For a beam with the cross-section shown (w = 15.5 in. and h = 23.0 in.), find the distance from the bottom surface of the beam to the centroid.

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.

A polymer beam of length L = 70 mm and a = 24 mm supports a load of P = 2.7 N at both ends. The beam has cross-sectional dimensions b = 2.0 mm and h = 7.5 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 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.

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 = 31 mm below the centroid.

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 29-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.

Loads P = 757 N and Q = 443 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 = 0.6 m and b = 1.0 m.

The internal shear force V at a certain section of an aluminum beam is 48 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.