A 50-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.

The internal shear force V at a certain section of an aluminum beam is 45 kN. The beam’s centroid is located 54.40 mm above the bottom surface of the beam, and the moment of inertia is Iz = 398,300 mm4. Determine the shear stress at point H, which is located 30 mm above the bottom surface of the beam.

Two cylindrical beams each support a shear force of 15.7 N. The outside diameter of the hollow beam is 58 mm, and its wall thickness is 3 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 = 78 mm and a = 22 mm supports a load of P = 4.9 N at both ends. The beam has cross-sectional dimensions b = 2.0 mm and h = 8.5 mm. Determine the magnitude of the maximum horizontal shear stress in the beam.

Two identical beams are loaded with w on opposite ends. Which beam will have the shear force with the largest magnitude?

A polymer beam of length L = 74 mm and a = 24 mm supports a load of P = 2.5 N at both ends. The beam has cross-sectional dimensions b = 2.5 mm and h = 8.7 mm. Determine the magnitude of the maximum horizontal shear stress in the beam.

A concentrated load of P = 22 kN is applied to the upper end of a 5-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.

Loads P = 764 N and Q = 377 N act on an oak beam. Determine the magnitude of the largest shear force (consider both positive and negative values) in the beam. Let a = 0.4 m and b = 0.8 m.

The internal shear force V at a certain section of a steel beam is 80 kN, and the moment of inertia is 64,867,500 mm4. Determine the horizontal shear stress at point H, which is located L = 46 mm below the centroid.

A concentrated load of P = 22 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.