Problem # $4.$

The bar shown has a cross sectional area $A=400$

$m{m}^2.$ A parabolically varying distributed load has an

intensity of $0k\frac{N}{m}$ near the left support and reaches

$10k\frac{N}{m}$ at $0\mathrm{.}6$ m from the left support. The equation is

given as: $=\frac{10}{0\mathrm{.}36}{x}^2$

The stress$-$strain relation of the bar material is

such that the strain is effectively equal to zero when

the stress is less than

$25$ MPa and varies linearly when the stress is between

$25$ MPa and $50$ MPa $.$

$($a$)-$ Determine the variation of the stress in the bar

as a function of $x$ where $x$ is measured from

the left support.

$($b$)$ Find the stress at $x=0,$ just before $x=0\mathrm{.}6m$ and just after

$x=0\mathrm{.}6m.$

Use the stress$-$strain diagram given below to determine

how the strain varies as a function

of the stress for $>25$MPa.

$($d$)$ Determine the elongation of the entire $1\mathrm{.}5$ m bar.