The textbook discusses six methods commonly used to design rectangular columns subjected to biaxial loads.

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

Ties act as shear reinforcement for columns.

When a column is under compression, the column shortens and contracts laterally.

Determine the required splice length for the epoxy-coated longitudinal bars in the following tied column made of normal-weight 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 = 28 in.Column thickness, h = 16 in.Clear cover to ties = 1.5 in.Number of longitudinal bars = 6Size of longitudinal bars = No. 8Size of ties = No. 3Concrete strength = 9,000 psiYield strength of longitudinal bars = 60,000 psiYield strength of ties = 40,000 psi

Determine the maximum axial strength φPn,max for the following circular tie column.Column diameter, h = 24 in.Number of longitudinal bars = 16Size of longitudinal bars = No. 8Size of ties = No. 4Concrete strength = 6,500 psiYield strength of longitudinal bars = 60,000 psiYield strength of ties = 60,000 psi

Determine the required splice length for the galvanized 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 = 24 in.Clear cover to ties = 1.5 in.Number of longitudinal bars = 12Size of longitudinal bars = No. 7Size of ties = No. 3Concrete strength = 5,000 psiYield strength of longitudinal bars = 60,000 psiYield strength of ties = 40,000 psi

Tied columns are less ductile than spiral columns, giving tied columns a lower strength-reduction factor.

ACI 318-14 Section 25.7.2.1 specifies that ties shall have a center-to-center spacing not exceeding the least of 16db of longitudinal bar, 48db of tie bar, and largest dimension of member.

Determine the maximum pitch, s, for the spirals in the following circular column.Column diameter, h = 28 in.Clear cover to spirals = 1.5 in.Number of longitudinal bars = 16Size of longitudinal bars = No. 8Size of spiral = No. 3Concrete strength = 7,500 psiYield strength of longitudinal bars = 60,000 psiYield strength of spiral = 60,000 psi