Comparisons of Slab Deflection Checking Methods

There is a belief among some proportion of practicing engineers that traditional methods of sizing slabs based on span/effective depth methods are conservative and therefore that a more detailed deflection estimate involving assessment of creep/cracking/shrinkage will allow thinner slabs to be proved as adequate. Below, comparisons are made for a very simple example (using BS8110 and EC2 design codes). It demonstrates that this expectation is not fulfilled and that the rigorous methods could be quite wasteful if applied un-necessarily. It demonstrates that the use of linear FE analysis along with appropriate stiffness multipliers is a very effective method for demonstrating serviceability compliance in normal circumstances.

Slab Depth and Deflection Comparisons

Standard Slab Details

The following is applied consistently throughout:

• A 6m span simply supported slab is considered
• Dead Load is taken as - Self weight + 1.5kN/m² finishes
• Imposed Load is taken 5kN/m² IL (including 1.0 for partitions).  This is applied regardless of the classification of the load type as "office" or "storage".

Comparison of Span / Eff depth checks for grade C20/25 concrete.

  

Notes:

• EC2 offers a small advantage compared to BS8110 when the "office" loading category is considered.
• The benefit of adding 50% reinforcement is limited to around a 10% reduction in slab depth.

Rigorous Deflection Calculations for grade C20/25 concrete.

Rigorous deflection calculations are performed for both the storage and office loads.

General Notes on the Calculation Method

The Concrete Centre Spreadsheet TCC31R is used throughout. The calculations implemented in this spreadsheet include allowance for cracking, creep, and shrinkage as specified in EC2 . An FE analysis cannot bring any more rigour to these calculations.  In practice the calculations applied in most if not all FE packages will involve simplifications and/or the use of simple adjustment factors in place of aspects of the more rigorous calculation.

When using TCC31R the user is required to provide input on the timing and nature of loading during construction. 

The following assumptions are applied consistently:

• Construction Loading includes propping load = 50% of slab load plus 0.75kN/m² construction load allowance.
• Construction Load is applied at the date stated in the tables and finishes at day 60.
• Partitions load is assumed to exist from day 60.
• Full dead + permanent imposed load is assumed to exist from day 90.

Storage Condition

 

Notes:

• A 310mm slab is borderline when EC2 span/effective depth showed 290 to be adequate.
• A 50% reinforcement increase is required to get the depth down to 290mm
• Cannot get anywhere near the 260 thick slab justified in BS8110 and EC2 span/eff depth when 50% reinforcement is introduced.
• Adding 50% reinforcement is allowing something less than a 10% reduction in slab depth.
• Adding 50% reinforcement reduces deflections by 10 to 15% and seems to have less effect on the deflection affecting the partitions.
• In all cases the deflection affecting partitions is very close to 50% of the permanent deflection.
• Decreasing slab depth by 6.5% results in deflection increase of 12%

Office Condition

 

Notes:

• In offices 30% of the IL is assumed to be permanent
• The permanent deflection does not include instantaneous deflection from the balance of the IL.
• Permanent Deflection (not total deflection) is checked against the span/250 limit.  This may seem unconservative, however the end result is still conservative by comparison with EC2 span/effective depth.
• A 290mm slab is borderline when EC2 span/effective depth showed 270 to be adequate.
• A 50% reinforcement increase only reduces the depth down to 275mm.
• Cannot get anywhere near the 255 thick slab justified in EC2 span/eff depth when 50% reinforcement is introduced.
• Adding 50% reinforcement is allowing something less than a 10% reduction in slab depth.
• Adding 50% reinforcement reduces deflections by 5 to 15% and seems to have less effect on the deflection affecting the partitions.
• In all cases the deflection affecting partitions is 40 to 50% of the permanent deflection.
• Decreasing slab depth by 5% results in deflection increase of 8%

Comparison of Span / Eff depth checks for grade C35/45 concrete.

 

Notes:

• EC2 offers very significant reductions by virtue of considering an increased concrete grade. This is generally accepted in principle, there is however some debate as to the degree of this apparent advantage. (Ref Paper by Alasdair Beal - The Structural Engineer 20th October 2009)
• In this example the reduction of slab depth allowable using EC2 is as much as 20% (290mm down to 230mm).  If stiffness is assumed to be proportional to h3 then this corresponds to a 50% reduction in stiffness. If stiffness is only assumed to be proportional to h2 then this still corresponds to a 35% reduction in stiffness.  Was there a 35 to 50% margin of overdesign in BS8110? It seems a reasonable question.
• The benefit of adding 50% reinforcement is limited to around a 10% reduction in slab depth.

Rigorous Deflection Calculations for grade C35/45 concrete.

Rigorous deflection calculations are performed for both the storage and office loads.

General Notes on the Calculation Method

The notes made in relation to C20/25 concrete apply.

