If M = 7.5 kip-ft, find the magnitude of the bending stress at a point 1.56 in. above the bottom surface of the beam. The moment of inertia about the z axis is 124.9 in.4, and the centroid of the section is located 4.7 in. above the bottom surface of the beam.

For the shape shown, b = 14 in. and d = 8 in. Calculate the vertical distance from point H to the z centroidal axis.

An aluminum [E = 13,570 ksi] bar is bonded to a steel [E = 29,950 ksi] bar to form a composite beam as shown. The composite beam is subjected to a bending moment of M = +442 lb-ft about the z axis. If the centroid of the equivalent all-aluminum beam is 0.594 in. above the bottom surface of the beam, and the moment of inertia about the z axis of the equivalent all-aluminum beam is 0.1791 in.4, find the magnitude of the maximum bending stress in the steel.

For the shape shown, b = 16 in. and d = 5 in. Calculate the vertical distance from point H to the z centroidal axis.

Use the graphical method to construct the shear-force and bending moment diagrams and identify the magnitude of the largest bending moment (consider both positive and negative peaks). Use w = 250 lb/in., a = 0.750 in. and b = 1.750 in. The reaction forces for this beam are Ay = Dy = 218.75 lb (both upward).

If M = 9.5 kip-ft, find the magnitude of the bending stress at a point 2.12 in. above the bottom surface of the beam. The moment of inertia about the z axis is 124.9 in.4, and the centroid of the section is located 4.7 in. above the bottom surface of the beam.

For the shape shown, b = 12 in. and d = 5 in. Calculate the vertical distance from point H to the z centroidal axis.

Use the graphical method to construct the shear-force and bending moment diagrams and identify the magnitude of the largest bending moment (consider both positive and negative peaks). Use w = 280 lb/in., a = 1.000 in. and b = 1.125 in. The reaction forces for this beam are Ay = Dy = 157.5 lb (both upward).

A 67-lb child and a 30-lb cardboard box are on an oak beam. Determine the vertical reaction force at the right end of the beam. Let a = 20 in., b = 27 in., and c = 43 in.

A steel pipe (D = 3.500 in.; d = 3.068 in.) supports a concentrated load of P = 621 lb as shown. The span length of the cantilever beam is L = 3 ft. Determine the magnitude of the maximum bending stress in the pipe.