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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.

A rectangular beam has a cross section of b = 18 in., h = 28 in., and d = 25.5 in. It is reinforced with three No. 7 Grade 60 bars. The concrete strength is 9,700 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 4.6421 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. 8 Grade 60 bars. The concrete strength is 6,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the gross moment of inertia, Ig, for the beam.

A rectangular beam has a cross section of b = 16 in., h = 30 in., and d = 27.5 in. It is reinforced with five No. 8 Grade 60 bars. The concrete strength is 6,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the transformed cross-sectional area of the bars, Ast.

A simply supported beam with dimensions of b = 14 in., h = 26 in., d = 23.5 in., and L = 24 ft supports a uniform service (unfactored) dead load of 1.879167 kips/ft including its own self weight plus a uniform service (unfactored) live load of 0.9 kips/ft. The beam is reinforced with two No. 8 Grade 60 bars. The concrete strength is 6,400 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 = 5,030.2 in.4.