Deflection of Slabs

Check Deflection of Slabs for BS 8110 Part 1

The method of checking the deflection of the slabs are similar to the checks of beam deflection. Checking slab deflection is included in the beam design section of BS 8110 Part 01.

The deflection can be checked by two methods. If you know the maximum deflection for the relevant load case, we can check whether it is with in the limit. Code gives the maximum limits of deflections base on the spans.

Other methods of check the deflection is that limiting the basic span over effective depth ratio to certain values given in table 3.9 of BS 8110 Part 01 1997.

The following table shows the basis span over depth ratios for the rectangular section and flange sections.

Depending on the type of the slab boundary condition, span over depth ratio is selected from the above table. For example, if the slab is simply supported, we select 20 as the basic span over depth ratio.

The values given in the above table can be modified by multiplying the factors found for tension reinforcements, compression reinforcements and for deflections due to the creep and shrinkage. Normally factors for creep and shrinkage are not applied.

The modification factor for tension reinforcements can be found from the table 3.10 of BS 8110 Part 01.
See the following figure.

 

If we know the service stress and the bending stress, we can directly find the modification factor from the above table or we can use the equations give bellow the table to calculate the modification factor.

The modification factor for compression reinforcement can be found form table 3.11 of BS 8110 Part 01 1997.

 

If we provide compression reinforcement, it can multiply by this factor and otherwise the factor is considered as 01 where we do not provide compression reinforcements.

Example

Data

Effective depth               = 120 mm
Reinforcement required  = 197 mm²
Reinforcement provided = 393 mm²
Span                                = 3000 mm
Bending Moment        = 4.8 kNm
Steel strength               = 460 N/mm²

No compression reinforcement is provide
Consider a simply supported slab for this example

Allowable span/ depth     = 20

Find the modification factor for tension reinforcements

since we know the characteristic strength of the steel, required reinforcement area and the provided reinforcement area, we can calculate the design service stress (fs) for the equation given below table 3.10.

f s                                     = 2x460x197 / (3×393)
                                         = 153.7 N/mm²

for the equation give bellow the table 3.10, modification factor can be found.

Modification factor   = [ 0.55 + (477 – 153.7) / { 120(0.9 + 0.33) ] ≤ 2
                                         = 2.19 > 2

Hence, modification factor is 2.

Allowable span/ depth ration   = 20 x 2 = 40
                                                 

Actual span / depth ratio           = 3000 / 120 = 25
                                                 

Allowable span over depth ratio is greater than the actual span over depth ratio.
Hence, deflection is OK.