Question

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.


If the magnitude of load P is increased till collapse and the plastic moment carrying capacity of steel beam section is 90 kNm, determine reaction R (in kN) (correct to 1-decimal place) using plastic analysis____.

Answer 1

From plastic theory:
$M_p=90kN-m$
$3M_p\theta =P\times 1.5\theta$

$\Rightarrow P=\left(\frac{3M_p}{1.5}\right)=\left(\frac{3\times 90}{1.5}\right)$

P = 180 kN


$\Rightarrow R\times 3+M_p=P\times 1.5$

$\Rightarrow R=\frac{(1.5\times 180-90)}{3}$

R = 60 kN