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, d = 23 in., w = 13.5 in., and t = 6 in. There are five No. 7 longitudinal tension bars and No. 5 stirrups at 6 in. o.c.

Find the zeros of the function. (5 points) f(x) = x2 – 6x + 8  

Researchers studying reinforced concrete have considered a mechanical explanation of Vc to be the Holy Grail.

Find the exact value of sin-1(-0.5). (5 points)

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 20 in., five epoxy-coated No. 9 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 4,000-psi lightweight concrete and a clear cover of 2 in.

State how many imaginary and real zeros the function has. (5 points)f(x) = x4 – 15×2 – 16  

Use the change of base rule to find the logarithm to four decimal places. (5 points) log942.45

Find the amplitude y = -5 sin x. (5 points)

In a singly-reinforced concrete beam, the compressive load C can be calculated by _______.

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (5 points) f(x) = 2060 ⋅ 0.9906x