Write the quadratic function in vertex form. y = x2 – 16x + 57 (5 points)

Determine the lightweight modification factor, λ, for a rectangular beam with b = 16 in. and d = 21 in., three epoxy-coated No. 7 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 5,000-psi lightweight concrete and a clear cover of 1.5 in.

A simply supported beam with dimensions of b = 16 in., h = 26 in., d = 23.5 in., and L = 18 ft supports a uniform service (unfactored) dead load of 2.133333 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.0 kips/ft. The concrete is normal-weight concrete. The beam is reinforced with 3 No. 5 bars. The concrete strength is 3,100 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the maximum applied bending moment due to the combined service loads (dead plus live), Ma.      

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b = 16 in. and d = 35 in. There are four No. 7 longitudinal tension bars and No. 5 stirrups at 12 in. o.c.

A rectangular beam has a cross section of b = 16 in., h = 22 in., and d = 19.5 in. It is reinforced with three No. 6 Grade 60 bars. The concrete strength is 3,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. Determine the strength φMn for this beam.

If φVc = 67 kip and Vu = 17 kip, are stirrups required?

When the steel ratio is small, flexural cracks extend higher into the beam and open wider.

A simply-supported beam has a 5 kip/ft uniformly-distributed load over the left half of its 9-ft span. What is the magnitude of the maximum shear force in the beam?

Simplify the expression. (5 points)

The textbook author recommends the use of 135° stirrups throughout, except in certain cases where 180° stirrups are needed to prevent overlap.