Prolilem II$.$

The nachine clement shown in Fure $1$ is loaded will glien loading types ul tie free end at lengili of $1.$

If the total strain eneras of the element h$.$ If the machine elentent is eylindrical har wlili $R$ and $L$ :

ansiler $(2-1-2-4)$

$2-1.$ The total strain due to the load $F$ is:

a $C=\frac{\frac{?}{PI}}{2*1E}+\frac{|I{I}^{\text{'}}}{2El}+\frac{T*l}{2GJ}+\frac{F^{\text{'}}l}{2*1G}.$

b$.U=\frac{p\text{:}1}{2IE}+\frac{n^{\text{'}}}{2EI}+\frac{r^2\text{I}}{2GJ}+\frac{F^{\text{'}}\text{I}}{2AG}.$

c$.C=\frac{\frac{?}{PI}}{2AE}+\frac{|I{I}^2}{2EI}+\frac{TI}{2GJ}+\frac{FI}{2AG}$

$2-2.$ The deflection due to the load $F$ is:

a$.{}_i=\frac{F^{\text{'}}}{2EI}+\frac{FI}{AG}$

b$.{}_r=\frac{Fl}{AG}.$

c$.{}_r=\frac{Fl}{AE}$

d$.{}_{,}=\frac{3P^{2}l}{2,E}+\frac{1}{1G}.$

$2-3.$ The bending moment deflection component is:

a$.{}_M=\frac{MI}{EI}+\frac{FI}{AG}.$

b$.{}_a=\frac{\text{M}\text{I}\text{I}}{IE}.$

c$.{}_M=\frac{F}{AG}+\frac{F^{\text{'}}l}{EI}$

d$.{}_N=\frac{(T+F)l}{JG}.$

$2-.$ The modulus of resilience is:

$u=\frac{{}^2}{2E}+\frac{F^{2}l}{2\text{A}\text{E}\text{I}}+\frac{T^2}{2\text{A}\text{G}\text{J}}+\frac{{}^2}{2G}.$

b$.u=\frac{{}^{2}l}{2E}+\frac{I}{2EI}+\frac{T^2}{2\text{A}\text{G}\text{J}}+\frac{{}^2}{2G}.$

c$.u=\frac{{}^2}{2E}+\frac{-F^2}{2EI}+\frac{T^2}{2\text{A}\text{G}\text{J}}+\frac{{}^2}{2G}$

d$.u=\frac{P^2}{2AE}+\frac{M^2}{2EI}+\frac{T^{\text{:}}}{2GJ}+\frac{F^{\text{:}}}{2AG}.$