Concrete Rectangular Columns

Columns are structural compression members which transmit loads from the upper floors to the lower levels and then to the soil through the foundations. Since columns are compression elements, failure of one column in a critical location can cause the progressive collapse of adjoining floors, and in turn, even the collapse of the entire structure.

The program generates the Pn-Mn nominal interaction diagram for a rectangular concrete column with up to five layers of reinforcing steel, and calculates the capacity of a short member when subjected to bending moment and axial load. The slenderness effect or secondary moments owing to the lateral deflection response under load are also considered.

Input Data

The input data required by the program includes the geometric characteristics of the section, the materials' properties and the applied combined ultimate loads, as shown in the figure below.

Example

As an example, consider the section shown below subjected to a bending moment of 200 k-ft and an axial load of 450 kips. f'c = 3000 psi, fy = 50 ksi. Find out if the section is adequate.

Output

Once the input data has been completed, choosing the Solve option from the Design menu can generate the tabulation of the interaction diagram. The figure to the right shows INT-DIAG program's template.

The program applies the appropriate ACI under-strength Phi factor to the applied loads in order to be compared with the nominal strength of the section. To determine a specific point of interest in the interaction diagram, enter a "k-Factor" value in the template, where the corresponding moment is calculated for a specified axial load. Note that "k" defines the position of the neutral axis as a fraction of "d" (measured from the top face).

In this example, the section is adequate to carry the imposed loads, since the point representing the acting loads appears into the useable area delimited by the interaction diagram and the coordinate axes.

Procedure

The following assumptions have been made:
a) Strains in reinforcement or concrete are directly proportional to the distance from the neutral axis.
b) Maximum useable strain at extreme concrete compression fiber is 0.003 in/in.
c) The Whitney rectangular stress distribution for concrete is used.
d) The elasto-plastic stress-strain relationship for reinforcing steel is used.
e) Tensile strength of concrete is neglected.

The interaction diagram is generated by defining several positions of the neutral axis and checking the external forces (P and M) for each condition that satisfies the equilibrium of forces. The program takes into account the correction of concrete forces for the area in the compression block displaced by vertical bars.