Question

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. If load P = 80 kN, find the reaction R (in kN) (correct to 1-decimal place) using elastic analysis ____.

Answer 1

From Elastic Theory:



From compatibility equation
Net deflection at C = 0

$\Rightarrow \frac{R{L}^3}{3EI}-\frac{P{L}_1^3}{3EI}-\frac{P{L}_1^2}{2EI}{L}_2=0$

$\Rightarrow \frac{R\times (3{)}^3}{3EI}=\frac{P\times (1.5{)}^3}{3EI}+\frac{P\times (1.5{)}^3}{2EI}$

$\Rightarrow R=\frac{3}{27}[\frac{80\times (1.5{)}^3}{3}+\frac{80\times (1.5{)}^3}{2}]$

$R=25kN$