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Methods of Plastic Analysis - Kinematic Method - Part 1

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Question

The ultimate collapse load (P) is terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with P acting at its mid span as shown in fig would be ________.

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Solution

$\frac{L}{2} θ = Δ$

External work done = load x deflection
$= P_{u} \times Δ$

$= P_{u} (\frac{L}{2} θ)$

$I n t e r n a l w o r k d o n e = M_{P} θ + M_{p} (2 θ)$
$= 3 M_{p} θ$

By principle of virtual work,

$P_{u} (\frac{L}{2} θ) = 3 M_{p} θ$

$∴ P_{u} = \frac{6 M_{p}}{L}$

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