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It’s relatively easy to estimate the natural frequency of a floor if its mass can be calculated.

Crack widths are a concern for several reasons. Which of the following is NOT one of these reasons?

The major serviceability limit states in reinforced concrete are caused by excessive deflections, excessive crack widths, and undesirable vibrations.

States at which the structure becomes unfit for its intended function are called limit states.

A simply supported beam with dimensions of b = 18 in., h = 22 in., d = 19.5 in., and L = 21 ft supports a uniform service (unfactored) dead load of 1.4125 kips/ft including its own self weight plus a uniform service (unfactored) live load of 0.8 kips/ft. The concrete is normal-weight concrete. The beam is reinforced with 2 No. 5 bars. The concrete strength is 9,100 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the maximum applied bending moment due to the combined service loads (dead plus live), Ma.      

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

A rectangular beam has a cross section of b = 14 in., h = 28 in., and d = 25.5 in. It is reinforced with two No. 6 Grade 60 bars. The concrete strength is 2,800 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracking moment, Mcr.

A rectangular beam has a cross section of b = 14 in., h = 24 in., and d = 21.5 in. It is reinforced with four No. 6 Grade 60 bars. The concrete strength is 4,000 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the modulus of rupture of the concrete, fr.

Excessive deflections can lead to cracking of partitions but not malfunctioning of doors and windows.

A rectangular beam has a cross section of b = 18 in., h = 26 in., and d = 23.5 in. It is reinforced with four No. 6 Grade 60 bars. The concrete strength is 5,200 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the assumed modulus of elasticity of the concrete, Ec.