Problem $6$

a$.$ The vertical post in the figure consists of two solid cylindrical

rods. The upper rod is $30cm$ diameter, while the lower rod is $10$

$cm$ diameter. Both rods are made of steel with elastic modulus,

$E_s=200$GPa. A downward load of $80kN$ is applied at the top of

the post while an upward load of $30kN$ is applied at the junction

between the two rods as shown in the figure. Assume the post

remains linearly elastic when subjected to these loads. Compute

the deformation at the top of the post due to the applied loads.

b$.$ A bar AB having two different prismatic cross sections is fixed

at both ends as shown in the figure. The left and right parts have

Young's modulus of E and $2$E$,$ respectively, while the area of

the left part is two times larger than that of the right part. The

total length of the bar $AB$ is $L,$ with corresponding lengths of

$0\mathrm{.}4L$ for the left and $0\mathrm{.}6L$ for the right part.

Determine all unknown support reactions and the displacement

at Point $C,$ indicating the direction.

c$.$ Consider the prismatic bar shown in the figure.

Draw axial force diagram $($AFD$)$ and axial displacement diagram $($ADD$)$ with values and signs.

d$.$ The axial force diagram $($AFD$)$ is provided for the prismatic bar shown in the figure. Draw the axial

displacement diagram $($ADD$).$ Report values.

e$.$ If the calculated deformation of a structural member under design loads is larger than the code$-$

specified criteria, what steps would you take to decrease the deformation response of the target member

when its length cannot be changed?