# Homework Help: Stress strain curve for concrete in Eurocode

1. Jun 29, 2013

### Sadeq

Hello,
I am doing simulation using Finite element for the concrete ,this I found the concrete model for the concrete in euro code as attached in the picture.

But what I don't understand is basically why the peak of the curve is not the Fck (compressive strength), because the curve maximum is fcm(average compressive strength).

So if I need to use the curve ,this doesn't make sense to me

Please anyone clarity this point for me.

The peak should be fck not the average???

Thank you all

2. Jun 29, 2013

3. Jul 1, 2013

### PhanthomJay

That curve appears incorrectly labeled. The peak stress is the stress at failure under increasing compressive load in a lab tests. Approximately 5 percent of samples of a grade of concrete would fail at a peak stress of fck or fcu, or less, while 95 percent would fail at a peak stress of greater than fck, with average peak stress of those samples being fcm. The peak stress for design is considered fck, giving a 95 percent confidence level that the peak failure stress will occur at fck or greater. Now to achieve the post peak response, the tests must be conducted by slowly controlling deformation instead of load, because by increasing load to failure, the specimen breaks at peak, and post peak response is lost. Post peak, the stress is reduced as strain increases, until an ultomaye strain is reached. While this stress value is lower than the peak stress, and cannot be called fck. The peak value is fck or greater, more like fcm on average. Fcm is always greater than fck , by 25 percent or so.

4. Jul 3, 2013

### pongo38

Jay said "That curve appears incorrectly labelled." . I looked at the code and it mentions fcm in the same place as the OP's diagram, at the top. The final stress, labelled as fcu in the OP's figure is not mentioned in my code diagram from EN 1992-1-1 2004. There may be a later edition. However, you might think that "cu" might originate from "compression" and "ultimate", and the code uses these subscripts at the ultimate strain.

5. Jul 3, 2013

### PhanthomJay

if fcu represents the compression strength at ultimate strain, then I agree that label is correct. I was interpreting fcu as the peak stress when testing is done on a cube sample instead of a cylinder, which yields values higher than fck, but I have minimum familiarity with Eurocode.

Regarding the peak stress, it is my understanding thst fcm is the average peak stress where most samples will fracture under increasing load. However, since a small fraction of samples will fail at a lower value, fck, fck is used as the fracture stress for safety. Thus, a Grade 30 mix will sometimes fail at 30 MPa, fck at peak, but most of the time it fails at 40 MPa or so, fcm at peak. When Grade 30 concrete is specified, the water/cement ratio is adjusted to shoot for fcm at peak of around 40 MPa, and if a few samples ( 1 in 20) fail at arpund 30 MPa, no one sweats over it, since design is based anyway on fck with a safety factor . As I understand it. In the States, I order 4000 psi concrete but design for 3000 psi. This way , if a sample tests after pour at below 4000 psi, I don't have to initiate a lawsuit against the supplier, who will only claim anyeay that the testing or curing of the cylinders in the field was
not done properly.

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