An unpressurized vessel is loaded by horizontal force Px = 80 N, vertical force Py = 190 N, and torque T = 5 N·m acting in the directions shown. Determine the magnitude of shear stress τyz at K on the outside of the vessel.Vessel geometry    height, h = 53 mm    outside diameter = 53 mm    inside diameter = 47 mm    wall thickness = 3 mm    cross sectional area = 471.24 mm2    Ix = Iz = 147,790 mm4    J = 295,580 mm4    Q = 3,754.5 mm3

A basketball with an inside diameter of 8.62 in. and wall thickness of 0.055 in. is constructed from a polymer that has a yield strength of 3.16 ksi. If the ball is inflated to a pressure of 7.1 psi, determine the factor of safety with respect to the yield strength.

A soccer ball with an inside diameter of 7.6 in. and wall thickness of 0.043 in. is constructed from a polymer that has a yield strength of 3.04 ksi. If the ball is inflated to a pressure of 5.6 psi, determine the factor of safety with respect to the yield strength.

A vessel is loaded by internal pressure p = 130 kPa, horizontal force Px = 100 N, vertical force Py = 180 N, and torque T = 6 N·m acting in the directions shown. Determine the normal stress σz at K on the outside of the vessel.Vessel geometry    height, h = 50 mm    outside diameter = 50 mm    inside diameter = 46 mm    wall thickness = 2 mm    cross sectional area = 301.59 mm2    Ix = Iz = 87,010 mm4    J = 174,020 mm4    Q = 2,305.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 120 N, vertical force Py = 150 N, and torque T = 3 N·m acting in the directions shown. Determine the normal stress σy at H on the outside of the vessel.Vessel geometry    height, h = 54 mm    outside diameter = 54 mm    inside diameter = 48 mm    wall thickness = 3 mm    cross sectional area = 480.66 mm2    Ix = Iz = 156,820 mm4    J = 313,630 mm4    Q = 3,906 mm3

An unpressurized vessel is loaded by horizontal force Px = 110 N, vertical force Py = 180 N, and torque T = 4 N·m acting in the directions shown. Determine the magnitude of shear stress τyz at K on the outside of the vessel.Vessel geometry    height, h = 48 mm    outside diameter = 48 mm    inside diameter = 42 mm    wall thickness = 3 mm    cross sectional area = 424.12 mm2    Ix = Iz = 107,830 mm4    J = 215,660 mm4    Q = 3,042 mm3

A Pop-A-Shot ball with an inside diameter of 6.42 in. and wall thickness of 0.042 in. is constructed from a polymer that has a yield strength of 3.16 ksi. If the ball is inflated to a pressure of 5.8 psi, determine the factor of safety with respect to the yield strength.

An unpressurized vessel is loaded by horizontal force Px = 90 N, vertical force Py = 150 N, and torque T = 4 N·m acting in the directions shown. Determine the normal stress σy at H on the outside of the vessel.Vessel geometry    height, h = 52 mm    outside diameter = 52 mm    inside diameter = 46 mm    wall thickness = 3 mm    cross sectional area = 461.81 mm2    Ix = Iz = 139,120 mm4    J = 278,240 mm4    Q = 3,606 mm3

A copper [E = 16,300 ksi; ν = 0.38] water line has an outside diameter of 0.630 in., a wall thickness of 0.036 in., and a yield strength of 5.91 ksi. If a factor of safety of 2.5 is required, determine the maximum pressure that the pipe may contain.

An unpressurized vessel is loaded by horizontal force Px = 80 N, vertical force Py = 150 N, and torque T = 4 N·m acting in the directions shown. Determine the normal stress σy at K on the outside of the vessel.Vessel geometry    height, h = 55 mm    outside diameter = 55 mm    inside diameter = 49 mm    wall thickness = 3 mm    cross sectional area = 490.09 mm2    Ix = Iz = 166,200 mm4    J = 332,400 mm4    Q = 4,060.5 mm3