Problem $3($Midterm $1-$ Fall $2023)$

The picture shows a truss subjected to a load $P$ at joint $C.$ Considering that the two bars have the same length, crosssection area A and modulus of elasticity $E$ :

a$.$ Compute the internal forces in bars $BC$ and $CD.$ Indicate if they are in compression or tension.

b$.$ Calculate the total deformation of the bars $BC$ and CD$.$

c$.$ Compute the displacement of joint $C.$

d$.$ Determine the principal stresses in the bar $BC$ and their angles of orientation $($principal planes$)$ with respect to the $x-$axis shown in the picture. Is there a shear stress in this plane?

e$.$ Indicate the maximum shear stress in the bar $BC.$ What is the angle of orientation with respect to the principal plane?

Answer the questions above in terms of L