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).

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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.

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

A simply supported beam with dimensions of b = 14 in., h = 30 in., d = 27.5 in., and L = 24 ft supports a uniform service (unfactored) dead load of 1.5375 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.2 kips/ft. The beam is reinforced with two No. 5 Grade 60 bars. The concrete strength is 7,600 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Using the effective moment of inertia, determine the immediate mid-span deflection of the beam due to the combined service loads (dead plus live).The effective moment of inertia Ie = 8,000 in.4.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 17 in. and d = 20 in., three epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 40 stirrups located every 12 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.5 in.

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 22 in., four epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 40 stirrups located every 12 in. along the span. Assume 4,000-psi lightweight concrete and a clear cover of 1.75 in.