Required Informatlon

A axb rectangle was scribed on the side of a large steel pressure vessel. After pressurization the biaxial stress condition at

the rectangle was observed. Knowing that $a=1\mathrm{.}8in,b=2$ in $p=18$ksi,$q=26$ksi,$E=29{10}^6$ and $v=0\mathrm{.}30.$

$($a$)$ Determine the change in length of side $AB.$

$($b$)$ Determine the change in length of side $BC$

$($c$)$ Determine the change in length of side $AC$

Multiaxlal state of stress

The multi$-$axial state of stress in the pressure vessel is described as$,{}_x=18(ksi),{}_y=26(ksi),{}_z=0($ksi$)$

State of straln

Using multi$-$axial Hooke's law, the state of strain in the pressure vessel can be described as

${}_x=\frac{{}_x-}{E}$

$u{}_y-$

$u{}_x=0\mathrm{.}351724{10}^{-3}$

${}_y=\frac{{}_y-}{E}$

$u{}_x-$

$u{}_x=0\mathrm{.}710345{10}^{-3}$

Change In length of sldes

Since side $AB$ is along the $x-$dir., change in length of side $AB$ is given as ${}_{AB}={}_{x}AB=0\mathrm{.}633103{10}^{-3}($in$)$

Since side $BC$ is along the $y-$dir., change in length of side $BC$ is given as ${}_{BC}={}_{y}BC=1\mathrm{.}42069{10}^{-3}($in$)$

The change in length of the diagonal $AC$ is gievn as