If the maximum normal stress on the shown $x-$section is ${}_{\text{m}\text{a}\text{x}}=125$MPa, find the distance a$.$

Solution:$-$

Cross Section properties are obtained from the textbook appendix and are listed as follows:

$A=45\mathrm{.}70{10}^{-4}{m}^2$

$S_y=92\mathrm{.}4{10}^{-6}{m}^3,S_z=34\mathrm{.}3{10}^{-6}{m}^3$

${}_A=\frac{P}{A}-\frac{M_{z}y}{I_z}-\frac{M_{y}z}{I_y}$

$=\frac{-150{10}^3}{45\mathrm{.}7{10}^{-4}}-\frac{0\mathrm{.}095150{10}^3}{343{10}^{-6}}-\frac{150{10}^{3}a}{92\mathrm{.}4{10}^{-6}}$

${}_a={}_{\text{m}\text{a}\text{x}}=-125$MPa

$a=51\mathrm{.}2mm$

$W20035\mathrm{.}9$