For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 15 in., d = 29 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 8 in. o.c. The stirrup hooks are 135°.

A beam has dimensions of b = 18 in., h = 24 in., and d = 21.5 in. and is reinforced with 4 No. 7 bars. The concrete strength is 9,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 0.970285 in. and the strain in the reinforcement is εs = 0.040209, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

Rigid end zones are commonly used in the structural analysis of reinforced concrete beams and columns.

Shrinkage cracks perpendicular to the span of the one-way design strips will be crossed by flexural reinforcement, which will limit the width of the cracks.

A concrete cover of at least one bar diameter is required to sufficiently bond the reinforcement to the concrete.

Simply supported beams loaded with only gravity loads develop positive bending moments throughout the span.

A beam has dimensions of b = 20 in., h = 12 in., and d = 9.5 in. and is reinforced with 4 No. 9 bars. The concrete strength is 3,800 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 4.371 in., does the reinforcement yield?

A beam has dimensions of b = 16 in., h = 24 in., and d = 21.5 in. and is reinforced with 2 No. 6 bars. The concrete strength is 9,100 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the strength Mn for this beam.

A classmate has suggested a beam design that has dimensions of b = 12 in., h = 26 in., and d = 23.5 in. and is reinforced with 5 No. 10 bars. Assuming a cover of 1.5 in. and a stirrup diameter of 0.5 in., does the reinforcement fit within a single row as suggested?

A beam has dimensions of b = 14 in., h = 26 in., and d = 23.5 in. and is reinforced with 3 No. 5 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the strength Mn for this beam.