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 mid-span 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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