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Composite Slabs

Composite slabs are a slab supported on steel decking. These can be modelled as a solid slab with adjustment to the in-plane (tpt_p) and bending (tbt_b) thickness. For a unit width the area of slab is AA concrete (AcA_c) and steel (AsA_s) are known as are the second moments of area (IcI_c and IsI_s) and the EE values (EcE_c and EsE_s).

Referring back to the concrete as the primary material the effective area is

Aeff=Ac+(EsEc)AsA_{eff} = A_{c} + \left( \frac{E_{s}}{E_{c}} \right)A_{s}

And the effective thickness (in-plane) is

tp=AeffA=Ac+(EsEc)AsAt_{p} = \frac{A_{eff}}{A} = \frac{A_{c} + \left( \frac{E_{s}}{E_{c}} \right)A_{s}}{A}

Give the centroid of the concrete (zcz_c) and steel decking (zsz_s) the centroid of the composite section is then

zeff=Aczc+(EsEc)AszsAc+(EsEc)Asz_{eff} = \frac{A_{c}z_{c} + \left( \frac{E_{s}}{E_{c}} \right)A_{s}z_{s}}{A_{c} + \left( \frac{E_{s}}{E_{c}} \right)A_{s}}

and the effective second moment of area (IeffI_{eff}) is

Ieff=[Ic+Ac(zczeff)2]+(EsEc)[Is+As(zszeff)2]I_{eff} = \left\lbrack I_{c} + A_{c}\left( z_{c} - z_{eff} \right)^{2} \right\rbrack + \left( \frac{E_{s}}{E_{c}} \right)\left\lbrack I_{s} + A_{s}\left( z_{s} - z_{eff} \right)^{2} \right\rbrack

And the effective thickness in bending is

tb=IeffI3=[Ic+Ac(zczeff)2]+(EsEc)[Is+As(zszeff)2]I3t_{b} = \sqrt[3]{\frac{I_{eff}}{I}} = \sqrt[3]{\frac{\left\lbrack I_{c} + A_{c}\left( z_{c} - z_{eff} \right)^{2} \right\rbrack + \left( \frac{E_{s}}{E_{c}} \right)\left\lbrack I_{s} + A_{s}\left( z_{s} - z_{eff} \right)^{2} \right\rbrack}{I}}