Question $6$

Displacement matching condition is given by:

$u_{x1}(\frac{L}{3})=u_{x2}(\frac{2L}{3})=u_o$

$u_{x1}(\frac{L}{3})=u_{x2}(\frac{2L}{3})=-u_{xo}$

$u_{x1}(\frac{L}{3})=u_{x2}(\frac{2L}{3})$

$u_{x1}(\frac{L}{3})=u_{x2}(\frac{L}{3})$The bar shown below fixed on one side and is loaded as shown below:

Question $3$

Boundary condition at $x=0$ is:

$P_1(0)=-p_{o}x$

$u_x(0)=0$

$P_1(0)=-F_1$

$P_1(0)=p_{o}x$

$u_x(0)=-u_o$

$P_1(0)=0$

$P_1(0)=F_1$

$u_x(0)=u_o$

$P_1(0)=p_{o}x+F_1+2p_o$

$P_1(0)=-p_{o}x+F_1-2p_o$

Question $4$

Boundary condition at $x=L$ is:

$P_2(L)=-p_{o}x+F_1-2p_o$

$u_{x2}(L)=0$

$u_{x2}(L)=u_o$

$P_2(L)=2p_o$

$P_2(L)=0$

$u_{x2}(L)=-u_o$

$P_2(L)=p_{0}x+F_1+2p_o$

$P_2(L)=-2p_o$

Question $5$

Force matching condition is given by:

$P_1(\frac{L}{3})+p_{o}x+F_1=P_2(\frac{L}{3})+2p_o$

$P_1(\frac{L}{3})=P_2(\frac{L}{3})$

$P_1(\frac{L}{3})+F_1=P_2(\frac{L}{3})$

$P_1(\frac{L}{3})=P_2(\frac{L}{3})+F_1$