Three toy blocks are stacked to form a channel shape. Each block has dimensions a = 23 mm and b = 69 mm. Determine the vertical distance from the table to the centroid of the shape.

A 62-lb child and a 167-lb adult are on an oak beam. Determine the magnitude of the largest shear force (consider both positive and negative values) in the beam. Let a = 25 in., b = 54 in., and c = 21 in.

A toy block and a cylinder are stacked to form a composite shape. The block has dimensions a = 25 mm and b = 75 mm. The cylinder has a diameter of b/2. Determine the moment of inertia about the horizontal centroidal axis for the shape which is located 58.351 mm above the table.

Load P = 0.8 lb is produced at the tip of a mallet as a percussionist strikes an instrument. The tip of the mallet is a rubber ball. The wooden shaft has a diameter of 0.30 in. and a length of L = 4.5 in. from the center of the tip to the percussionist’s hand. Assuming the percussionist’s hand acts like a fixed support, determine the maximum bending stress in the shaft.

A polymer beam of length L = 80 mm supports a load of P = 3.4 N at its center. The beam has cross-sectional dimensions b = 2.0 mm and h = 8.7 mm. Determine the magnitude of the horizontal shear stress at H, which is located a = 1.7 mm from the top.

A composite beam consists of a Southern pine [E = 9.0 GPa] timber that is reinforced on its lower surface by a steel [E = 200 GPa] plate. Assume the following dimensions:b1 = 150 mmd = 325 mmb2 = 100 mmt = 14 mmCalculate the distance to the centroid of the transformed section from the bottom surface of the steel plate.

If Mz = 35,800 lb-ft, find the magnitude of the bending stress at a point H. For the beam cross section, assume b = 8.750 in. c = 3.500 in. d = 6.125 in.t = 0.875 in. The centroid of the cross section is located 3.250 in. above the bottom surface of the beam. The moment of inertia about the z axis is 107.2992 in.4.

A polymer tee beam has cross-sectional dimensions a = 1.7 mm, b = 7.9 mm, c = 2.1 mm, and d = 3.0 mm. The vertical distance from the bottom of the beam to the centroid is 5.5466 mm. Determine the moment of inertia around a horizontal axis located at the centroid.

A composite beam consists of a Southern pine [E = 7.5 GPa] timber that is reinforced on its lower surface by a steel [E = 200 GPa] plate. Assume the following dimensions:b1 = 175 mmd = 350 mmb2 = 125 mmt = 12 mmCalculate the distance to the centroid of the transformed section from the bottom surface of the steel plate.

Load P = 8.0 lb is produced at the nylon tip of a Regal Tip Quantum 1000 drumstick as a percussionist strikes a drumhead. The hickory shaft has a diameter of 0.53 in. and a length of L = 10.0 in. from the center of the tip to the percussionist’s hand. Assuming the percussionist’s hand acts like a fixed support and that the shaft has a constant diameter, determine the magnitude of the maximum horizontal shear stress in the shaft.