A progressive destabilization in compressed elastic structures of sandwich construction is identified, whereby a triggering bifurcation into an overall mode of buckling is rapidly followed by secondary bifurcation into an unstable combination of at least two local modes. A six degree-of-freedom analysis for a sandwich strut is provided, which tracks equilibrium paths for a perfect system, specifically pinpointing states of secondary bifurcation. The analytical model allows for the independent variation of bending and shear in the section, components that are found in significantly different combinations in the overall and local forms of buckling that make up the interaction. An optimum wavelength for local buckling is identified, which maximizes the interactive effect by bringing the primary and secondary bifurcations together. Examples of sandwich sections drawn from the literature are tested. Although the critical loads of two of the contributing modes are often considerably higher than the third (typically by multiples of two or more), the preference for the broken symmetry of the interactive form is such that secondary bifurcation into the combination of modes is always to be expected.

Interactive buckling in sandwich structures

A closed-form expression for the in-plane horizontal stiffness of a viscously damped, uniform, inclined cable in harmonic motion is presented. The cable is presumed to be deflected in a parabolic profile at its position of static equilibrium, and all dynamic displacements are assumed to be small. The stiffness expression is valid for an arbitrary angle of inclination of the cable chord in the range between zero and 90 degrees. In addition, a simpler solution, valid over a narrower range of the parameters, is included and its accuracy examined.

Comprehensive numerical data are presented and discussed, with particular emphasis on explaining the physical significance of the results and providing insight into the action of the cable and into the parameters that control it. Finally, a simple, single-degree-of-freedom model is proposed which reproduces with good accuracy the salient features of the response of the prototype cable over a wide range of conditions.

Dynamic stiffness of parabolic cables

This paper deals with the stability behavior of web-tapered beams subjected to bending loads. According to the current AISC specifications, a tapered member is treated as prismatic with modified length and cross section identical to that of the tapered member's smaller end. Modification factors are used to determine the modified length and also to account for the moment gradient within the unbraced length and the restraining effect for adjacent spans. In this paper, these factors are evaluated via a finite-element analysis and compared to the ones proposed by the current specifications. The current design specifications for steel tapered beams are reexamined, and modifications that cover a wider range of geometry and loading cases are proposed.

Lateral-Torsional Stability of Steel Web-Tapered I-Beams

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Response Analysis of Dynamically Loaded Composite Panels

The problem of lateral torsional stability of cantilevers with continuous elastic or rigid lateral restraint is examined via a direct variational approach and in view of three major influence parameters: (1) Height of application of lateral restraint; (2) height of application of a point load above the shear center; and (3) stiffness of the elastic restraint. The derived free‐end force boundary conditions are examined and a quandry regarding their validity is addressed. Finally, the results of an experimental study are reported, providing some guidance in assessing the buckling of continuously restrained cantilevers.

Stability of Continuously Restrained Cantilevers

Large deflection of rectangular sandwich plates

The free vibration of a guyed tower has been analyzed taking into account the effect of the masses of the guys. Linearized differential equations of motion were derived for a guyed tower based on the assumption that the static deflection shape of the guys is a catenary. The results were evaluated to determine the effect of the following parammeters: (1) Effect of the static shape of the guys; (2) number of degrees-of-freedom of the mast and of the guys; (3) ambient temperature on the dynamic behavior of guyed towers.

Dynamics of Guyed Towers

Closure to “Elastic Lateral Buckling of Continuous Beams”

The results of an experimental study, 48 tests, of the flexural-torsional buckling behavior of two-span beams and rigid frames are presented and compared with the theoretically predicted behavior: the greatest difference between experiment and theory is 18%. The variables considered are the axial and torsional stiffness of the lateral bracing attached to the beam at the interior support and to the rigid frame at the knee.

Experimental Study of Flexural-Torsional Buckling

With the increasing use of plastic design methods in structural engineering, it becomes necessary to obtain a better understanding of the effect of partial cross-sectional yielding on the flexural-torsional buckling behavior of laterally braced beams. The equations needed to study the buckling behavior of partially yielded beams and frames have been developed. These equations have been used to investigate the strengthening effect of lateral bracing on the buckling capacity of simply supported rectangular beams subject to the following loading conditions: pure moment; concentrated load at midspan; and concentrated loads at the third points of the beam.

Alois J. Hartmann

Papers

Large deflection of rectangular sandwich plates

Dynamics of Guyed Towers

Closure to “Elastic Lateral Buckling of Continuous Beams”

Experimental Study of Flexural-Torsional Buckling

Inelastic flexural--torsional buckling