Problem $2$

The pressure tank shown has a $10-mm$ wall thickness and can be simplified to be of a perfect hollow

cylindrical shape and the end$-$caps can be simplified to be flat. The density of the tanks material is

${}_{\text{s}\text{t}\text{e}\text{e}\text{l}}=7850k\frac{g}{m^3}.$ The density of the stored fluid under the pressure of $p=1$MPa is $35k\frac{g}{m^3}.$ The

tank can freely rotate about the supports $($like hinged supports$).$ The distance between the supports

is $2\mathrm{.}5m.$ Determine

$($a$)$ the maximum normal stress due to bending and its position

$($b$)$ the shearing stress distribution in this cross$-$section

c$)$ draw the stress distributions in the cross$-$section for a$)$ and b$)$

If the right support settles during installation unevenly to give a twist of $1$ about the longitudinal

axis of the tank:

c$)$ what shear stresses due to torsion will be caused by that?

d$)$ draw the stress distribution in the center cross$-$section

d$)$ Determine the principle stresses at the top and bottom and half the height of the tank in this

cross$-$section and draw the corresponding stresses element.

a$)$

$a$