Mixture law for a concrete slab (vibration)

[pilafa]

Hi,

I want to study vibration on a simple reinforced concrete structure with FEA.
The amplitudes are small, so all the materials stay in the linear domain.

I wonder if it is acceptable to use a Rule of Mixtures to calculate an equivalente Young Modulus (E_c= E_f*V_f+ E_m*V_m).

Thanks,
Pierre

 

[IDS]

If the concrete is uncracked, yes. Unfortunately reinforced concrete becomes highly non-linear after cracking, and concrete structures are usually cracked at working loads.

Have a look through the "Structural engineering other technical topics" forum to see the problems that causes.

http://www.eng-tips.com/threadminder.cfm?pid=507

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[pilafa]

Hi Doug,

Thank you for your answer.

Since it's a "noise vibration" problem, I am confident that the amplitudes will be very small.

Now my concern about using the Rule of Mixture is that the properties of a reinforced concrete beam are not isotropic.

I am thinking about using the Rule of Mixture in the longitudinal direction (align with the steel), and the concrete properties in the transverse direction (perpendicular to the steel bars)...but I don't find any reference on that.

Someone knows if it's a valid approach, or have reference on that?

(a third approach would be to use Rule of Mixture in every direction)

Thanks.
Pierre

 

[gravityandinertia]

Since it's a "noise vibration" problem, I am confident that the amplitudes will be very small.

I don't know if you are thinking correctly about this or not. While the loads for your analysis may be small, if it has EVER seen a large enough load to crack it (other than the loads you want to analyze for vibration), then what IDS said above stands true. Rule of mixtures won't work. It makes sense, once concrete cracks, it doesn't uncrack just because it's unloaded.

You may have already understood that, I just wasn't sure by your response since it wasn't addressed.