Plastic Theory of Bending
It the
Though the actual stress-strain relationship in the plastic range is complex, an idealized elastoplastic material such as mild steel may be considered to have a stress- strain diagram as shown in figer.
Consisting of two straight-line segments. As long as the loading is in elastic range, the value of stress is less than the
Practically, a structure does not fail as soon as the stress at an edge of the weakest cross-section reaches the yield point. The structure continues to sustain the load as long as a
The assumptions made in the plastic theory are as follows:
1. The material has a single yield point and can undergo considerable strain at yield without further increase in stress.
2. The value of yield stress is the same in tension and compression.
3. Transverse sections remain plane throughout the loading so that the strain is proportional to the distance from the neutral axis.
4. The collapse of the whole structure does not take place till the formation of the plastic hinges at all the required points is not complete.
5. As a plastic hinge develops at any cross-section, the moment of resistance remains constant at that point till the collapse of the whole structure takes place.
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