A rectangular beam with cross section b = 14 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 1.70 kips/ft, including its own dead load. The beam is simply supported with a 18-ft span. It is reinforced with four No. 5 Grade 60 bars, two 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 7,200 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 four bars is φMn = 106.4 kip-ft, and the strength of the remaining two bars is φMn = 53.8 kip-ft. If the distance from the support to the theoretical cutoff point is 4.792 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

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).

Graph the expression sec2 x – sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression. (5 points)

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A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 2.00 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with four No. 7 Grade 60 bars, two 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 3,000 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 four bars is φMn = 169.9 kip-ft, and the strength of the remaining two bars is φMn = 89.74 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

You have 2 hours to complete this exam. Please submit a 500 word novel summary here.  The summary should not have any quotes.  It should give an overview of the plot of the novel that you chose to read. This essay must be in MLA format. The essay may be organized in any manner that you choose.  It can have any number of paragraphs that you would like.   Please be sure to include all major characters and events.  You may include pertinent details, minor characters, and minor events as you choose.

Determine the lightweight modification factor, λ, for a rectangular beam with b = 16 in. and d = 23 in., five galvanized No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 6,000-psi normal-weight concrete and a clear cover of 2 in.

Which type of reinforcement is frequently used in bridge decks?

Use the arc length formula and the given information to find r. s = 12 cm, θ = 36°; r = ? (5 points)  

A rectangular beam has a cross section of b = 16 in., h = 28 in., and d = 25.5 in. It is reinforced with two No. 5 Grade 60 bars. The concrete strength is 4,600 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. Determine the strength φMn for this beam.