging pattern in this paper. Structures are therefore generally weak-beam, strong-column designed with a column overdesign factor (COF). In reality however, the designed weak-beam, strong-column structures may not collapse according to the preferable failure mode because of large uncertainties in external loads and member strengths. These uncertainties may change the COF and the structure may collapse according to some unpreferable failure modes such as the weak story mechanisms. The object of this paper is probabilistic evaluation of the target values of COFs for which the occurrence probability of unpreferable failure modes can be limited to within a specific tolerance. A stochastic limit analysis procedure using the linear programming method and the first-order reliability method is developed, and the likely failure modes of weak-beam, strong-column designed structures are investigated using this procedure. The target value of COF is discussed in probabilistic terms. It is found that a much higher value of COF is required in the case of uncertain loads and member strengths than is expected in deterministic cases.

This paper presents an efficient simulation-based technique to estimate the system reliability of structures that experience variation in loads and resistance over time. To arrive at a realistic reliability estimate of such structures, random process description of load variation and consideration of resistance degradation and periodic repair must be included. An adaptive importance sampling methodology for estimating the time-dependent system reliability of brittle structures is presented in this paper. In the proposed method, a simple enumeration scheme is used to identify one complete failure sequence of the structural system. This defines the initial failure domain to start the simulation. As the simulation progresses, the initial failure domain is refined adaptively to include other significant failure sequences and to accurately estimate the failure probability of the system. The proposed method removes the idealized simplifying assumptions of earlier analytical methods, facilitates easy addition of the reliability analysis module to structural analysis, and provides a fast and accurate estimate of the failure probability. Numerical examples presented to illustrate the application of the proposed method demonstrate its efficiency and promise.

The weakness of existing relationships correlating off-axis modulus of elasticity E_θ to shear modulus G₁₂ for wood composite panels is demonstrated through presentation of extensive experimental data. A new relationship is proposed that performs better than existing equations found in the literature. This relationship can be manipulated to calculate the shear modulus G₁₂ of orthotropic specimens such as wood-based panels solely from off-axis tension (or compression) tests. The proposed relationship reduces to classical theory for the isotropic case. In all cases tested, the newly proposed relationship is a better fit to the data than the traditional orthotropic elasticity equation.

This paper evaluates momentless, or funicular, arches designed using Bernoulli-Euler beam theory and evaluates the errors associated with the Bernoulli-Euler and straight-beam approximations. When arches support hydrostatic pressure imposed by water of finite depth, the funicular arch shape depends on the ratio of the water depth to the arch height. Shallow momentless arches [in which the arch height is less than (1/10) the arch span] under deep water (where the water depth is greater than 10 times the arch height) are nearly parabolic in shape. On the other hand, tall momentless arches [in which the arch height is almost (1/2) the arch span] under deep water are nearly semicircular in shape. Momentless arches of intermediate aspect ratios are neither semicircular nor parabolic. The error arising from using straight beam theory (for the bending stresses only) is less than 5% for ratios of beam-depth to radius of curvature less than (1/2). Analyses including bending, shear, and axial deformations and hydrostatic pressure applied to the outer surface of the arch show that the internal moments can reach 10% of the moments of a straight beam of equal span, depending on the thickness and shape of the arch.