The straight line theory is a plastic calculation that gives a good estimate of the concrete and steel stresses at ultimate loads. It is used to calculate the stiffness, EI, at ultimate loads, for deflection calculations, and steel stresses, for use in crack-width or fatigue calculations.

A simply supported beam with dimensions of b = 16 in., h = 22 in., d = 19.5 in., and L = 24 ft supports a uniform service (unfactored) dead load of 2.066667 kips/ft including its own self weight plus a uniform service (unfactored) live load of 0.8 kips/ft. The beam is reinforced with three No. 8 Grade 60 bars. The concrete strength is 6,400 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 = 4,148.9 in.4.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 23 in., three galvanized No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 2 in.

At service loads, the reinforcing steel is in the elastic range of behavior.

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 24 in., four epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 12 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 1.5 in.

Failure of a hooked anchorage rarely involves crushing of the concrete inside the hook.

Cracks due to shear are able to cross into the compression zone of the member.

Vertical cracks that extend almost to the zero-strain axis of a member are likely _______ cracks.

For economy, some of the bars can be cutoff where they are no longer needed.

A rectangular beam has a cross section of b = 16 in., h = 22 in., and d = 19.5 in. It is reinforced with four No. 6 Grade 60 bars. The concrete strength is 7,900 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the gross moment of inertia, Ig, for the beam.