ANALYSIS OF BRIDGE DECK SLABS BY YIELD LINE THEORY

Abstract

There are additional forces as being statically equivalent to the shear force and twisting moments on the yield lines. Johansen(9) avoided becoming too involved in this argument by inventing the concept of nodal force (forces acting at nodes, i.e. junctions of yield lines). Johansen found that these nodal forces, which were sometimes zero, sometimes upwards and some-times downwards, and which _were statically equivalent to the unknown twisting moments and shears, had certain special valuewhen the worst layout of yield lines was investigated. Returning, however, to the historical Set:Nonce of events, in 1957 Mansfield(16) broke new ground by invent-ing,a method of finding the worst layout for a system of yield lines involving nen-c*rcular fans of any shape. This he did by employing the calculus of variations, in order to predict the boundary shape of the fans. Mansfield acknowledged that Rzhanitsyn (Moscow 1954) had independently discoverddthe same approach. This comments, however, seems to imply that he was apparantly unaware that JohanseA6) in 1943 had achieved similar solutions with special shaped fans without any calculus of variations at all-in fact by the use of nodal force theory. By 1960 therefore, the idea was gaining ground that, whatever minimised solutions could be found by the work equation, there must be the equivalent technique to