Question

A beam of uniform rectangular section 100 mm wide and 240 mm deep is simply supported at its ends. It carries a uniformly distributed load of 9.125 KN/m run over the entire span of 4m. Find the deflection at the centre of E= 1.1×10^4 N/mm^2

Answer 1

Given quantities:

$W=9.125*10^3\frac{N}{m}$

$L=4m$

$E=1.1*10^4 \frac{N}{mm^2}=1.1*10^10\frac{N}{m}$

$b = 10^{-1}m$

$h=0.24m$

$x-?$

$y-?$

$x=\frac{WL^2}{6EI}=\frac{12*WL^2}{6Ebh^3}=2\frac{WL^2}{Ebh^3}=2*\frac{9.125*10^3*16}{1.1*10^{10}*0.1*(0.24)^3}=19.2mm$

$y=\frac{WL^2}{8EI}=\frac{12*WL^2}{8Ehb^3}=1.5\frac{WL^2}{Ehb^3}=14.4mm$