Exam 12: Applications of Plane Stress Pressure Vessels and Combined Loadings

A thin-walled cylindrical tank, under internal pressure p, is compressed by a force F = 75 kN. Cylinder diameter is d = 90 and wall thickness $t = 5.5$ mm. Allowable normal stress is 110 MPa and allowable shear $110 \mathrm { MPa }$ stress is 60 MPa. The maximum allowable internal pressure $60 \mathrm { MPa }$ $p _ { \max }$ is approximately:

The pressure relief valve is opened on a thin-walled cylindrical tank, with the radius-to-wall thickness ratio of 128, thereby decreasing the longitudinal strain $150 \times 10 ^ { - 6 } \text {. Assume } E = 73 \mathrm { GPa } \text { and } v = 0.33$ original internal pressure in the tank was approximately:

A segment of a drive shaft ( $\left( d _ { 2 } = 200 \mathrm {~mm} , d _ { 1 } = 160 \mathrm {~mm} \right)$ is subjected to a torque $T = 30 \mathrm { kN } \cdot \mathrm { m } \text {. The }$ allowable shear stress in the shaft is 45 MPa. The maximum permissible compressive load $45 \mathrm { MPa }$ P is approximately:

A cylindrical tank is assembled by welding steel sections circumferentially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure is 2.0 MPa. The maximum tensile stress perpendicular to the welds $2.0 \mathrm { MPa }$ is approximately:

A thin-walled cylindrical tank with a diameter of 2.0 m and wall thickness of 18 mm is open at the top. The height $h$ of water (weight density $= 9.81 \mathrm { kN } / \mathrm { m } ^ { 3 }$ ) in the tank at which the circumferential stress reaches $10 \mathrm { MPa }$ in the tank wall is approximately:

A cylindrical tank is assembled by welding steel sections circumferentially. Tank diameter is 1.5 m, thick- ness is 20 mm, and internal pressure is $2.0 \mathrm { MPa }$ maximum tensile stress in the cylindrical part of the tank Is approximately:

A cylindrical tank is assembled by welding steel sections in a helical pattern with angle $\alpha = 50 ^ { \circ }$ . Tank diameter is 1. diameter is $1.6 \mathrm {~m}$ , thickness is $20 \mathrm {~mm}$ , and internal pressure is $2.75 \mathrm { MPa }$ . Modulus $E = 210 \mathrm { GPa }$ and Poisson's ratio $v = 0.28$ . The circumferential strain in the wall of the tank is approximately:

A cylindrical tank is assembled by welding steel sections circumferentially. Tank diameter is 1.5 m, thick- ness is 20 mm, and internal pressure is 2.0 MPa. The maximum shear stress in the heads is approximately: $2.0 \mathrm { MPa }$

A cylindrical tank is assembled by welding steel sections circumferentially. Tank diameter is 1.5 m, thick- ness is 20 mm, and internal pressure is 2.0 MPa. The maximum stress in the heads of the tank is approximately:

A cylindrical tank is assembled by welding steel sections in a helical pattern with angle $\alpha = 50 ^ { \circ }$ . Tank diameter is 1.6 m, thickness is 20 mm, and internal pressure is 2.75 MPa. Modulus $2.75 \mathrm { MPa }$ $E = 210 \mathrm { GPa }$ and Poisson's Ratio ν = 0.28. The normal stress acting perpendicular to the weld is approximately:

A thin-walled cylindrical tank with a diameter of 200 mm has an internal pressure of 11 MPa. The yield $11 \mathrm { MPa } .$ stress in tension is 250 MPa, the yield stress in shear is 140 MPa, and the factor of safety is 2. $250 \mathrm { MPa }$ $140 \mathrm { MPa }$ permissible thickness of the tank is approximately:

A cylindrical tank is assembled by welding steel sections circumferentially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure is 2.0 MPa. The maximum shear stress in the cylindrical part of the $2.0 \mathrm { MPa }$ tank is approximately:

A thin-walled spherical tank has a diameter of 0.75 m and an internal pressure of 20 MPa. The yield $20 \mathrm { MPa }$ stress in tension is 920 MPa, the yield stress in shear is 475 MPa, and the factor of safety is 2. $475 \mathrm { MPa }$ of elasticity is 210 $\text { GPa, }$ Poisson's ratio is 0.28, and maximum normal strain is $1220 \times 10 ^ { - 6 }$ The minimum permissible thickness of the tank is approximately:

A thin-walled spherical tank with a diameter of 1.5 m and wall thickness of 65 mm has an internal pres- sure of 20 MPa. The maximum shear stress in the wall of the tank is approximately: $\text { MPa. }$

A cylindrical tank is assembled by welding steel sections in a helical pattern with angle $\alpha = 50 ^ { \circ }$ . Tank diameter is 1.6 m, thickness is 20 mm, and internal pressure is 2.75 MPa. Modulus $2.75 \mathrm { MPa } \text {. }$ $E = 210 \mathrm { GPa }$ 210 GPa and Poisson's Ratio ν = 0.28. The longitudinal strain in the the wall of the tank is approximately: