C-2Short-term deflection

C-2.1

The short-term deflection may be calculated by the usual methods for elastic deflections using the short-term modulus of elasticity of concrete, $E_{\mathrm{c}}$ and an effective moment of inertia $I_{\mathrm{eff}}$ given by the following equation:

$\begin{aligned} l_{\mathrm{eff}} & =\frac{l_{\mathrm{r}}}{1.2-\frac{M_{\mathrm{r}}}{M} \frac{z}{d}\left(1-\frac{x}{d}\right) \frac{b_{\mathrm{w}}}{b}} ; \text { but } \\ l_{\mathrm{r}} & \leq l_{\mathrm{eff}} \leq l_{\mathrm{gr}}\end{aligned}$

where

• = moment of inertia of the cracked section,

$f_{\mathrm{cr}} l_{\mathrm{gr}}$

• $M_{r}=$ cracking moment, equal to $\frac{f_{c r} \cdot g}{y_{t}}$ where $f_{c r}$ is the modulus of rupture of concrete, $I_{g r}$ is the moment of inertia of the gross section about the centroidal axis, neglecting the reinforcement, and $y_{t}$ is the distance from centroidal axis of gross section, neglecting the reinforcement, to extreme fibre in tension.

$M=$ maximum moment under service loads,

$z=$ lever arm,

• $x \quad=$ depth of neutral axis.

$d=$ effective depth,

• $h_{w}=$ breadth of web, and
• $b \quad=$ breadth of compression face.

For continuous beams, deflection shall be calculated

using the values of $I_{r}, I_{g}$ and $M_{r}$ modified by the following equation:

$X_{e}=k_{1}\left[\frac{X_{1}+X_{2}}{2}\right]+\left(1-k_{1}\right) X_{o}$

where

$X_{e}=$ modified value of $X$,

$X_{1}, X_{2}=$ values of $X$ at the supports,

= value of X at mid span,

= coefficient given in Table 25, and

$X=$ value of $I_{r}, I_{g}$ or $M_{r}$ as appropriate.