A concentrated load of P = 34 kN is applied to the upper end of a 2-m-long pipe as shown. The outside diameter of the pipe is D = 330 mm and the inside diameter is d = 300 mm. Determine the magnitude of the maximum vertical shear stress in the pipe.

Two cylindrical beams each support a shear force of 12.3 N. The outside diameter of the hollow beam is 54 mm, and its wall thickness is 4 mm. Determine the diameter of the solid beam that would create the same value of Q in both beams.

Two cylindrical beams each support a shear force of 12.9 N. The outside diameter of the hollow beam is 54 mm, and its wall thickness is 6 mm. Determine the diameter of the solid beam that would create the same value of Q in both beams.

A polymer beam of length L = 75 mm and a = 29 mm supports a load of P = 4.2 N at both ends. The beam has cross-sectional dimensions b = 2.9 mm and h = 7.3 mm. Determine the magnitude of the maximum horizontal shear stress in the beam.

The magnitude of Q for a hollow circular cross section will be _______ the magnitude of Q for a solid circular cross section with the same outside diameter.

A 47-mm-diameter solid steel shaft supports the loads shown. The ground reactions and shear-force diagram are shown. Determine the magnitude of the maximum horizontal shear stress in the shaft.

Two bars have the same moment of inertia around their horizontal centroidal axes. The hollow bar has an outside diameter of 2.300 in. and a wall thickness of 0.460 in. Determine the diameter of the solid bar.

A polymer beam of length L = 72 mm and a = 23 mm supports a load of P = 4.0 N at both ends. The beam has cross-sectional dimensions b = 2.4 mm and h = 8.8 mm. Determine the magnitude of the maximum horizontal shear stress in the beam.

Two bars have the same moment of inertia around their horizontal centroidal axes. The hollow bar has an outside diameter of 1.275 in. and a wall thickness of 0.255 in. Determine the diameter of the solid bar.

For a beam with the cross-section shown (w = 15.0 in. and h = 22.0 in.), find the distance from the bottom surface of the beam to the centroid.