Plastic Theory of structure analysis- A short introduction

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Here is a brief introduction to the plastic Theory of structure analysis.

• Plastic Theory of structural analysis:

Any ductile material like steel, after reaching the yield point undergoes plastic strain. After following a certain path the stress strain curve will end up at a certain distance from the yield point.
This path of the curve is known as the plastic region of the stress strain curve.
The highest stress value before reaching the rupture is known as the ultimate strength of the material.

In simple theory of bending, we assume that stress and strain vary linearly along the cross section of the steel along its depth. Stress is zero at the neutral axis and maximum at the extreme fibers.

After the stress reaches the yield point the extreme fibers will not take any further stress but the internal fibers still have not reached the yield stress so, the plastic strain will start when the every layer reaches the yield stress.

Plastic Theory of Structural Analysis

This produces another stress diagram which is shown in the figure above(first from right). For the third diagram the moment of resistance is calculated which is known as the plastic moment of resistance. 

• Load Factor: The ratio of the plastic moment of resistance to the working moment of resistance is known as the load factor. For a rectangular cross section beam this value comes out to be 1.5(fy/fb). So, if fy/fb = 1.5, then Load factor = 2.5

• Shape Factor: The ratio of the plastic moment to the yield moment is known as the Shape factor. Mp/My is known as shape factor. It may be remembered that shape factor is the property of a section which depends only upon the geometry of the cross section.

• Collapse Load:

Once the section reaches the plastic stage, it acts likes a plastic hinge. So, to analyse a structure we have to form the plastic hinges at the place where bending moment takes up the maximum values. These hinges take up the moment equal to plastic moment and after that they will collapse. 

The theory behind the analysis of the collapse load is very simple. The external work done is equal to the internal work done. That means collapse load multiplied by the corresponding displacement is equal to the plastic moment multiplied by the respective rotation of the joints. 

It will not be possible to show here an example to you so, let's keep that to future.

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