Journal of Structural Engineering

A finite‐element method of analysis is presented for the elastic flexural‐torsional buckling of non‐prismatic I‐section beam‐columns. The formulation presents a general approach to the problem, in which the coupling of torsion and bending is simplified by adopting the web mid‐height as an arbitrary axis of twist. By making this simplification, the formulation does not sutler from the restrictions of other solutions, such as the use of uniform elements and finite differences. Buckling stiffness and stability matrices are developed, and these may be readily included in existing finite‐element programs. The method is shown to be in good agreement with the more complex finite‐integral treatment, and its scope is demonstrated by application to the buckling of tapered cantilevers.

TWO failure mechanisms in reinforced concrete slabs with steel bars inclined to the direction of principal moments are presented. Both mechanisms refer to failures due to the yielding of steel. The first failure mechanism occurs when no slip between the crack surfaces is possible, while the second mechanism is accompanied by a slip of crack surfaces. For both mechanisms, equations are derived that predict the ultimate load and the direction of ultimate crack. Derived equations have been applied to slab strips reinforced with longitudinal and transverse reinforcement or with only transverse reinforcement, subjected to combined torsion and bending. Experimental and theoretical results show a very good agreement.

Three sets of real earthquake records are selected to represent seismic ground motions in the low, normal, and high a/v (peak ground acceleration/peak ground velocity) ranges. The inelastic responses of single‐degree‐of‐freedom stiffness degrading systems to the three sets of records are analyzed statistically to investigate the significance of such ground motion characteristics on structural damage. Both damage due to peak inelastic deformation and cumulative fatigue‐type damage due to a large number of reversed inelastic deformations are considered. Three damage parameters, each reflecting information on peak inelastic deformation, stiffness deterioration, and hysteretic energy dissipation, respectively, are used to measure structural damage. The mean values of the three damage indicators are obtained for the three sets of accelerograms, and the corresponding dispersion characteristics are examined. It is found that ground motion a/v range has a significant effect not only on peak inelastic response but also on hysteretic energy dissipation and stiffness deterioration of stiffness degrading systems. The effect on hysteretic energy dissipation is more pronounced than that of peak inelastic response.

Earthquake resistant design of key structures at major industrial facilities is often performed with an energy‐absorbing or strong‐motion dissipating mechanism in mind. The energy is usually dissipated through the deformation or damage of less critical components in order to prevent or decrease the potential of a more catastrophic failure of a structure. This paper presents a simplified approach for evaluating the effects of energy dissipation through deformations in foundation bolts of tall industrial columns subjected to strong earthquake ground motion. In particular, changes in the failure probability of a column in the more critical mode of skirt buckling are studied as a function of bolt yielding. The post‐yielding nonlinear response motion of the structure is considered in the failure probability evaluation. Although the procedure presented in this paper is applied to tall industrial columns, it can be used for a variety of other types of structures with only minor modifications.

As the design process is refined, second‐order (stability) analysis becomes more important for both steel and concrete structures. Softening in concrete members, defined as the loss of moment capacity at advanced curvatures, is a material instability. The presence of significant axial force in a softening member raises the possibility of double or interactive instability, i.e., instability from large axial forces and instability from softening. Stability functions for members with finite softening lengths are derived. Computer program SOAPS (Second‐Order Analysis with Plasticity and Softening), developed for the stability analysis of plane frames with elastic‐plastic‐softening characteristics, incorporating stability functions and the $P‐\Delta$ effect, is used. Three examples are presented to demonstrate the application of program SOAPS. Increasing axial loads reduce the critical softening parameter for any hinge and therefore may also reduce the number of hinges formed before collapse. Consideration of stability effects may lead to a different order of hinge formation and large reductions in collapse load.

A simple analytical model is proposed to describe the effects of local buckling of circular cross section on the maximum strength and behavior of tubular beam‐columns. The behavior is presented in the form of load‐deflection and load‐shortening relationships. These relationships are developed on the basis of an assumed deflection method coupled with the moment‐thrust‐curvature relationship including the softening branch of the relationship due to the local cross‐sectional distortion. The analytically obtained maximum strength interaction curves of beam‐columns show a reasonably good agreement with the available experimental results. The trend of the analytical load‐deflection and load‐shortening curves is very similar to that of the available experimental results. It is found that the effects of the local buckling on the behavior and strength of tubular beam‐columns become more severe with an increase in diameter‐to‐thickness ratio, and with a decrease in slenderness ratio.

