People exercising can cause vibration problems in buildings.

Almost universally, all of the longitudinal bars in a column are the same size.

Tied columns may be any shape required.

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

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 = 240 kip and Mu = 80.0 kip-ft.b = 24 in.h = 20 in.fc’ = 4 ksify = 60 ksiγ = 0.75ρg = 0.03

For tied columns in nonseismic regions, ties are spaced roughly the width of the column apart.

A simply supported beam with dimensions of b = 18 in., h = 28 in., d = 25.5 in., and L = 23 ft supports a uniform service (unfactored) dead load of 2.225 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.4 kips/ft. The beam is reinforced with four No. 8 Grade 60 bars. The concrete strength is 6,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Using the effective moment of inertia, determine the immediate mid-span deflection of the beam due to the combined service loads (dead plus live).The effective moment of inertia Ie = 11,798 in.4.

A rectangular beam has a cross section of b = 16 in., h = 30 in., and d = 27.5 in. It is reinforced with five No. 7 Grade 60 bars. The concrete strength is 10,000 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the neutral axis location of the cracked beam (measured from the top of the beam).

Misalignment of columns from floor to floor cannot cause eccentricities in columns.

Use the interaction diagrams found in Appendix A of the textbook to determine whether the following rectangular tied column with bars in 2 faces can safely support a load of Pu = 312 kip and Mu = 249.6 kip-ft.b = 26 in.h = 12 in.fc’ = 4 ksify = 60 ksiγ = 0.6ρg = 0.02