Storage Condition

 

Notes:

• A 260mm slab is required when EC2 span/effective depth showed 250 to be adequate.
• A 50% reinforcement increase is required to get the depth down to 250mm
• Cannot get anywhere near the 225 thick slab justified in EC2 span/eff depth when 50% reinforcement is introduced.
• Adding 50% reinforcement is allowing something less than a 10% reduction in slab depth.
• Adding 50% reinforcement reduces deflections by 20%.
• In all cases the deflection affecting partitions is 50 to 60% of the permanent deflection.
• Decreasing slab depth by 8% results in deflection increase of 10%

Office Condition

 

Notes:

• In offices 30% of the IL is assumed to be permanent
• The permanent deflection does not include instantaneous deflection from the balance of the IL.
• Permanent Deflection (not total deflection) is checked against the span/250 limit.  This may seem unconservative, however the end result is still conservative by comparison with EC2 span/effective depth.
• A 240mm slab is borderline when EC2 span/effective depth showed 230 to be adequate.
• A 50% reinforcement increase reduces the depth down to 230mm.
• Cannot quite get down to the 225 thick slab justified in EC2 span/eff depth.
• Adding 50% reinforcement is allowing something less than a 10% reduction in slab depth.
• Adding 50% reinforcement reduces deflections by 5 to 15% and seems to have less effect on the deflection affecting the partitions.
• In all cases the deflection affecting partitions is 40 to 50% of the permanent deflection.
• Decreasing slab depth by 4% results in deflection increase of 7%

Deflection Estimates using Linear FE Analysis

Guidance on Short Term E values are given in the codes. It is made clear that there is potentially significant variation in these values. Typical values for the concrete grades being considered in this document are:

 

To give an estimate of total deflection that can be compared to the span/250 limit it is recommended that the short term values indicated above are significantly reduced to allow for effects of creep, cracking and shrinkage.  General guidance on this has been:

• Storage Condition - Reduce by a factor of 6
• Office Condition - Reduce by a factor of 4

 

Therefore, an FE analysis can be carried out using the adjusted E values and deflection contours can be reviewed.  For this example the total deflection limit = 6000/250 = 24mm

 

Example results using the above guidance are given below.

FE Analysis Results for C20/25

Storage Condition (EC2 material properties)

 

Office Condition (EC2 material properties)

 

FE Analysis Results for C35/45

Storage Condition (EC2 material properties)

 

Office Condition (EC2 material properties)

 

Overall Summary of Minimum Slab Depths

The table below shows the minimum depths that could be considered adequate for each of the examples under consideration. In all cases reinforcement is not being added in order to control deflection.

 

Notes:

• In every case rigorous deflection estimation cannot justify the slab depths that are considered adequate based on EC2 span / effective depth.
• For the storage condition the E/6 adjustment to stiffness results in very reasonable slab depths being deemed adequate.
• For the office condition the E/4 adjustment leads to a slab that is definitely too thin in one case (*).  In general this advice seems quite reasonable / borderline when the adjustment is applied to the BS8110 properties. It may not be completely adequate as Engineers move to the use of EC2 properties in analysis models. E/5 may be better advice for the office situation.

Summary

Key observations from this exercise and all other work done on this topic are:

1. BS8110 span /effective depths appear to assume a low grade of concrete and do not differentiate between different loading conditions. It seems logical that the depths given by BS8110 will be conservative when higher grades of concrete are used and when the loading is transient rather than sustained.
2. EC2 span /effective depths deal with this and seem to allow significantly reduced slab depths when both of these factors are introduced. The magnitude of the benefit introduced by EC2 is open to some debate.
3. Rigorous deflection estimation:
   • Does introduce benefits compared to BS8110 when higher concrete grades are considered.
   • Is never able to justify the slab depths that are considered adequate based on EC2 span / effective depth.
   • In general it seems that at least 50% extra reinforcement needs to be added in order to match the thicknesses deemed adequate by span / effective depth
4. Deflection Checks based on Linear FE estimation:
   • Does introduce benefits compared to BS8110 when higher concrete grades are considered.
   • Is generally not able to justify the slab depths that are considered adequate based on EC2 span / effective depth.
   • For office loading situations the suggested E/4 adjustment should be used cautiously, E/5 may be a more prudent minimum adjustment, especially if the higher short term E values introduced in EC2 are assumed as the starting point.
5. If reinforcement is added in order to reduce slab depth:
   • Adding reinforcement has an impact but it is not significant and may not be economic.
   • Adding 50% to the tension reinforcement will allow slab depth to be reduced by less than 10%.  (Typically only 20mm for slabs up to around 300mm thick)
6. If reinforcement is added in order to reduce deflection:
   • Calculations suggest that adding 50% to the tension reinforcement will reduce total deflection by 10 to 20%.
   • Where concern relates more to the deflection occurring after the introduction of walls and other sensitive/brittle finishes then adding 50% to the tension reinforcement has less impact - perhaps only 5 to 10%.
7. Adjusting the slab depth has the greatest direct impact of deflection.
   • Rigorous calcs suggest a 5 to 10% reduction in depth leads to a 10 to 20% increase in deflection.
8. Where concern relates to the estimation of deflection affecting brittle finishes:
   • In theory this is significantly affected by construction stage events and the time at which the brittle finish is applied.
   • The concrete centre spreadsheet may be used to determine the reasonable ratio between this deflection and total deflection. For the examples considered this ratio varied from 40 to 60%.  For each specific example the variation of this ratio was less than 10%.
   • Based on this the maximum deflections affecting brittle finishes can be estimated to some reasonable degree of accuracy.
9. Overall Accuracy:
   • It has to be remembered that regardless of the apparent sophistication of deflection estimate techniques, estimates are still estimates and a significant margin of uncertainty exists.