(Clauses 21.3.2, 22.2.1 and 41.1) CALCULATION OF DELEFCTION C-1 Total Deflection

The total deflection shall be taken as the sum of the short-term deflection determined in accordance with C-2 and the long-term deflection, in accordance with C-3 and C-4.

C-2 Short-term Deflection

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

I _ {\mathrm{eff}} = \frac {I _ {\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}

I _ {\mathrm{r}} \leq I _ {\mathrm{eff}} \leq I _ {\mathrm{gr}}

where

$I_{\mathrm{r}} =$ moment of inertia of the cracked section,

$M_{\mathrm{r}} =$ cracking moment, equal to $\frac{f_{\mathrm{cr}}I_{\mathrm{gr}}}{y_{\mathrm{t}}}$ where

$f_{\mathrm{cr}} =$ modulus of rupture of concrete,

$I_{gr}$ = 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,

$x =$ depth of neutral axis,

$d =$ effective depth,

$b_{\mathrm{w}} =$ breadth of web, and

$b =$ breadth of compression face.

For continuous beams, deflection shall be calculated using the values of $I_{\mathrm{r}}$ , $I_{\mathrm{gr}}$ and $M_{\mathrm{r}}$ modified by the following equation:

X _ {\mathrm{e}} = k _ {1} \left[ \frac {X _ {1} + X _ {2}}{2} \right] + \left(1 - k _ {1}\right) X _ {\mathrm{o}}

where

X _ {\mathrm{e}} = \text { modified value of } X,

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

$X_{\mathrm{o}} =$ value of $X$ at mid span,

$k_{1} =$ coefficient given in Table 29, and

$X =$ value of $I_{\mathrm{r}}, I_{\mathrm{gr}}$ or $M_{\mathrm{r}}$ as appropriate.

C-3 Deflection Due to Shrinkage

The deflection due to shrinkage $a_{\mathrm{cs}}$ may be computed from the following equation:

a _ {\mathrm{cs}} = \mathrm{k} _ {3} \psi_ {\mathrm{cs}} l ^ {2}

where

$k_{3}$ is a constant depending upon the support conditions:

0.5 for cantilevers,

0.125 for simply supported members,

0.086 for members continuous at one end, and

0.063 for fully continuous members,

$\psi_{\mathrm{cs}}$ is shrinkage curvature $= k_{4}\frac{\varepsilon_{\mathrm{cs}}}{D}$

where $\varepsilon_{\mathrm{cs}}$ is the ultimate shrinkage strain of concrete (see 5.2.4),

k _ {4} = 0. 7 2 \times \frac {P _ {\mathrm{t}} - P _ {\mathrm{c}}}{\sqrt {P _ {\mathrm{t}}}} \leq 1. 0 \text {for} 0. 2 5 \leq P _ {\mathrm{t}} - P _ {\mathrm{c}} < 1. 0

= 0. 6 5 \times \frac {P _ {\mathrm{t}} - P _ {\mathrm{c}}}{\sqrt {P _ {\mathrm{t}}}} \leq 1. 0 \text {for} P _ {\mathrm{t}} - P _ {\mathrm{c}} \geq 1. 0

where

P _ {\mathrm{t}} = \frac {1 0 0 A _ {\mathrm{st}}}{b d} \text {and} P _ {\mathrm{c}} = \frac {1 0 0 A _ {\mathrm{sc}}}{b d}

and $D$ is the total depth of the section, and $l$ is the length of span.

Table 29Values of Coefficient, {k}_{1}

Table 29 Values of Coefficient, $k_1$ (Clause C-2)
$k_2$	0.5 or less	0.6	0.7	0.8	0.9	1.0	1.1	1.2	1.3	1.4
$k_1$	0	0.03	0.08	0.16	0.30	0.50	0.73	0.91	0.97	1.0
NOTE — $k_2$ is given by: $k_2 = \frac{M_1 + M_2}{M_{\text{F1}} + M_{\text{F2}}}$ where $M_1, M_2$ = support moments, and $M_{\text{F1}}, M_{\text{F2}}$ = fixed end moments.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

C-4 Deflection Due to Creep

The creep deflection due to permanent loads $a_{\mathrm{cc(perm)}}$ may be obtained from the following equation:

a _ {\mathrm{cc(perm)}} = a _ {\mathrm{i,cc(perm)}} - a _ {\mathrm{i(perm)}}

where

$a_{\mathrm{i,cc(perm)}} =$ initial deflection plus creep deflection due

to permanent loads obtained using an elastic analysis with an effective modulus of elasticity.

$E_{\mathrm{ce}} = \frac{E_{\mathrm{c}}}{1 + \theta}$ ; $\theta$ being the creep coefficient, and

$a_{\mathrm{i(perm)}} =$ short-term deflection due to permanent load using $E_{\mathrm{c}}$ .

Annex C(Clauses 21.3.2, 22.2.1 and 41.1) CALCULATION OF DELEFCTION C-1 Total Deflection

C-2 Short-term Deflection

C-3 Deflection Due to Shrinkage

C-4 Deflection Due to Creep

Annex C(Clauses 21.3.2, 22.2.1 and 41.1) CALCULATION OF DELEFCTION C-1 Total Deflection

C-2 Short-term Deflection

C-3 Deflection Due to Shrinkage

C-4 Deflection Due to Creep