A long, narrow steel sheet was wound around the mandrel and welded along the flat edge of the spiral joint to make a cylindrical pressure vessel. The spiral welds have a longitudinal axis with each alpha $=55$ degrees. The inner radius of the vessel is r $=1\mathrm{.}8$ m$,$ and the thickness of the wall is t $=20$ mm$.$ The coefficient of material E $=200$ GPa and the Poisson's ratio is $0\mathrm{.}3.$ Answer the following question when the internal pressure p is $800$ kPa.

Main stress in circumferential direction: Sigma $1=$ pr$/$t

Main stress in the longitudinal direction: Sigma $2=$ pr$/2$t

a$)$ Induce the circumferential and longitudinal principal stresses.

b$)$ Find the maximum shear stress $($tau max$)$z in the plane and the maximum shear stress $($tau max$)$x in the plane.

c$)$ Find the strain in the circumferential and longitudinal directions.

d$)$ Find the vertical stress and shear force acting parallel and perpendicular to the direction of the spiral weld.$$

$.$

$=55.r=1\mathrm{.}8mt=20mm$

$.E=200$GPa $v=0\mathrm{.}3.p800$kPa $$

$.$

$$ : ${}_1=\frac{pr}{t}$

$$ : ${}_2=\frac{pr}{2t}$

a$).$

b$)({}_{\text{m}\text{a}\text{x}}{)}_z({}_{\text{m}\text{a}\text{x}}{)}_x.$

c$).$

d$)$

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