Question #210151

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.  



1
Expert's answer
2021-06-29T00:23:52-0400

Ultimate bending moment = 1.5140=210kN.m1.5*140 = 210 kN.m

I=bd312=150250312=19.53107I= \frac{bd^3}{12}= \frac{150*250^3}{12}=19.53*10^7

y=d2=2502=125mmy=\frac{d}{2}=\frac{250}{2}=125 mm

=σmax=MyI=21010612519.53107=134.41N/mm2=\sigma_{max}=\frac{My}{I}=\frac{210*10^6*125}{19.53*10^7} = 134.41 N/mm^2

Hence compressive stress = 134.41N/mm2-134.41 N/mm^2

Hence tensile stress = 134.41N/mm2134.41 N/mm^2


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