Question

A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gauge pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is
1. 35
2. 70
3. 140
4. 280

Answer 1

Correct Answer - Option 3 : 140

Explanation:

Circumferential stress of hoop stress σ_h 

\({σ _1} ={σ _h} = \frac{{pd}}{{2t}} = \frac{{2 \times 14\;}}{{2 \times 0.05}} = 280MPa\)

Longitudinal stress σ_L 

\({σ _2} ={σ _L} = \frac{{pd}}{{4t}} = \frac{{2 \times 14\;}}{{4 \times 0.05}} = 140MPa\)

As this is the case of a thin cylinder:

Radial stress \({σ _r} =0\)

Maximum shear stress \({τ _{max}} = \max \left\{ {\frac{{{\sigma _1} - {\sigma _2}}}{2},\frac{{{\sigma _1}}}{2},\frac{{{\sigma _2}}}{2}} \right\}\)

τ_max  = \(\frac{{σ _h}-{σ _r}}{{2}}=\frac{{σ _1} }{2} = \frac{280}{2}=140~ MPa\)

 

Maximum In-Plane shear stress/Surface shear stress:

\(τ_{max,inplane}=\frac{{σ _1}-{σ _2}}{{2}}\)

Maximum wall shear stress/Out plane shear stress/Absolute shear stress:

\(τ_{max,abs}=\frac{{σ _{max}}-{σ _{min}}}{{2}}=\frac{σ_1}{2}\)