Answer:
Pressure causing this deformation is 3.43 Mpa
Maximum in-plane shear stress is 0 Mpa
Absolute maximum shear stress at a point on the outer surface of the vessel is 87.4 Mpa
Explanation:
Maximum normal strain is [tex]\frac {0.012}{20}=0.0006[/tex]
[tex]\frac {pr (1-v)}{2Et}=0.0006[/tex]
[tex]\frac {p\times 1000mm(1-0.3)}{2\times 200\times 10^{3}\times 10}[/tex]
P=3.42857 Mpa
Therefore, internal pressure causing deformation is [tex]3.42857 Mpa\approx 3.43 Mpa[/tex]
Stress along direction 1 and 2 is given by [tex]\frac {pr}{2t}[/tex]
[tex]\sigma_1=\sigma_2=\frac {pr}{2t}=\frac {3.42857\times 1000mm}{2\times 10 mm}=171.42857 Mpa[/tex]
Maximum in-plane shear stress is given by [tex]\frac {\sigma_1-\sigma_2}{2}=\frac {171.42857 Mpa-171.42857 Mpa}{2}=0 Mpa[/tex]
Absolute maximum shear stress, [tex]\tau_{max}=\frac {\sigma_1+p}{2}=\frac {171.42857 Mpa+3.42857 Mpa}{2}=87.42857 Mpa\approx 87.4 Mpa[/tex]
