Write the following trigonometric expression in terms of sine and cosine, and then simplify. ​ sin 2 x (1 + cot 2 x)

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 17 in. and d = 22 in., five epoxy-coated No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 10 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 2 in.

What is the easiest way to test the bond strength of bars in a laboratory?

Find the fourth roots of 16(cos 200° + i sin 200°). (5 points)

A rectangular beam with cross section b = 16 in., h = 28 in., and d = 25.5 in. supports a total factored uniform load of 1.40 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with five No. 5 Grade 60 bars, three of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 5,400 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. The strength of the five bars is φMn = 173.4 kip-ft, and the strength of the remaining two bars is φMn = 70.44 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Use an addition or subtraction formula to find the exact value of the expression. ​

Find the zeros of the function. (5 points) f(x) = x2 + 9x + 20  

Which type of reinforcement is frequently used in bridge decks?

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.

Solve the exponential equation. Express the solution set in terms of natural logarithms.4 x + 4 = 5 2x + 5