A solid steel shaft with a diameter of 9.8 mm is subjected to the axial load and torques shown. Determine the magnitude of shear stress τxy in segment (2) of the shaft. Assume that P = 2,000 N, TA = 13.6 N·m, TB = 32.5 N·m, TC = 17.1 N·m, TD = 40.0 N·m, and TE = 41.8 N·m.

An unpressurized vessel is loaded by horizontal force Px = 100 N, vertical force Py = 150 N, and torque T = 3 N·m acting in the directions shown. Determine the magnitude of shear stress τxy at H on the outside of the vessel.Vessel geometry    height, h = 54 mm    outside diameter = 54 mm    inside diameter = 50 mm    wall thickness = 2 mm    cross sectional area = 326.73 mm2    Ix = Iz = 110,600 mm4    J = 221,190 mm4    Q = 2,705.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 80 N, vertical force Py = 170 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 = 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

An unpressurized vessel is loaded by horizontal force Px = 60 N, vertical force Py = 170 N, and torque T = 4 N·m acting in the directions shown. Determine the magnitude of shear stress τxy at H on the outside of the vessel.Vessel geometry    height, h = 55 mm    outside diameter = 55 mm    inside diameter = 51 mm    wall thickness = 2 mm    cross sectional area = 333.01 mm2    Ix = Iz = 117,090 mm4    J = 234,190 mm4    Q = 2,810.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 80 N, vertical force Py = 160 N, and torque T = 3 N·m acting in the directions shown. Determine the normal stress σy at K on the outside of the vessel.Vessel geometry    height, h = 53 mm    outside diameter = 53 mm    inside diameter = 49 mm    wall thickness = 2 mm    cross sectional area = 320.44 mm2    Ix = Iz = 104,340 mm4    J = 208,690 mm4    Q = 2,602.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 110 N, vertical force Py = 170 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 = 44 mm    wall thickness = 2 mm    cross sectional area = 289.03 mm2    Ix = Iz = 76,592 mm4    J = 153,180 mm4    Q = 2,117.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 90 N, vertical force Py = 200 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 = 46 mm    outside diameter = 46 mm    inside diameter = 42 mm    wall thickness = 2 mm    cross sectional area = 276.46 mm2    Ix = Iz = 67,042 mm4    J = 134,080 mm4    Q = 1,937.3 mm3

An aluminum CO2 [E = 10,100 ksi; ν = 0.33] bottle has an outside diameter of 3.21 in., a wall thickness of 0.153 in., and a yield strength of 53.8 ksi. If a factor of safety of 3.1 is required, determine the maximum pressure that the bottle may contain.

For the surface at B on the outlet pipe, the hoop stress is considered to be in the x direction.

For the following cylindrical vessel at surface A, the hoop stress is considered to be in the y direction.