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

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

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?    

An aluminum CO2 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 y direction.

An aluminum CO2 bottle has an outside diameter of 3.25 in., a wall thickness of 0.156 in., and a yield strength of 59.1 ksi. If a factor of safety of 3.5 is required, determine the maximum pressure that the bottle may contain.

An unpressurized vessel is loaded by horizontal force Px = 60 N, vertical force Py = 160 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 = 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

A Pop-A-Shot ball with an inside diameter of 6.39 in. and wall thickness of 0.044 in. is constructed from a polymer that has a yield strength of 3.34 ksi. If the ball is inflated to a pressure of 5.4 psi, determine the factor of safety with respect to the yield strength.

A wooden ruler with length L = 12 in. carries loads Px = 15 lb and Py = 6 lb. The ruler has a rectangular cross section with a thickness of 0.200 in. and a height of 1.205 in. Determine normal stress σx on the bottom surface of the ruler at B.

A vessel is loaded by internal pressure p = 110 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 σx 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