| Summary: | Our objective in this paper is to solve a second order differential equation for a long, simply supported column member subjected to a lateral axial load using Heun's numerical method. We will use the solution to find the critical load at which the column member will fail due to buckling. We will calculate this load using Euler's derived analytical approach for an exact solution, as well as Euler's Numerical Method. We will then compare the three calculated values to see how much they deviate from one another. During the critical load calculation, it will be necessary to calculate the moment of inertia for the column member.
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