Question

A 6 m simply supported beam carries an ultimate live load of 50kN at midspan. Determine the plastic moment of the beam.

Answer 1

External deformation = Internal deformation.

EWD= IWD

EWD= Ultimate load $\times$ $\delta$

while $\delta = \frac{l}{2} \theta$

EWD = $w_u \times \frac{l}{2} \theta$

from the diagram

IWD = $M_P\theta + M_P2\theta + M_P0 = 4M_P\theta$

IF IWD = EWD

then $4M_P\theta= w_u \times \frac{l}{2} \theta$

$M_P= \frac{wuL}{8} = \frac{50 \times 6}{8} = 37.5 KNm$