Buckling

Question 1

A mass is supported at the top of a bar, length L, by a spring k and rotational spring kr at the base of the bar, what is the force applied vertically down on the mass which causes the bar to buckle?

Answer 1

F* = kL + kr/L

Question 2

What is the natural frequency of a system at buckling load?

Answer 2

Zero

Question 3

A mass is supported at the top of a bar, length L, by a spring k and rotational spring kr at the base of the bar, what is the equilibrium position of the mass after buckling?

Answer 3

x* = +- acos (F/kL)

Question 4

How do you determine the maximum vertical force before buckling of a rigid bar?

Answer 4

Draw a free body diagram which assumes rotation ϴ and find moment balance

Question 5

For a hinged bar (2 sections) with vertical force applied at the top, how must the free body diagram be constructed?

Answer 5

One with both sections displaced and one which is just the displaced upper section

Question 6

What is snap through buckling?

Answer 6

A type of instability in which an elastic system under load will snap from one equilibrium state to another

Question 7

What is an example of snap through buckling?

Answer 7

A jumping popper toy

Question 8

What is snap back buckling?

Answer 8

When crack formation dissipates more energy than is used forming the crack, so load and displacement simultaneously reduce to counter this

Question 9

What is a downside of assuming symmetry in buckling analysis?

Answer 9

The symmetrical buckling system may fail at a larger load than the non-symmetrical, meaning the capacity is overestimated