Bending moment for pipes at various strain levels

[Tor Person]

Allowable moment (M) for elastic deformation is calculated as M = Section modulus x allowable stress. How to calculate the moment for plastic deformation e.g. in a bending machine?

 

[LittleInch]

You try substituting the yield stress values for the "allowable stress" values.

Once it goes plastic though all sorts of things start changing such as the section modulus, thickness, shape and hence it is a simple question with a complicated answer depending on how much plastic deformation and what sort of shape the metal thing (pipe? rod? beam?)is in the first place.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[JGard1985]

Agree with LittleInch, once you yield unless you assume some sort of bi-linear material with strain hardening, the stiffness at the plastic moment is essentially zero (i.e. its a mechanism). Plastic deflection isn't really a term. More often term is ductility (multiple of yield deflection) but this is often used for impulsive/impactive loads with energy methods, not long term force application.

Jeff
Pipe Stress Analysis
Finite Element Analysis

http://www.xceed-eng.com

 

[Chumpes]

once you go plastic you have to describe the effect of plastic strain on the bended object. going plastic can be seen as having an elongated material for which stress cannot go above YS. some quite simple mechanical calculations could then be used to describe the residual deflexion.

 

[Tor Person]

The attached chart is used in the offshore pipeline industry where plastic deformation and straightening is common with e.g. reeling in cases up to 2.5%. DNV specifications allows up tp 5% by using material with the additional requirement P (plastic).