Plastic Modulus 4

[WARose]

What would you say is a generally accepted value for the plastic modulus of structural steel (A36 or A992)? The elastic is 29,000 ksi......but I am having a difficult time finding an agreed upon value for Ep .

 

[DaveAtkins]

As far as I know, there is no such thing as the plastic modulus of elasticity. Once steel yields, the stress-strain curve is no longer linear.

DaveAtkins

 

[WARose]

A book I have sort of approximates one by a straight line from the proportional limit to the failure stress.

 

[desertfox]

hi see this link

http://www.engineersedge.com/material_science/section_modulus_12893.htm

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[gravityandinertia]

What you are talking about is called the tangent modulus as a way of approximating things. If you are looking for a rough estimate a lot of times these are assumed to be 10% of the elastic modulus. However, you will need to use appropriately large factor safeties for anything on this if you are not sure about the real value of it.

 

[gravityandinertia]

If you have a more specific question on a type of problem you are working on, I have dealt with some analyses like this in the past.

 

[WARose]

Thanks for the info gravityandintertia. I was coming out with more than 10%......so I will take your advice to heart.

 

[gravityandinertia]

Keep in mind 10% is when you don't have anything else to go off. If you know the yield stress, yield strain, failure strain, and failure stress, you can calculate the tangent modulus as well.

 

[grogannc]

I used to do a lot of work in the non-linear region. As said you would be talking about the tangent modulus using ultimate stress/strain. This would be what material models define as a bi-linear curve that you see in FEA a lot. The interesting part of non-linear analysis is that beyond yield the additional stress isn't all that helpful. In most cases when looking at engineering stress-strain curves it doesn't get you all that much. Energy absorption is what you are after at that point but then you are talking transient loads. A common criteria or measure of this would be the ductility ratio which is more or less the strain of interest in the plastic region divided by the strain at the proportional limit. I'm rambling at this point.

 

[rb1957]

Ramberg-Osgood parameters ?

What type of structure are you looking at ?

We're not looking at plastic bending, right?

another day in paradise, or is paradise one day closer ?

 

[WARose]

rb1957: no, it's not a bending situation......just axial compression (i.e. impact). I found a way to estimate stress after the plastic wave front had passed.....but I needed to get an idea as to Ep.

 

[daranguiz]

Try EN 1993-1-5 . Annex C. Paragraph c.6

the angles of the curve are: atan(E) and atan (E/10000).

 

[rb1957]

a compression member going plastic and not buckling ?

Ramberg-Osgood parameters are a way of modelling the elastic-plastic material curve.

another day in paradise, or is paradise one day closer ?

 

[daranguiz]

@rb1957 it can happen for not very slender columns. That's why in the AISC or Eurocode the buckling curve only start following the Bleich or Euler shape after a certain value of slenderness.

 

[rb1957]

agreed, just not typical design (for me) ... Etan is a good approach

another day in paradise, or is paradise one day closer ?

 

[WARose]

@daranquiz: thanks for the info. That being Eurocode, should I use GPa as the units for E? I found that code on-line and couldn't find the units specified.

@rb1957: Yes......or more accurately: how much compression is it seeing prior to buckling?

 

[daranguiz]

@WARose It depends of the units you are using for stress. Normally you should use E=210000 or E=200000 MPa if you are using fy in MPa.
I made a mistake on my previous post. It should be atan(E/10000).

 

[rb1957]

its probably just semantics but in the plastic range I'd call it "collapse" or "crushing" rather than buckling.

another day in paradise, or is paradise one day closer ?

 

[WARose]

I made a mistake on my previous post. It should be atan(E/10000).

Are you sure it wasn't right the first time? I found that code on-line, and the atan(E/100) value is for a material with a work hardening range (like steel).

 

[canwesteng]

Inelastic buckling occurs before crushing. It is non conservative to use Euler's equation of buckling for inelastic buckling, but code equations account for this. Is this what you're looking at?