A client once contacted us with the following query:
He wanted to model a slab like the one below in CEDRUS:
Made of unidirectional precast elements (lightened sheets of 1.20 m wide, 20 cm deep and 10 cm of compression slab).
The cross section is entered in FAGUS to be dimensioned and to obtain its mechanical characteristics:
With the aid of FAGUS, they obtained the inertia of the cross section and, with the classic formula, the inertia corresponding to a solid slab of 10 and 30 cm:
They realised that the inertia of the lightened sheet was similar to the one of the 30 cm slab, which means that the result should be similar to the ones introduced for a 30 cm isotropic slab.
CEDRUS indicates, in its manual, how the orthotropic material has to be used and illustrates this with two examples:
Our client introduced a 0.30 m isotropic slab and obtained the following strains for a service envelope of the ACI:
And characterising the slab as orthotropic and entering the values as d11, d22, d33, they obtained these strains for the same envelope:
This is 20 times more than the expected deflection.
The mistake that our client made is very simply detectable.
In the case of the orthotropic lightened slabs, for a width of 1.20 m, as it is indicated in the manual:
d11=b/EJy = 1.20/EJy
And the value of Jy is obtained in FAGUS-7 as Iy, since the axes in FAGUs are: ‘y’-horizontal and ‘x’-vertical, therefore, d11=1.2/(34*1e6*0.002455)=1.44 e-5 [1/KNm].
Now d22=1/EJx, and we only consider the compression sheet, so Jx will be 1/12 b·e^3 -> d22=1/(34e6*1/12*1*(0.1)^3)=3.53 e-4 [1/KNm].
As it is indicated in the manual, d33 = 2d22 = 7.06e-4 but beware, HERE IS THE TRICK! We have to pay special attention to the axes:
- If the lightening is in the X direction in CEDRUS, the values d11,d22,d33 that must be entered are the ones calculated:
- If the lightening is in the Y direction in CEDRUS (as it is in this case), then we must switch values d11 and d22 and adjust d33 conveniently so that it is twice the value of d22:
- We must also check that d11*d22>d12*d21 OK
Therefore, the results that we obtain (this time they are correct) are:
We can see that they are far more similar to the ones of an isotropic slab, slightly bigger, and the modulation every 1.20 m is clearly observable.