Relationship b/w Steel Strain and Concrete Crack in Elastoplastic Region 1

[hofasa]

Hello. ACI 224R Eq 4-2a shows a linear correlation b/w concrete crack width and reinforcing steel stress in a reinforced concrete beam (see attached). This equation is valid when the steel is in elastic region. After the steel yields, the stress-strain curve becomes nonlinear (E becomes variable) and the equation is no longer valid.
Does anyone know how to calculate the concrete crack width in the elastoplastic region (after the steel reinforcement yields but before it reaches it's ultimate strength or concrete fails)?
Thanks,

 

[bugbus]

There are plenty of research papers that cover this situation. But if your structure is into the yield range of the steel, surely you are well beyond the concern of crack widths?

 

[ThomasH]

What is the purpose of the analysis? It does not seem lika a normal design situation.

E becomes variable

I would say that E is not useful for this. You need to calculate the strain in the reinforcement. When you have the strain in the reinforcement and the spacing between the cracks you should be able to calculate the effect on the crack width.

 

[hofasa]

Thanks bugbus and ThomasH for your replies.
The research papers I have access to consider the steel in elastic region as it is the main purpose of design per codes.
This case is an atypical case. There is an existing reinforced concrete pier (with a bridge deck on top) that has cracked. Elastic analysis shows that the steel has already yielded before the crack reaches the measured width in the field but there is no sign of concrete failure in the compression zone. I assume the crack width grows proportional to the increase of steel strain beyond the yield point. Checking with the moment curvature diagram for the pier section, the calculated steel strain is less than the steel strain associated with the ultimate strength of the concrete section. This gives us an insight that how much the crack width can grow before the pier collapses so we can come up with a retrofit plan and the client can shut down the operation beforehand.

 

[human909]

Well that question escalated quickly!

hofasa, photos would be fantastic for us following along at home.

 

[SWComposites]

Sounds highly risky. And unlikely to hold up in court if it fails before predicted and injures someone.