Design of Short Reinforced Concrete Columns With Small Eccentricity:

This design guide is intended to provide guidance for the safe design and economical construction of reinforced concrete columns with small eccentricity. Design of long columns or columns with large eccentricity is outside the scope of this design guide.

This design guide is based on the requirements of ACI 318.

To use this design guide the column being designed must first be defined as a short column, which is a column meeting one of the following conditions:

For braced structures the column's slenderness ratio, klu/r <= 34 - 12(M1/M2) <= 40.

For unbraced structures the column's slenderness ratio, klu/r <= 22 , [k > 1].

Where klu/r is the slenderness ratio, M1 and M2 are the end moments acting on the column.  M2 is the larger (in absolute value) of the two end moments.  klu is the effective length of the column and r is the radius of gyration of the column.

Next, the column must have small eccentricity.  For the column to have small eccentricity it must meet one of the following conditions:

For a spiral column the normalized eccentricity, Mu/Puh < 0.05.

For a tied column the normalized eccentricity, Mu/Puh < 0.1.

Where Mu is the moment on the column, Pu is the axial load on the column and h is the dimension of the column perpendicular to the axis of bending.

ACI 318 Code Requirements of Tied Columns:

• Longitudinal bars must have a clear distance between bars of at least 1.5 times the bar diameter, but not less than 1.5 in (3.81 cm).
• Ties must be at least no. 3 if the longitudinal reinforcement consists of no. 10 in size or smaller.  For bars larger than no. 10, or when bundles are used in the longitudinal reinforcement, the minimum tie size is no. 4.  (Note:  the maximum practical tie size is usually no. 5.)
• The concrete cover must be at least 1.5 in (3.81 cm) over the outermost surface of the tie steel.
• At least four longitudinal bars are needed for columns with square or circular ties.
• The ratio of longitudinal steel area to the gross column area, (reinforcement ratio, pg), must be between 0.01 and 0.08. [0.01 <= pg <=0.08]
• Center-to-center spacing of ties must not exceed the smallest of 16 longitudinal bar diameters, 48 diameters of the ties, or the smaller exterior column dimension.
• Every corner and alternating longitudinal bar must be supported by a tie corner.  The included angle of the tie cannot be more than 135 deg. (Note: this is not applicable to round tied columns)
• No longitudinal bar can be more than 6 in (15.24 cm) away from a bar that is properly restrained by a corner.

ACI Code Requirements For Spiral Columns:

• Longitudinal bars must have a clear distance between bars of at least 1.5 times the bar diameter but not less than 1.5 in (3.81 cm).
• The minimum spiral wire diameter is 3/8 in (0.953 cm).  (Note:  the maximum practical size is 5/8 in (1.59 cm) diameter.)
• The clear distance between sprials cannot exceed 3 in nor be less than 1 in.
• The concrete cover should be at least 1.5 in (3.81 cm) from the outermost surface of the spiral steel.
• At least six longitudinal bars are to be used for spiral columns.
• The ratio of the longitudinal steel area to the gross column area, (reinforcement ratio, pg), must be between 0.01 and 0.08. [0.01 <= pg <= 0.08].
• The ratio of volume of spiral reinforcement to the volume of the column core, (spiral reinforcement ratio,ps) must be: ps = 0.45(Ag/Ac-1)(f'c/fy).
• The spiral pitch, s to satisfy the spiral reinforcement ratio must be: s = (4Asp/psDc). Where Asp is area of spiral wire and Dc is diameter of core.

Common spiral wire sizes to use:

• For column diameter up to 15 in (38.1 cm), using no 10 longitudinal bars or smaller, spiral wire size = 3/8 in (0.953 cm).
• For column diameter up to 15 in (38.1 cm), using longitudinal bars larger than no 10, spiral wire size = 1/2 in (1.27 cm).
• For column diameter of 16 in (40.64 cm) to 22 in (55.88 cm), spiral wire size = 1/2 in (1.27 cm).
• For column diameter of 23 in (58.42 cm) and larger, spiral wire size = 5/8 in (1.59 cm).

Design Process:

• If the column size is not known, select a value of the reinforcement ratio, pg, between the limits of 0.01 and 0.08 and then solve for the required column area, Ag, required for the factored load, Pu, on the column.  The area of steel, Ast, can then be determined from the gross area, Ag, and the reinforcement ratio, pg, where, Ast = pgAg.
• If the column design is known, the column ultimate load, Pu, capacity can be determined from the area of steel, Ast and the gross area Ag.