C-3Floor frequency

The fundamental natural frequency can be estimated by assuming full composite action, even in non-composite construction. This frequency, $f_{1}$ for a simply supported one way system is given by

$f_{\mathrm{i}}=156 \sqrt{E I_{\mathrm{T}} / W L^{4}}$

where

• $E \quad=$ modulus of elasticity of steel, MPa
• $\begin{aligned} l_{\mathrm{T}} & =\text { transformed moment of inertia of the one } \\ & \text { way system (in terms of equivalent steel) } \\ & \text { assuming the concrete flange of width equal } \\ & \text { to the spacing of the beam to be effective, } \\ & \text { in } \mathrm{mm}^{4} ;\end{aligned}$
• $L \quad=$ span length, in mm; and
• $W=$ dead load of the one way joist, in N/mm

If the one way joist system is supported by a flexible beam running perpendicular with the natural frequency $f_{2}$, the floor frequency may be reduced to $f_{r}$, given by: