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Abstract

An assessment is made between the bucking of a multi-bay, multi-storey frame structure with rigidly jointed connections, resulting from changes in frame geometry requested by the client.  A stability analysis approach is adopted, using s and c functions or n and o functions, for various substitute frames.  These are based on the principal of multiplies, including the Grinter frame approach commonly used in design practice.

Introduction

Figure 1 shows a multi-bay, multi-storey steel frame structure in which the loading, and members properties are as labelled, and all connections are fully rigid.  The frames are braced out-of-plane.  Column bases are assumed to form fully rigid foundations.  The frame conforms to the principal of multiplies hence it can be analysed using a suitable substitute frame.

The span lengths of beams, l, are ?m, the column heights, h, are ?m and the beam properties are IiB = ?IiC, at each storey level i.  The critical load of the structure is found to be W = ?p2EI/l2.

Figure 1 – Frame geometry.

Procedure

Systematic stiffness matrix methods

A stiffness matrix method approach is adopted, using s and c stability functions, or n and o stability functions for various substitute frames, including the well-know Grinter frame.

Explain the principle of multiples and demonstrate that the problem given conforms to the principle to which the various substitute frames and then applicable.

The stiffness matrix formulations for the various substitute frames are compared in Eqns (1) – (?), together with associated illustrations in Fig. 2.

Figure 2 – Illustration of Principle of Multiples applied to the frame given.

The frame can be obtained by fastening together p frame(s) with configuration (a), q frame(s) with configuration (b) and r frame(s) with configuration (c), which are situated side by side in the appropriate way.

Figure 3 – Comparison of substitute frames.

The numerical calculations are programmed into a spreadsheet, but the numerical results are summarised here, in full, for the various frame substitute frames adopted.

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