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# steel and concrete composite section

## steel and concrete composite section

(OP)
Hi, all. I am doing a dynamic modelling of a building. SOme of the beams are made up with 2 W-sections side by side encased in concrete. ANy suggestion on how to model the equivalent section? I suppose the total area of section can be calc by Ac+As(Es/Ec), but what E do you use? Ec or an equivalent E? how would you calculate the equivalent E?

Thanks in advance for all suggestion.

Peter Lee
www.neillandgunter.com

Peter Lee
www.neillandgunter.com

### RE: steel and concrete composite section

Hi n9yz

Correct me if I am wrong as I am no civil or structural engineer but for a beam of two materials I would proceed as
follows:- Assuming that the steel and concrete are connected
ridgidly together the bending moment:-

M=Mc + Ms

M= Ec*Ic/(R) + Es*Is/(R)

but Es/Ec = m = modular ratio

M= (Ic/(R) + m*Is/(R))*Ec

divide thru by R

M=(Ic+m*Is)*Ec/R   and Ec/R= fc/y

: M=(Ic+m*Is)*(fc/y)

where fc=stress
Is,Ic= second moments of area for steel
and concrete beam.

R = radius of curvature of beam

Ec,Es = modulus of elasticity of materials

y = distance to neutral axis

By using this method I have found the equivalent
second moment of area of a complete concrete beam by
using the modular ratio and converting the steel part
into a equivalent concrete part.So you can now
calculate stress using Ec only. Alternatively you can
turn the concrete portion into an equivalent steel beam
if you desire again using m however the formula would
look like this:-

M=(Ic/(m))+Is)*(fs/y)

hope this helps

regards desertfox

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