Young's Modulus of Cracked Concrete...

[hockley]

I first posted this question in the Seismology forum. So far I haven't received the answer I'm after there - perhaps subscribers to this forum may be able to help...

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...

2 suggestions received (see Seismic forum)...

...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?

 

[WillisV]

Hockly,

You are correct in saying that literally "Young's modulus of cracked concrete is perhaps a contradition in terms..." in that of course the modulus remains the same for cracked or uncracked concrete. Cracked sections are typically taken into account for analysis by modifying the moment of inertia of the secion as has already been pointed out in the seismology forum - often using ACIs recommended crack factors in Chapter 10.

However you are also correct in noting that modifying E would have the exact same effect considering the stiffness matrix consists of EI terms (e.g. 12EI/L^3, 6EI/L^2, 4EI/L) in which there is a one to one relationship between the modulus E and the moment of intertia I. Therefore you will get the same output results for a cracked column using Ecr = 0.7Eact as you would with Icr = 0.7Igross.

 

[miecz]

I believe it is common practice to reduce the stiffness of flexural members by 50%, and that of compression members by 20%.

 

[dawn836]

well Willis V
i think you forgot a point that there is also axial stiffness EA/L and this axial stiffness is not included in the reduction for cracked section
so when u modify Young`s modulus then u will increase axial deformation of column leading to more settelment for node between column and beam or column and slab.
but anyway i do not think this will affect as long as all columns will have same reduction in axial stiffness

Do you Agree?

 

[WillisV]

Agree on both points - axial stiffness will decrease with a reduced modulus, however I do not think the overall effect will be considerable on the lateral deflection and force distribution unless the building exibits considerable p-delta effects. Obviously it does have a direct contribution on direct vertical deflection if one is interested in that value. Certainly something to consider.

 

[MSDw]

There can be a slight differnece between the cracked section and the uncracked section in regard to the value of E. As the value of E. is taken from some function of the uniaxial compression test of a concrete specimen. this can be the case for the cracked section, but not for the uncracked section which can be under biaxial loading, hence a more confined environment. But..i think the difference is not of that huge significance.

MSDw