Example 83 Propped Cantilever
A propped cantilever is L m long and supports a collapse load of w kN/m as shown in Figure 8.7. Determine the position of the plastic hinges and the required plastic moment of resistance Mp.
Solution:
The collapse load=w kN/m
The number of hinges required to induce collapse=(ID+1)=2 (see Figure 8.1)
The possible hinge positions are at the support A and within the region of a distributed load since these are the positions where the maximum bending moments occur. In this case the maximum moment under the distributed load does not occur at midspan since the bending moment diagram is not symmetrical. Consider the final bending moment diagram:
Figure 8.8
The maximum bending moment (i.e. Mp) occurs at a distance 'x' from the roller support and can be determined as follows;
Since the moment is a maximum at position 'x' the shear force at 'x' is equal to zero.
This is a standard value, i.e. for a propped cantilever the plastic hinge in the span occurs at a distance x=0.414L from the simply supported end and the value of the plastic moment Mp=0.0858wL2
This is a standard value, i.e. for a propped cantilever the plastic hinge in the span occurs at a distance x=0.414L from the simply supported end and the value of the plastic moment Mp=0.0858wL2
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