Question

A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to $M_p$ , the minimum load at which the beam would collapse is _____.

Answer 1

A continuous beam is said to be collapsed if any part of the beam is collapsed.
In continuous beam, failure of individual span is considered and the correct mechanism is the one for which loading is minimum.

Mechanism - 1 Failure of IJ

From BMD

$\frac{PL}{4}=M_p+\frac{M_p}{2}$

$P=\frac{6M_p}{L}$

Mechanism - 2: Failure of HI

From BMD

$\frac{PL}{4}=M_p+M_p$

$P=\frac{8M_p}{L}$

$\text{Hence, Minimum load}=6M_p/L$