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Steel Designers' Manual - 6th Edition (2003)
Therefore the moment at the fixed end of a propped cantilever
= 3Ax
L
2
where A = the area of the free BM diagram, AB being considered as a simplysupported
beam
x = the distance from the prop to the CG of the free BM diagram
and L = the span.
The reactions at each support may be found by employing a modified form of the
formula used for beams built-in at both ends:
SFA = the simple support reaction at A = - M
L
SFB = the simple support reaction at B = + M
L
where A is the propped end and B is built-in.
10.2.2 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.
10.3 Fixed, built-in or encastré beams
Fixed, built-in or encastré beams 327
When the ends of a beam are firmly held so that they cannot rotate under the action
of the superimposed loads, the beam is known as a fixed, built-in or encastré beam.
The BM diagram for such a beam is in two parts: the free or positive BM diagram,
which would have resulted had the ends been simply-supported, i.e. free to rotate,
and the fixing or negative BM diagram which results from the restraints imposed
upon the ends of the beam.
Normally, the supports for built-in beams are at the same level and the ends of
the beams are horizontal. This type will be considered first.
B
B