(Solved): mechanics At the proportional limit, a 32mm wide by 12mm thick bar elongates 1.7mm un ...

mechanics

At the proportional limit, a $32\mathrm{mm}$ wide by $12\mathrm{mm}$ thick bar elongates $1.7\mathrm{mm}$ under an axial load of $29.8\mathrm{kN}$. The bar is $1.8\mathrm{m}$ long. If Poisson's ratio is 0.28 for the material, determine: (a) the modulus of elasticity. (b) the proportional limit. (c) the change in each lateral dimension. Answers: (a) The modulus of elasticity $E=$ GPa. (b) The proportional limit ${?}_{PL}=$ $\mathrm{MPa}$ (c) The change in width $=$ $\mathrm{mm}\text{. }$ The change in thickness $=$ $\mathrm{mm}$. The $d=16?\mathrm{mm}$-diameter solid rod passes through a $D=21?mm$-diameter hole in the support plate. When a load $P$ is applied to the rod, the rod head rests on the support plate. The support plate has a thickness of $b=10\mathrm{mm}$. The rod head has a diameter of $a=32\mathrm{mm}$, and the head has a thickness of $t=10\mathrm{mm}$. The shear stress in the rod head cannot exceed $125\mathrm{MPa}$, the punching shear stress in the support plate cannot exceed $90\mathrm{MPa}$, and the bearing stress between the rod head and the support plate cannot exceed $120\mathrm{MPa}$. Determine the maximum value of $P_{\max }$ that can be supported by the structure. Answer: $P_{\max }=$ $\mathrm{kN}$