Beams - Propped Cantilevers, Sinking of Supports - Steel Structures.

Propped cantilevers
Beams which are built-in at one end and simply-supported at the other are known as propped cantilevers. Normally, the ends of the beams are on the same level, in which case bending moments and reactions may be derived in two ways: by employing the Theorem of Three Moments or by deflection formulae.Appropriate formulae for propped cantilevers under various types of loading are  presented in the Appendix Bending moment, shear and deflection tables for propped cantilevers.

Sinking of supports
When the supports for a loaded propped cantilever do not maintain the same relative levels as in the unloaded condition, the BM and SF may be obtained by using the deflection method (Fig. 10.2).When the prop, B, sinks the load which it takes is reduced, while the fixing moment at the other end is increased. Two special cases arise: the first when the prop sinks so much that no load is taken by the prop, and the second when the built-in end sinks so much that the fixing moment is reduced to zero, i.e. the cantilever resembles a simple support beam. The two special cases are shown in Fig. 10.2.

Bending moment diagram for propped cantilever with sinking support
Fig. 10.2 Bending moment diagram for propped cantilever with sinking support

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