Young's Modulus of Cracked Concrete 2

[hockley]

I want to calculate the lateral free vibration frequencies and mode shapes of a multi-storey building (in order to carry out a Response Spectrum Analysis). In order to do this I am using a 3D finite element model.

Can anybody tell me the relative value of Young's (elastic) modulus that I should use for the slabs and the walls respectively in order that my (elastic) model reflects the fact that the floor slabs will be uncracked whilst the shear walls will be cracked to some degree (and hence "softer").

I realise that "Young's modulus of cracked concrete" is perhaps a contradiction in terms, but being new in the Seismic Analysis game I would appreciate advice on how this physical reality is normally dealt with in linear elastic models.

 

[UcfSE]

I think you would look at using a cracked moment of inertia for your different members instead of a cracked modulus of elasticity. If you are in the US, check out the ACI 318 section 10.10 and 10.11, specifically 10.11.1 if applicable to your case.

 

[Qshake]

I'm not sure this is dealt with by way of reducing the modulus. Obviously the objective we're after is to modify the terms of the stiffness matrix which is dependent on E but also I and in fact, the flexural rigidity term EI.

My suggestion is to modify I for cracked section properties and to leave E alone. In fact, ACI has a section for modifying Ig, the gross moment of inertia for cracked section properties.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[hockley]

Thanks for the suggestions, but I fear that for a large 3D finite element model it would almost impossible (and certainly impractical) to go around and modify all the second moments of area (Ixx, Iyy & Ixy) for all the elements comprising the shear walls.

Unless I am mistaken, a much shorter route to the same result can be obtained by modifying E for the wall elements - remember, I'm only trying to get a handle on the relative stiffness of the shear walls with respect to the floor slabs.

Has anyone else done this before? I was under the impression that this was fairly common practice (though I concede I am in Europe - not the US).

Thanks for the comments so far, anyone got any further wisdom on the subject?

 

[JAE]

I don't think this is common in the US.

With shearwalls, modifying the E for ALL the wall elements would be to suggest that the whole wall is cracked equally - which is never the case.

Usually, one can interate a few times, studying the Von Mises or primary stresses in the elements under service loads and reduce the thickness of the elements for which the stress has exceeded the cracking stress. This would get you closer to the real effective stiffness of the shearwall relative to the floor structures.