Reinforced concrete stress/strain - with Moment and Axial Load - Service loads 1

[mte12]

I've been looking for a method to estimate stress and strain in reinforced concrete, when subject to moment and axial load, particularly bars in tension. This is at service loads which may not necessarily be at ultimate state.

Is there a prescriptive method available to follow?

 

[HTURKAK]

If you are looking for elastic stresses , you may use working stress design method and look to the old Reinforced Concrete books . If this is a specific case , you may post the details to get better responds.

 

[mte12]

Thanks HTURKAK, the methods in textbooks as far as I can see deal with ultimate case or 4 conditions for column (pure axial, pure bending, balanced and neutral axis at edge).

For other cases, not sure about input for neutral axis location and strains in concrete and steel.

 

[IDS]

This is also covered by new reinforced concrete design books. Standard deflection and crack width calculations are based on elastic response in the steel and concrete in compression.
The basis of the calculation is to find the neutral axis depth for which the eccentricity of the reaction forces is equal to the eccentricity of the applied loads, then scale the maximum concrete stress so that the total reaction bending moment is equal to the applied moment. This is usually done with an iterative procedure, but I prefer to use a closed form solution, which you can read more about at: https://newtonexcelbach.com/2008/11/05/reinforced-concrete-section-analysis-7-rectangular-sections/

 

[mte12]

Ok thanks Doug I'll look into it, looks very complicated

 

[mte12]

Doug, your spreadsheet is very detailed and uses visual basic, having a bit of a hard time understanding it.
I was wondering if there's any literature which explains the method to someone not familiar with concrete.

I didn't get to checking, but is it correct that the force in concrete is based on a curve (similar to a parabola), rather than a block. And how do you calculate for the area under curve?
And guess you use an iterative procedure?

 

[IDS]

For service loads it is normal practice to take the stress/strain relationship as linear elastic for the concrete in compression as well as the steel, and to ignore all tension in the concrete. That is what the EStress function in the spreadsheet, and the detailed output on the results sheet allows you to check that the output forces and moments are consistent with the calculated Neutral Axis depth and compression face strain. The spreadsheet uses a closed form solution to find the Neutral Axis depth, and it isn't obvious how that works (although there is detailed information in the blog), so to simplify things I have added an on-sheet calculation using the Excel Goal Seek function:

If you change any of the input details, or the applied moment and/or axial force, you can use Goal Seek to adjust the NA depth in cell J8 to the value to reduce the "reaction offset" in cell K17 to zero. I have also attached the spreadsheet so you can see all the formulas, which are quite straightforward.

 

[hardbutmild]

I did an example in an earlier thread:

Stress in Cover Plate in Uncracked Concrete Beam - Structural engineering general discussion

Hello, I need some help determining the stress in a "stiffening beam" at service level loads. At the service level moment, the concrete is uncracked. I'm not exactly sure why, but the fact that the concrete is uncracked has made this analysis extremely confusing to me, so I wanted to get a...

www.eng-tips.com

Picture should be here also:

https://res.cloudinary.com/engineering-com/image/upload/v1718980099/tips/001_xg95yh.png

You should be able to see there how I got stresses in concrete, tension and compression reinforcement.
In short, both concrete and steel are elastic, so stress distribution in concrete is a triangle. You can assume that concrete in tension does not exist and you say that instead of steel you have more concrete. Basically if there is no axial force it comes down to the fact that first moment of area above and below the neutral axis must be the same. That way you get n.a. depth and from there it's simple to do a classic elastic analysis I guess.