A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 9 No. 6 bars at a depth of 16 in. The top row contains 7 No. 7 bars at a depth of 12 in. Determine the effective (centroidal) depth, d, of the steel.

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, b1 = 27 in., b2 = 11 in., d1 = 6 in., d2 = 17 in., and that there are three No. 6 longitudinal tension bars and No. 3 stirrups at 7 in. o.c. The stirrup hooks are 90°.

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x + 14)2 (5 points)

Use ACI 318-14 Table 25.4.2.2 to determine the development length for the straight tension bars (no hooks) in a rectangular beam with b = 16 in. and d = 24 in., five galvanized No. 6 Grade 60 bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 6 in. along the span. Assume 8,000-psi lightweight concrete and a clear cover of 1.75 in.

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?

Identify the cardiac cell structure outlined in BLACK and indicated with a BLACK arrow.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 28 in., b2 = 14 in., d = 49 in., h1 = 4 in., h2 = 42 in., h3 = 8 in., and t = 7 in. There are six No. 6 longitudinal tension bars and No. 4 stirrups at 11 in. o.c.

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. (5 points)

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 12 in., d = 27 in., and that there are four No. 9 longitudinal tension bars and No. 4 stirrups at 10 in. o.c. The stirrup hooks are 135°.

Find the inverse of the function. f(x) = 5×3 – 3 (5 points)