The Secant Formula and Column Buckling

by Danielle Keirsey

Submitted : Spring 2010

Columns, in structural engineering, are defined as vertical structures that transfer the weight or load of the above structure to the foundation below through compression. The critical load or buckling load can be determined by using Euler’s buckling formula. In the case of real columns, the secant solution can solve this problem. This requires solving the following differential equation for a column assuming the boundary conditions are simply supported, which means at its ends the deflection is zero. After solving the differential equation, the maximum deflection can be calculated and the relationship between the deflection and eccentricity, as well as the relationship between the deflection and the load will be obvious.

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