Chapter 9.4, Problem 76P

Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case.

In order to increase the strength of the pressure vessel, filament winding of the same material is wrapped around the circumference of the vessel as shown. If the pretension in the filament is T and the vessel is subjected toan internal pressure p, determine the hoop stresses in the filament and in the wall of the vessel. Use the free-body diagram shown, and assume the filament winding has a thickness t and width w for a corresponding length L of the vessel.

The wide-flange beam is subjected to the 50-kN force. Determine the principal stresses in the beam at point A located on the web at the bottom of the upper flange. Although it is not very accurate, use the shear formula tocalculate the shear stress.

The steel pipe in (Figure 1) has an inner diameter of 3.41 in and an outer diameter of 3.66 in. If it is fixed at C and subjected to the horizontal 60-lb force acting on the handle of the pipe wrench at its end, determine the principal stresses in the pipe at point A, which is located on the outer surface of the pipe.

A thin hollow spherical container has a diameter 1 m and a thickness of 4 mm is subjected to an internal pressure. Determine the internal pressure the tensile stress of the element in the sphere is 500 kPa.

The cylindrical tank with a spherical end cap has an outer radius of 2 m and a wall thickness of 50 mm. If the tank is pressurized to 3.5 MPa, determine the longitudinal and circumferential stresses in the cylinder, and the stress in the end cap.   (Show free body diagram and complete solution)

Determine the normal and shear stresses at point Aand B. The cross-section of the bar is 12x12 mm.

The gas storage tank is fabricated by bolting together two half cylindrical thin shells and two hemispherical shells as shown. If the tank wall has a thickness of 50 mm for cylindrical and hemispherical shells, The bolts were installed as 40 bolts/meter. The tank and the 25 mm diameter bolts are made from material having an allowable normal stress of 150 MPa and 250 MPa, respectively. The tank has an inner diameter of 4 m. What is the maximum pressure that tank can contain.

If the box wrench is subjected to the 50-lb force, determine the principal stresses and maximum in-plane shear stress at point B on the cross section of the wrench at section a–a. Specify the orientation of these states of stress and indicate the results on elements at the point.