Find the period of the function. y = -5 cos x (5 points)

A rectangular beam has a cross section of b = 16 in., h = 22 in., and d = 19.5 in. It is reinforced with two No. 7 Grade 60 bars. The concrete strength is 8,200 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracked moment of inertia, Icr. The neutral axis location of the cracked beam (measured from the top of the beam) is 3.6543 in.

A rectangular beam has a cross section of b = 14 in., h = 22 in., and d = 19.5 in. It is reinforced with three No. 5 Grade 60 bars. The concrete strength is 5,800 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the neutral axis location of the cracked beam (measured from the top of the beam).

A rectangular beam has a cross section of b = 16 in., h = 28 in., and d = 25.5 in. It is reinforced with three No. 8 Grade 60 bars. The concrete strength is 7,900 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracked moment of inertia, Icr. The neutral axis location of the cracked beam (measured from the top of the beam) is 5.7824 in.

Find all solutions in the interval [0, 2π). tan x + sec x = 1 (5 points)

Determine the lightweight modification factor, λ, for a rectangular beam with b = 17 in. and d = 24 in., three galvanized No. 9 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 8 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 2 in.

The straight line theory is a plastic calculation that gives a good estimate of the concrete and steel stresses at ultimate loads. It is used to calculate the stiffness, EI, at ultimate loads, for deflection calculations, and steel stresses, for use in crack-width or fatigue calculations.

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The fatigue strength of longitudinal bars is less than that of stirrups.

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.