A beam has dimensions of b = 14 in., h = 28 in., d’ = 2.5 in., and d = 25.5 in. It is reinforced with 2 No. 5 bars on the compression side and 4 No. 8 bars on the tension side. The concrete strength is 3,100 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.205 in., determine the strain in the compression reinforcement, ε’s.

Compute φVn for the cross section shown. Assume f’c = 4,500 psi, fyt = 60,000 psi, b1 = 24 in., b2 = 13 in., d = 23 in., h1 = 6 in., h2 = 14 in., h3 = 8 in., t = 8 in., and that there are six No. 6 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 60,000 psi, b = 10 in., d = 26 in., and that there are four No. 7 longitudinal tension bars and No. 4 stirrups at 8 in. o.c.

; g(x) = 8x – 7Find f(g(x)). (5 points)

You are seeing this patient 2 years after initial treatment.  She has failed to respond to all medical treatment for her OA knee pain, it is significantly impacting her quality of life. The therapy that could be recommended by the American Academy of Orthopedics is:

Following your pitch presentation which of the following would you expect an investor or pitch competition judge to ask about your team?

Find the inverse of the function. f(x) = 2×3 – 4 (5 points)

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 35 in., b2 = 11 in., d1 = 6 in., d2 = 25 in., and that there are three No. 7 longitudinal tension bars and No. 3 stirrups at 6 in. o.c. The stirrup hooks are 90°.

Compute φVn for the cross section shown. Assume f’c = 5,000 psi, fyt = 40,000 psi, d = 28 in., w = 22.5 in., t = 4 in., and that there are four No. 7 longitudinal tension bars and No. 3 stirrups at 10 in. o.c.

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.