Lecture 11

Question 1

What happens in plastic collapse?

Answer 1

A hinge forms where a crack would have

Shear bands form at 45degrees to the load

Question 2

What is flow stress?

Answer 2

The average of the yield stress and UTS

Question 3

Why are residual stresses a problem?

Answer 3

Whilst they are in balance, in certain orientations of loading they are additive with the load

Question 4

What assumptions are made in plastic collapse analysis?

Answer 4

• The material is perfectly plastic

- Small deformity theory can be applied to the structure (ie must be used on materials like steel, and not rubber)

Question 5

Which basic relations must be satisfied for the deformation of the structure to find the exact solution?

Answer 5

• Stress equilibrium and yield criterion (e.g. von Mises)
• Constitutive relation (stress as a function of strain)
• Strain compatibility

Question 6

Why are the lower and upper bound theories used?

Answer 6

To find a range for the solution

Question 7

What foes the lower bound solution assume?

Answer 7

Stress equilibrium only

Question 8

What does the upper bound solution assume?

Answer 8

A deformation failure mode must be assumed that satisfies the compatibility equations

Question 9

What equation gives the critical plastic collapse load?

Answer 9

Pcritical = B(W - a)*sigmaY

Area of ligament x yield stress

Question 10

What equation gives critical stress for plastic collapse in the lower bound tension solution?

Answer 10

sigmacritical = ((W - a)/W)*sigmaY

Question 11

What does the upper bound solution do/give?

Answer 11

• Equates the internal energy to external work done

- Solution is either correct or too high

Question 12

What is the equation for the critical moment in the lower bound bending solution?

Answer 12

Mcritical = 0.25B((W - a)^2)*sigmaY

Question 13

What is the equation for the critical moment in the upper bound bending solution?

Answer 13

Mcritical = 0.39B((W - a)^2)*sigmaY