An unpressurized vessel is loaded by horizontal force Px = 60 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 = 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

A 62-year-old female patient is recovering from a complex brainstem surgery to remove a benign tumor located near the junction of the pons and medulla. Postoperatively, she experiences difficulty swallowing, hoarseness, and a loss of the gag reflex on the right side. She also complains of diminished taste sensation in the posterior third of her tongue and impaired movement of her soft palate. The attending physician explains to the student that multiple cranial nerves emerge directly from the brainstem, and in this case, nerves involved in swallowing, laryngeal control, and posterior taste sensation have likely been affected. Question: To accurately localize the neurological impact of this surgery, the  student must recall how many pairs of cranial nerves originate directly from the brain and brainstem. What is the correct number?    

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.