This paper discusses the issues involved in using simplified second‐order inelastic analysis for design of steel‐frame structures. In particular the elastic‐plastic hinge method is examined and the assumptions inherent in its use are outlined. It is shown that this method does not always lead to an accurate representation of inelastic behavior, and that it does not furnish enough information for assessment of the ultimate strength of individual members. An alternative approach called the refined plastic‐hinge method is introduced, and its design implications are discussed. The refined plastic‐hinge approach accounts for inelastic stiffness degradation, and a column tangent‐modulus expression is utilized to represent the effective stiffness of the element when it is loaded with large axial loads. This paper highlights and illustrates the qualities and limitations of these two inelastic analysis methods with regard to their acceptability for use in predicting the ultimate strengths of steel frames and their...

Second‐Order Refined Plastic‐Hinge Analysis for Frame Design. Part II

Optimal design of Schwedler and ribbed domes via hybrid Big Bang–Big Crunch algorithm

Dome structures provide cost-effective solutions for covering large areas without intermediate supports. In this article, simple procedures are developed to reach the configuration of the geodesic domes. A new definition of dome optimization problems is given which consists of finding optimal sections for elements (size optimization), optimal height for the crown (geometry optimization) and the optimum number of elements (topology optimization) under determined loading conditions. In order to find the optimum design, the recently developed meta-heuristic algorithm, known as the Charged System Search (CSS), is applied to the optimum design of geodesic domes. The CSS takes into account the nonlinear response of the domes. Using CSS, the optimum design of the geodesic domes is efficiently performed.

Geometry and topology optimization of geodesic domes using charged system search

The stability equations for plane frames with prismatic columns according to the buckling mode (as sidesway inhibited, partially inhibited, and uninhibited frames) are derived in a classical manner. In addition, an approach that evaluates the effective length K-factor, the critical axial load, and the sway-magnification factor δs for an entire story in plane framed structures is presented. The three-way frame classification and the proposed corresponding stability equations overcome the paradoxes of the current two-way classification of “braced” and “unbraced” frames. Moreover, the proposed equations are applicable to the stability analyses of multistory multibay plane frames with rigid, semirigid, and simple connections. It is shown that the stability equation of frames with sidesway partially inhibited has been the “missing link” to a full understanding of the elastic stability behavior of frames, and is the key to solving the paradoxes of current methods. Four detailed examples are presented that demon...

Story Stability of Braced, Partially Braced, and Unbraced Frames: Classical Approach

A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks

Members carrying both axial force and bending moment are subjected to an interaction between these effects. The analysis of a beam-column using stability functions as an alternative to the stress stiffness matrix is discussed. Explicit expressions for stability functions for three-dimensional beam-columns, in terms of member length, cross-sectional properties, axial force, and the end moments, are derived. The effect of flexure on axial stiffness and the effect of axial force on flexural stiffness and stiffness against translation are considered in the derivation of stability functions. The effect of axial force on torsional stiffness and the effect of torsional moment on axial stiffness are neglected. The nonlinear stiffness matrix of a three-dimensional beam-column using the stability functions is presented by modifying the linear elastic stiffness matrix for a beam-column (which includes the effect of shear deformations) available in the literature. A numerical example showing the calculation of stability functions for a given beam-column is also presented.

Mohan Selvappalam

Papers

Stability Functions for Three‐Dimensional Beam‐Columns