12. Buckling

Question 1

What is buckling?

Answer 1

When a critical load is exceeded a beam or strut will become unstable and suddenly fail by bending sideways. This sudden unstable increase in deflection is buckling.

Question 2

What is Eulers critical buckling equation? How is deflection related to this equation?

Try to derive it!

Answer 2

Note:
* Derivivation shown and equation at the end
* See how the equation relates to a deflection of a half-sine waveform.
* The amplitude doesn’t matter in this case. It’s arbitary as the point of P = Pcrit, it is unstable anyway.

Question 3

What would the buckling modes for a simply supported beam look like for 2π, and 3π = nL, in eulers critical buckling formula and deflection? why might this not occur?

Answer 3

Note:
* This may not occur due to it requiring pinning in those positions so that it reaches 4Pcrit or 9Pcrit. Otherwise it will just buckle to the half sine wave at Pcrit.

Question 4

With regards to buckling what happens when:

• P<Pcrit
• P=Pcrit
• P>Pcrit

Answer 4

Question 5

Which direction will buckling occur?

Answer 5

The side with the smallest second moment of area.

Question 6

What is eulers cirtical buckling equation, when considering different boundary conditions?

Answer 6