Plastic Collaspe Flashcards

1
Q

What happens in plastic collapse?

A

A hinge forms where a crack would have
Shear bands form at 45degrees to the load

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2
Q

What is flow stress?

A

The average of the yield stress and UTS

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3
Q

Why are residual stresses a problem?

A

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

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4
Q

What assumptions are made in plastic collapse analysis?

A

-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)

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5
Q

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

A

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

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6
Q

Why are the lower and upper bound theories used?

A

To find a range for the solution

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7
Q

What foes the lower bound solution assume?

A

Stress equilibrium only

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8
Q

What does the upper bound solution assume?

A

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

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9
Q

What equation gives the critical plastic collapse load?

A

Pcritical = B(W - a)*sigmaY
Area of ligament x yield stress

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10
Q

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

A

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

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11
Q

What does the upper bound solution do/give?

A

-Equates the internal energy to external work done
-Solution is either correct or too high

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12
Q

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

A

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

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13
Q

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

A

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

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