Question

A beam is subjected to equal bending moments M = 6.5 kip-ft, as shown. The cross-section of the beam is also shown. The top rectangular area (1) has cross-section dimensions b1 x d1, as shown, where b1 = 6.5 in. and d1 =1.50 in. The left and right rectangular legs (2) and (3) are of dimensions b2 x d2 as shown, where b2=0.75 in. and d2=6.0 in. Determine: (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H, which is located yH = 1.0 in. below the z centroidal axis. State whether the normal stress at H is tension or compression. (c) the maximum bending stress produced in the cross section. State whether the stress is tension or compression. Calculate the cross-sectional areas A1, A2, and A3 for areas (1), (2), and (3), respectively. Answers: A1 = in.2. A2 = in.2. A3 = in.2.

Part 2 Determine the location of the y direction centroids of areas (1), (2), and (3) with respect to the reference axis at the bottom of the cross-section.

Part 3 Determine the centroid location in the y direction for the beam cross-section with respect to the reference axis at the bottom of the cross-section.

Part 4 Determine the moment of inertia Ic1 for area (1) about its own centroid, y1.

Part 5 Determine the moment of inertia Iz1 for area (1) about the z centroidal axis of the cross-section.

Part 6 Determine the moment of inertia Ic2 for area (2) about its own centroid, y2.

Part 7 Determine the moment of inertia Iz2 for area (2) about the z centroidal axis of the cross-section.

Part 8 Determine the moment of inertia Ic3 for area (3) about its own centroid, y3.

Part 9 Determine the moment of inertia Iz3 for area (3) about the z centroidal axis of the cross-section.

Part 10 Determine the moment of inertia Iz for the cross-section about the neutral axis.

Part 11 Determine the section moduli Stop and Sbot of the cross-section. Note which one is the controlling section modulus.

Part 12 Determine the bending stress at point H (positive if tensile, negative if compressive).

Part 13 Determine the maximum bending stress produced in the cross section. Make a note on paper of whether the stress is tension or compression. Note that the maximum bending stress is the bending stress with the largest absolute value. However, report the answer here using the correct sign according to the flexure formula.

Answer 1