Euler's formula is used to determine the critical load of a column, and Secant's formula is used to calculate the deformations and stresses of a column under eccentric loadings.

Here, it was assumed that the column is initially a straight homogenous prism and all the stresses are within the proportional limit.

In real life, the materials of columns are not ideal, and the design of a column is based on an empirical formula derived from numerous laboratory experiments.

For example, the data of many steel columns are recorded for an applied centric load and increasing it until failure.

For large columns, Euler's formula can be used to predict the failure, and the critical stress depends on the modulus of elasticity.

On the other hand, for short columns, failure occurs majorly because of yield strength.

For the columns of intermediate lengths, failure is a complex process and it depends on both yield and the modulus of elasticity.

For each of the above cases, the empirical formula is modified slightly to design steel columns.