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Explain how the limit state of serviceability is taken care in the design.
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There are 2 provisions for serviceability criteria:

1) Deflection check

2) Calculation of crack width

1) Deflection check

Calculate fs value with help of the formulae: $Fs = 0.87fyAstr/Astp$

Find out pt% (percentage steel)

Now, from the graph at pg. 38 of IS456:2000, find the value of depth. (dp)

Calculate the required depth with the help of the formula:

Dr =short effective span/S/D ratio $\times$ M.F.

Compare dr and dp interest the result whether the check for deflection is safe. Id dr<dp then="" it="" is="" safe="" <="" p="">

2) Calculation of crack width:

The design surface crack width can be calculated from the following equation:

$ W_{cr} = 3 a_{cr} e_m/ 1 + 2(a_{cr} –C_{min})$ -------------------- H - x Where, $a_{cr} =$ distance from the point considered to the surface of the nearest longitudinal bar.

$C_{min} =$ minimum cover to the longitudinal bar

$e_m =$ average steel strain at the level considered.

H = overall depth of the member

x= depth of the neutral axis. (refer IS code 456:2000 for further reference)

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