When a section cracks, its moment of inertia decreases, leading to a decrease in the stiffness of the beam.

At a point subjected to plane stress, the stresses are σx = –60 MPa, σy = –40 MPa, and τxy = 100 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 7 No. 7 bars at a depth of 20 in. The top row contains 3 No. 6 bars at a depth of 16 in. Determine the effective (centroidal) depth, d, of the steel.

Vertical stirrups are preferable over inclined stirrups when _______.

Use the interaction diagrams found in Appendix A of the textbook to determine whether the following rectangular tied column with bars in 4 faces can safely support a load of Pu = 780 kip and Mu = 608.4 kip-ft.b = 12 in.h = 26 in.fc’ = 4 ksify = 60 ksiγ = 0.75ρg = 0.04

Cracks in a member lower the member’s moment of inertia, thereby decreasing the member’s stiffness.

A simply supported beam with dimensions of b = 14 in., h = 28 in., d = 25.5 in., and L = 18 ft supports a uniform service (unfactored) dead load of 2.008333 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.5 kips/ft. The beam is reinforced with five No. 5 Grade 60 bars. The concrete strength is 7,900 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the effective moment of inertia, Ie.The cracked moment Mcr = 101.6 kip-ft, and the maximum applied bending moment due to the combined service loads (dead plus live) Ma = 142.1 kip-ft. The neutral axis location of the cracked beam (measured from the top of the beam) is 5.0866 in.

Cracks in a member increase the member’s moment of inertia, thereby decreasing the member’s stiffness.

A rectangular beam has a cross section of b = 16 in., h = 26 in., and d = 23.5 in. It is reinforced with four No. 8 Grade 60 bars. The concrete strength is 7,000 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracking moment, Mcr.

Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 60,000 psi, b1 = 29 in., b2 = 13 in., d1 = 7 in., d2 = 14 in., and that there are three No. 9 longitudinal tension bars and No. 3 stirrups at 6 in. o.c.