How to Design a Circular RC Column for Bending?

It is relatively straightforward to do a hand calculation of bending moment resistance (or required tensile reinforcement) for a rectangular RC column. But how about a circular one? How can you calculate the bending resistance and depth to rebar in a circular coordinate system? Well, there is an easy approximate way to do this, called the Whitney method. 

Whitney Method Procedure

The Whitney method is based on converting a circular RC column to an equivalent rectangular column which is much easier to design by hand calculation methods.

For a given circular RC column with diameter D, you can convert it into an equivalent rectangular beam section as illustrated below. The transformed height, H*, is 80% of the original column diameter. The width is adjusted so that you get the same area of the original circular column.

Half of the rebars are moved to the bottom of this new section, and the other half to the top. The distance between the steel rebars is { 2/3 times original column diameter }.
Once you have the equivalent rectangular section, you can easily calculate the bending moment resistance. See an example below.

Example

Below is our example circular column, with 8no. H32 rebars, fy = 500 N/mm2. Let's say that the design yield strength of the rebar is fyd = fy / 1.15 = 435 N/mm2 for this example.

Following the rules mentioned above, we can get a transformed rectangular section.

We can get a good estimate of the design-resisting moment as:

Area of steel in tension,

Resisting moment,

Let's approximate the lever arm,

Therefore,