Plastic theory & collapse mechanisms

Question 1

When do buildings collapse?

Answer 1

Buildings collapse when a sufficient number of hinges form to produce a mechanism

Question 2

How can the load factor be calculated?

Answer 2

𝜆 = P_c/P
- P_c = critical load
- P = working load

Question 3

What happens when a beam collapses?

Answer 3

When beam collapses all work done by the external load is used to rotate the hinge

Question 4

What does energy conservation state?

Answer 4

External work = Internal work

Question 5

How can external work be calculated?

Answer 5

∑P*𝛿

Question 6

How can internal work be calculated?

Answer 6

∑M_p*𝜃

Question 7

In what case does only one hinge need to be formed?

Answer 7

For statically determinate

Question 8

In what case are more hinges needed for collapse?

Answer 8

For statically indeterminate

Question 9

How can lowest collapse load be found with respect to x?

Answer 9

By differentiating P_c

Question 10

When you have multiple collapse mechanisms how do you obtain the most critical one?

Answer 10

The lowest load factor

Question 11

What does the most critical mechanism depend on?

Answer 11

Depends on the relative magnitudes of the loads, the span size, and the number of hinges