TABLE OF CONTENTS The theory presented in this chapter extends the ultimate load analysis of structures, begun in Chapter 18 for beams and frames, to reinforced concrete slabs.
Structural engineers, before the development of ultimate load analysis, designed reinforced concrete slabs using elastic plate theory. This approach, however, gives no indication of the ultimate load-carrying capacity of a slab and further analysis had to be carried out to determine this condition. Alternatively, designers would use standard tables of bending moment distributions in orthogonal plates with different support conditions. These standard tables were presented, for reinforced concrete slabs, in Codes of Practice but were restricted to rectangular slabs which, fortunately, predominate in reinforced concrete construction. However, for non-rectangular slabs and slabs with openings, these tables cannot be used so that other methods are required. The method presented here, yield line theory, was developed in the early 1960s by the Danish engineer, K.W. Johansen.
There are two approaches to the calculation of the ultimate load-carrying capacity of a reinforced concrete slab involving yield line theory. One is an energy method which uses the principle of virtual work and the other, an equilibrium method, studies the equilibrium of the various parts of the slab formed by the yield lines; we shall restrict the analysis to the use of the principle of virtual work since this was applied in Chapter 18 to the calculation of collapse loads of beams and frames.
A slab is assumed to collapse at its...
