Lesson #34

Reading: 13: 1-3

 

 

Column Buckling

 

When a beam or column experiences a compressive load, it can become unstable and buckle or bow, resulting in large displacements.  This could result in the member collapsing or at least failing to perform its intended function.  We would like to be able to predict these types of failures.

 

Let’s consider a simply supported beam with a compressive load and look at the deflection problem.

 

 

As P is increased, we will eventually reach the point of instability.  At this point, with any disturbance or imperfection, large displacements could result.

 

 

These displacements result in bending moments in the beam.

 

 

Make a cut in the beam at an arbitrary location x and draw a free body diagram of one part of the beam.

 

SM = 0:     M + P v = 0

 

                   M = - P v

 

 

 

Now apply the second order differential equation.

 

E I v’’ = M = - P v

 

 

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