How to determine a reinforced concrete cross-section stiffness (or young's modulus)? 1

[cesaramorim]

I came across a problem while modeling my structure in tricalc. The deflection on one of the slabs is too big, unless i place a beam with high stiffness adjacent to it.

I'm trying to solve this by using a steel beam, but, since I cant mesh together the beam with the slab for modeling reasons, i'm using a reinforced concrete beam instead, with a high height. To make sure my steel beam will work as the concrete beam I have there, they both need the same stiffness (and i'm not yet sure that's enough by itself). However I can't find the stiffness of the concrete beam.

I tought of using elastic equations, and reverse the beam deflection to get is stiffness using the following:

deflection = 5*load*span^4/(384 * stiffness)

But this feels like cheating. So am I missing something basic here? Or is there a way to find the concrete beam stiffness? (I could assume that it was not reinforced, but that would give me a smaller stiffness than the real one)

Thanks in advance

 

[mike20793]

I'd model the system that you're trying to find the stiffness of and apply a point load of 1 kip at the area of interest and then look at the deflection at that point. I use it all the time for diaphragm analysis.

 

[cesaramorim]

Great tip, but it wouldn't work because the area of the reinforcement depends on the load. Tricalc doesn't give me that kind of control. I will however try to analyse exactly the cross-section he provides, and replicate it on sap2000. Using a unitary load as you say, maybe that way i'll get the element stiffness.

 

[KootK]

Can you just model a concrete beam and alter it as required and then, at the end, just ensure that you're your steel beam provides at least as much stiffness as the concrete beam that you're replacing? It's not as though you're ever going to know the load drawn to the beam with any great degree of accuracy anyhow. Spending a lot of time getting it modeled just right is probably wasted effort anyhow.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JAE]

Don't forget that concrete beam stiffnesses are an estimate only. The effective moment of inertia is based on the applied moment, the cracked moment of inertia of the beam, and the gross moment of inertia (using ACI 318's method for Ie). I'm not sure what your software does with a concrete beam - does it reduce the stiffness based on a semi-cracked stiffness? Just be sure you know what your program is doing.



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