$3.$ A strut with a solid circular cross section carries a compressive axial load.

Length $\backslash (\backslash$boldsymbol$\{\backslash$ell$\}\backslash$mathbf$\{=1200$ ~$\}\backslash$mathbf$\{$m m$\}\backslash$quad $\backslash )$ diameter $\backslash (\backslash$mathbf$\{$d$\}=\backslash$mathbf$\{12\}\backslash$mathbf$\{$~ m m$\}\backslash )$

Modulus of Elasticity E $\backslash (\backslash$mathbf$\{=206,000\}\backslash$mathbf$\{$M P a$\}\backslash )$

One end is fixed; the other end is rounded $($rounded $=$ pinned$)$

$($strut end kept in line but free to rotate at the pinned connection$)$

a$.$ Find the cross$-$section area A and the modulus I. $(10$ pts $)$

b$.$ Give the recommended end condition constant C for this setup.

pts$)$

c$.$ Find the critical load $\backslash (\backslash$mathrm$\{$P$\}\_\{\backslash$mathrm$\{$cr$\}\}\backslash ).(12$ pts$)$

d$.$ Find the compressive normal stress at the critical load. $(5$ pts$)$