## Structural analysis

The primary purpose of structural analysis in building structures is to establish the distribution of internal forces and moments over the whole or part of a structure and to identify the critical design conditions at all sections. The geometry is commonly idealised by considering the structure to be made up of linear elements and plane two-dimensional elements.

The type of analysis should be appropriate to the problem being considered. The following may be used: linear elastic analysis, linear elastic analysis with limited redistribution, and plastic analysis. Linear elastic analysis may be carried out assuming cross sections are uncracked (i.e. concrete section properties); using linear stress-strain relationships, and assuming mean values of elastic modulus.

For the ultimate limit state only, the moments derived from elastic analysis may be redistributed (up to a maximum of 30%) provided that the resulting distribution of moments remains in equilibrium with the applied loads and subject to certain limits and design criteria (e.g. limitations of depth to neutral axis).

Regardless of the method of analysis used, the following principles apply:

■ Where a beam or slab is monolithic with its supports, the critical design hogging moment may be taken as that at the face of the support, but should not be taken as less than 0.65 times the full fixed end moment.

■ Where a beam or slab is continuous over a support that may be considered not to provide rotational restraint, the moment calculated at the centre line of the support may be reduced by (FEd,sup f/8), where FEd,sup is the support reaction and t is the breadth of the support.

■ For the design of columns the elastic moments from the frame action should be used without any redistribution.

Bending moment and shear force co-efficients for beams are given in Table 6; these are suitable where spans are of similar length and the other notes to the table are observed.

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