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What does the symbol f​r ​represent in the transition from I​g​ to I​cr ​equation?

Compute the axial compressive strength Pn and moment capacity Mn of the following tied column when the largest strain in the concrete is 0.003 and the strain in the tension reinforcement is 0.003. Note that you should not include φ in the answer and that you should not consider Pn,max.b = 14 in.h = 22 in.Clear cover to ties = 1.5 in.Number of longitudinal bars = 6Size of longitudinal bars = No. 9Size of ties = No. 4Concrete strength = 8,500 psiYield strength of longitudinal bars = 60,000 psiYield strength of ties = 60,000 psi

Unbalanced moments in the beams cannot cause eccentricities in columns.

Use the interaction diagrams found in Appendix A of the textbook to determine whether the following rectangular tied column with bars in 2 faces can safely support a load of Pu = 312 kip and Mu = 249.6 kip-ft.b = 26 in.h = 12 in.fc’ = 4 ksify = 60 ksiγ = 0.6ρg = 0.02

Misalignment of the reinforcement can cause eccentricities in columns.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 10 No. 8 bars at a depth of 16 in. The top row contains 8 No. 6 bars at a depth of 11 in. Determine the effective (centroidal) depth, d, of the steel.

A simply supported beam with dimensions of b = 18 in., h = 28 in., d = 25.5 in., and L = 23 ft supports a uniform service (unfactored) dead load of 2.225 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.4 kips/ft. The beam is reinforced with four No. 8 Grade 60 bars. The concrete strength is 6,700 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 = 11,798 in.4.

Because designers have little control over the arrangement of the bars in a circular column, the interaction diagram should be computed for the most favorable bar orientation.

Tied columns are used when ductility is important or where high loads make it economical to utilize the extra strength from the higher φ factor.

Determine the required splice length for the epoxy-coated longitudinal bars in the following tied column made of lightweight concrete. Assume that some of the longitudinal bars are in tension and that the connection should be designed as a Class B contact lap splice. Use ACI 318-14 Table 25.4.2.2 to calculate the development length, and assume that the ties satisfy the Code minimum.Column width, b = 22 in.Column thickness, h = 18 in.Clear cover to ties = 1.5 in.Number of longitudinal bars = 14Size of longitudinal bars = No. 7Size of ties = No. 3Concrete strength = 7,500 psiYield strength of longitudinal bars = 60,000 psiYield strength of ties = 40,000 psi