Composite action in slab of timber and concrete, deflection

[Mlindblom]

I have modelled a composite floor slab of 200 mm timber with 120 mm concrete on top (also called a TCC). I am trying to verify the deflection given by Abaqus with the analytical solution given by the "gamma method". My problem is i can not get close enough results. My Abaqus result show a midspan deflection of 6 mm while the gamma method shows a deflection of 3.3 mm. Any guidance will be very appreciated!

I first want to study 100% composite action. In the gamma method i use gamma equals to 1 and in Abaqus i set the connection between the concrete and timber surface to "tie".

Dimensions:
Concrete: 8x2.4x0.12 m
Timber: 8x2.4x0.2 m

Material data:
Concrete
E-modulus: 33 Gpa
Poisson: 0.2

Timber
E1: 12GPa
E2: 0.5 GPa
E3 0.9 GPa
Nu: 0.3
G12: 600 MPa
G13: 600 MPa
G23: 60 MPa

Load and BC:
Load: 3500 N/m2
BC: Pinned in one end and locked in Z in one end (simply supported).

 

[BridgeSmith]

I haven't done any timber and concrete composites, but I've done alot of steel and concrete composite beams. For those, we transform the concrete into a equivalent area of steel by dividing by the modular ratio (Esteel/Econcrete) to calculate the moment of inertia. Then we'd use calculated I and the E for the material that wasn't transformed (in our case, steel) to calculate the deflection.

 

[Mlindblom]

Could you elaborate a bit? If i have concrete height 0.12 and timber 0.2 with Ec=33GPa and Et=12GPa, the modular ratio becomes: Ec/Et=12/33=0.3636... How do i use the ratio to transform the timber part to a concrete part?

 

[BridgeSmith]

You would multiply the width of the timber by .3636, maintaining the height, to model it as an equivalent area of concrete, in order to do the section properties calculations. The I and S that you get, would be equivalent to a section that was all concrete. Then you can calculate the deflection using the I you calculated for the transformed section and Ec.

Edit: That assumes that the timber and concrete actually make a composite section, i.e. there is a rigid connection between the two with enough shear capacity for them to act as a single piece. Otherwise, you just calculate the bending stiffness using Ic*Ec and It*Et and sum them.