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Methods of Plastic Analysis - Kinematic Method - Part 1

Collapse load...

Question

Collapse load for a fixed beam of span L having moment capacity $M_{p}$ subjected to concentrated load at mid span is $k \frac{M_{p}}{L}$ . The value of k is____.

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Solution

From kinematic method,
$M_{p} θ + M_{p} (2 θ) + M_{p} θ = P Δ$
$4 M_{p} θ = P θ (\frac{L}{2})$
$P = \frac{8 M_{p}}{L}$
$k = 8$

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