Concrete Circular 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.

Although tied columns are most commonly used because of the lower construction costs, spirally bound circular columns are also used where increased ductility is needed, such as in earthquake zones. The ability of a spirally reinforced column to sustain the maximum load at excessive deformation prevents the complete collapse of the structure before total redistribution of moments and stresses is complete.

Failure in concrete columns could occur as a result of material failure or by loss of lateral structural stability. If a column fails due to material failure, it is classified as a short column, as opposed to the slender column whose failure is by buckling.

The program generates the axial load vs. bending moment interaction diagram of an unconfined circular concrete column, with uniform arrangement of non-prestressed reinforcing bars. The program takes into account the slenderness effects.

Input Data

The required input data includes the materials' properties, the applied factored loads and the geometric characteristics of the section such as the column diameter and number and size of reinforcing bars, as shown in the figure to the right.

The program also allows optional input where clear cover other than 1.5 inches, or where other than minimum size #3 or #4 circular ties or spirals are desirable. Thus, the results are directly applicable for precast columns with small cover or where severe exposure requires more concrete protection for reinforcement.

The actual layout of vertical bars has been conservatively selected as least effective overall to produce the lowest value in moment for steel areas.

Example

As an example, consider an 18" short spirally reinforced round column subject to an axial load of 165 k and a bending moment of 110 k-ft. It is reinforced with seven #8 vertical bars equally spaced as shown in thr figure below. Generate the interaction diagram and find out if the section is adequate. f'c = 4 ksi and fy = 60 ksi.

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 left shows the 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.

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 column section has been divided in a number of layers of the same thickness. The strain, and therefore the stress, is assumed to be constant in all the thickness of each segment and equal to that present at its mid-depth.

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.

The program generates the diagram with the actual curve stress-strain of the concrete rather than using the equivalent rectangular stress distribution. This is in recognition of the fact that the Whitney's stress block, although simpler, is not correctly applicable to non-rectangular compression areas, since the centroids of the actual and idealized blocks do not coincide.