$11$:$21$ C

$47$

Homework$-2.$pdf

$5$ of $5$

Problem $3(40$ points$)$

Plastic bar AB of rectangular cross$-$section $(b=0\mathrm{.}75$ in and $h=1\mathrm{.}5in)$ and length $L=2ft.$ is fixed at A and has a spring support $(k=18$kip$\frac{s}{i}n.)$ at C$.$ Initially, the bar and spring have no stress. When the temperature of the bar is raised by $100F,$ the compressive stress on an inclined plane pq at $L_{}=1\mathrm{.}5ft$ becomes $950$ psi $.$ Assume the spring is massless and is unaffected by the temperature change. Let $=55\frac{{10}^{-6}}{}F$ and $E=400$ksi.

a$)$ What is the shear stress ${}_{}$ on the plane pq $?$ What is the angle $?$

b$)$ Draw a stress element oriented to plane pq $,$ and show the stresses acting on all faces of this element.

c$)$ If the allowable normal stress is $+-1000$ and the allowable shear stress is $+-560,$ what is the maximum permissible value of spring constant $k$ if the allowable stress values of the bar are not to be exceeded?

d$)$ What is the maximum permissible length L of the bar if the allowable stress values in the bar are not to be exceeded? $($Assume $k=18$kip$\frac{s}{i}n)$

e$)$ What is the maximum permissible temperature increase $(T)$ in the bar if the allowable stress values

in the bar are not to be exceeded? $($Assume $L=2ft$ and $k=18$kip$\frac{s}{i}n).$

Solution: