Limit state of serviceability for flexural members

Limit state of serviceability for flexural members:

Deflection

The check for deflection is done through the following two methods specified by IS 456:2000 (Refer clause 42.1)

1      Empirical Method

In this method, the deflection criteria of the member is said t o be satisfied when the actual val ue of span to depth ratio of the member is less than the permissible values. T he IS code procedure for calculating the permissible values are as given below

a.                 Choosing the basic values of span to effective depth ratios (l/d) from the following,  depending on the type of beam

Cantilever        =       8

Simply supported     =       20

Continuous      =       26

b.    Modify the value of basic span to depth ratio to get the allowable span to depth

ratio.

Allowable  l/d = Bas ic l/d x M_t x M_c x M_f

Where, M_t = Mo ification factor obtained from fig 4 IS 456:200 0. It depends on the area of tension reinforcement provided and the type of steel.

M_c = Modificatio n factor obtained from fig 5 IS 456:2000. Thi s depends on the area of compress ion steel used.

M_f = Reduction f actor got from fig 6 of IS 456:2000

Note: The basic values of l/d mentioned above is valid upto spans of 10m. The basic values are multiplied by 10 / span in meters except for cantilever. For cantilevers whose span exceeds 10 m the theoretical method shall be used.

2      Theoretical method of checking deflection

The actual deflections of the members are calculated as per procedure given in annexure 'C' of IS 456:2000. This deflection value shall be limited to the following

i.      The final deflection due to all loads including the effects of temperature, creep and shrinkage shall not exceed span / 250.

ii.    The deflection including the effects of temperature, creep and shrinkage occurring after erection of partitions and the application of finishes shall not exceed span/350 or 20 mm whichever is less.