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For a beam with the cross-section shown (w = 15.0 in. and h = 23.5 in.), find the distance from the bottom surface of the beam to the centroid.

A 14-ft-long simply supported timber beam carries a P = 10.5-kip concentrated load at midspan as shown. The cross-sectional dimensions of the timber are also shown. At section a-a, determine the magnitude of the shear stress in the beam at point K.

A polymer beam of length L = 76 mm and a = 23 mm supports a load of P = 4.0 N at both ends. The beam has cross-sectional dimensions b = 2.3 mm and h = 7.2 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 3.500 in. and a wall thickness of 0.700 in. Determine the diameter of the solid bar.

Two identical beams are loaded with w and 2w. Which beam will have the shear force with the largest magnitude?

Two bars have the same moment of inertia around their horizontal centroidal axes. The hollow bar has an outside diameter of 1.750 in. and a wall thickness of 0.350 in. Determine the diameter of the solid bar.

A polymer beam of length L = 70 mm and a = 30 mm supports a load of P = 5.0 N at both ends. The beam has cross-sectional dimensions b = 2.0 mm and h = 8.9 mm. Determine the magnitude of the maximum horizontal shear stress in the beam.

A 38-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 = 670 N and Q = 492 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 = 1.0 m.

A 37-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.