A numerical procedure for tracing the inelastic post‐buckling load‐deflection path of tubular struts is proposed. The analysis accounts simultaneously for both the geometrical and material nonlinearities with special emphasis placed on the influence of strain‐unloading. An iterative numerical arc‐length technique is employed in the solution procedure, but once strain‐unloading is detected, iterations are suppressed and the procedure converted to a pure incremental method with arc‐length constraint only. Predictions of the maximum loads and of the post‐buckling load‐deflection paths using the proposed approach compared very well with other published analytical results and with tests. The approach is simple and may be applied to general thin‐walled cross sections and to include cyclic loading.

Empirical hysteretic models are developed for masonry shear walls using the results of cyclic tests performed by different investigators on 37 single‐story walls. The models account for the deteriorating nature of the response of masonry shear walls to cyclic loads, and distinguish between the hysteretic characteristics of walls with shear or flexural modes of failure. These models are used to compute the nonlinear response of single‐story reinforced masonry shear walls to 16 recorded earthquake ground motions with different intensities and frequency contents. The effects of the deteriorating nature of masonry shear wall hysteretic behavior on its nonlinear seismic response characteristics are investigated by comparing the computed responses of masonry walls and some hysteretically stable (e.g., elasto‐plastic) systems. The effects of the wall dominant failure mode (shear or flexure) on its response to earthquakes are also evaluated. Suggestions are made for the required strength of masonry shear walls located in regions with different seismic risks.

A new approach for selecting optimum members in steel frames from standard hot‐rolled sections is illustrated. The approach is applied to an example 8‐story, 3‐bay planar frame subjected to vertical and horizontal loads. In the example, optimum members are defined as those which minimize total frame weight while satisfying combined stress constraints under specified loading conditions. The approach computes the discrete optimum from the continuous optimum. It is implemented as a pre‐ and post‐processor to state‐of‐the‐art nonlinear continuous optimization algorithms. The approach is general, robust, and efficient in that a minimum number of structural analyses are required. The approach uses a convex hull generation algorithm, nonlinear programming algorithms, linearization, and a variation on the branch and bound method. The approach does not require the standard sections to be ordered in any way, nor does it require any approximate relationships between section properties.

Reliability of structural members with nonlinear material property subjected to combined live load processes is studied. An earlier study using an envelope process yields very wide bounds of values for the first moment of load exceedances (number of loads exceeding a predetermined threshold deformation, ${\Delta }_0$) and damage duration (total time a process has deformation larger than ${\Delta }_0$). By assuming that only the sustained load causes permanent deformation, and by modifying the concepts used in a prior study for a contiguous rectangular pulse, a refinement on the bounds of the expected number of combined load exceedances and damage duration are found. In addition, the relationship between linear and nonlinear structural response is examined for different elastic limits both in load exceedances and in damage duration.

Two approaches are used to derive differential equations, stiffness coefficients, and fixed‐end forces for the analysis of structural systems composed of Timoshenko beam‐columns that may be supported by an elastic foundation. The analysis is for the evaluation of the critical static axial load and buckling mode‐shapes of a structure with consideration of elastic media, bending, and shear deformations. The two approaches differ in terms of the assumed shear component of the static axial load on the cross section. The first approach is based on the assumption that the shear component of the axial load is calculated from the total slope, which consists of the bending and shear slope. In the second approach, the shear component of the axial load, however, is calculated only from the bending slope. Analytical expressions for a typical simple beam are derived to show the influence of a foundation parameter on the buckling modes. It is observed that the critical axial loads are significantly reduced when shear deformations are considered for smaller slenderness ratios, but they are remarkably increased when the elastic media are included for all slenderness ratios. The first approach yields less buckling load than the second, and the difference between them becomes more pronounced for beams with low slenderness ratios and higher modes. Numerical examples are provided that illustrate the application.

The dynamical behavior of a masonry arch with and without jointing material is investigated. Two modes of response are studied: the elastic mode and the dynamical response of the arch after being transformed into a mechanism. The elastic free vibration frequencies considering the effect of the lateral load are formulated. The rocking of the mechanism is discussed and formulated. The cases where rocking leads to the total failure of the arch are considered. The conditions in which the elastic response is transformed into rocking are studied and the energy associated with it is assessed.

The discontinuity in the ground motion arising from the truncation of earthquake accelerograms may produce inaccuracies in the response of long period structures with low damping. The termination of the ground motion at a point where the acceleration is low and the use of a small time step during free vibration following the truncation of the record generally improve the results. However, these conditions are insufficient to guarantee acceptable results in all cases. An acceleration pulse is described which, when added to the end of the truncated record, eliminates the abrupt termination of the ground motion. The use of this suffixed pulse removes the uncertainty in the selection of the time of truncation and permits the use of a reasonable time step during free vibration.