Columns with Lateral loads(Beam Columns)

Hi,
Columns with the lateral/transverse/horizontal loading are known as the beam columns. These columns can be analysed by using the differential equation of the elastic curve. Consider a pinned ends columns, applied with axial thrust P, and a transverse central point load W at center C.

• Steps:

1.  Write down the equation of the bending moment at any point x distant from the end A.
2.  Write down the differential equation in the form of moment and then write down the solution of it. The solution of the equation gives the deflection at any point on the beam.
3.  If you differentiate the deflection equation it will give you the slope.
4. There will two constants of integration in equation in the second step, which you have to find out by the condition that, when x =0, y= 0 and when x=l/2, dy/dx = 0.
5. Finally when the deflection equation is ready, you can find out the maximum deflection also.
6. Find out the maximum bending moment and then using maximum bending moment you can find out the maximum stress in the column.

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