Increased yield strengths of reinforcing steels have increased the importance of the Serviceability Limit State in reinforced concrete design, with SLS reinforcement stresses, crack widths, or deflections often controlling the design.

Elastic analysis of a rectangular section under pure bending can be solved easily with a quadratic equation, but for more complex shapes or combined bending and axial load an iterative process is normally used to determine the position of the neutral axis and section strains and stresses.

Click on: RC NA Depth for a paper presenting closed form solutions for any symmetrical reinforced concrete section, with any number of layers of reinforcement, under combined bending and axial load.

An extract from the paper is shown below:

Future posts will describe how these equations can be conveniently solved in an Excel VBA UDF, including calculation of concrete and reinforcement strains and stresses.