Answer to Question #210151 in Civil and Environmental Engineering for Ri Jin

Question

A wooden beam with a rectangular section 150mm wide and 250 deep can resist a 140 kN-m bending stress. Determine the maximum compressive and tensile stress in the section if the beam material is non-isotropic with the tensile modulus of elasticity twice the compressive modulus.  

Answer 1

Ultimate bending moment = $1.5*140 = 210 kN.m$

$I= \frac{bd^3}{12}= \frac{150*250^3}{12}=19.53*10^7$

$y=\frac{d}{2}=\frac{250}{2}=125 mm$

$=\sigma_{max}=\frac{My}{I}=\frac{210*10^6*125}{19.53*10^7} = 134.41 N/mm^2$

Hence compressive stress = $-134.41 N/mm^2$

Hence tensile stress = $134.41 N/mm^2$