Slab deflection methods
Concrete is considered a durable and economic material for floors systems. However, reinforced concrete slabs deflect. The magnitude of the deflection is more complicated for concrete as deflection increases with time. It’s long term behavior is characterized by cracking caused by flexure, shrinkage and creep. If this is not taken into consideration by allowing adequate tolerances to glass facades and internal partitions for example then problems can arise.
Tekla Structural Designer provides two alternative methods for checking deflections. Either:
- Deemed-to-satisfy checks, or
- A rigorous theoretical deflection estimation using iterative cracked section analysis
A couple of deemed-to-satisfy checks are presented here.
- The use of a limiting span-to-depth ratio (L/d) method. This method is assumed to ‘be adequate for avoiding deflection problems in normal circumstances’. It can only be considered as a rough deflection estimate and is not intended to predict how much a member will actually deflect. Total deflection is expected to be < span / 250 (Eurocode) or < span / 250 (US) and deflection affecting sensitive finishes is expected to be < span / 500 (Eurocode) or < span / 480 (US)
- A linear analysis with adjusted analysis properties.
It is important to appreciate that these deemed-to-satisfy methods do not predict actual deflections even though the linear analysis method provides a total deflection that can be checked against the span / 250 (Eurocode) or < span / 250 (US) limit mentioned above.
When normal deflection limits do not apply, for example, due to stricter usage limits, glazed cladding systems or where a faster pace of construction is applied then the ‘deemed-to-satisfy’ checks are no longer applicable - the alternative is a rigorous deflection estimation which is the primary topic for this guide.
Rigorous theoretical deflection estimation
The rigorous theoretical deflection assessment takes into account cracking, creep and shrinkage over time.
In the UK, rigorous deflection estimation is taken to mean deflection estimation in accordance with the Concrete Society Technical Report 58.
The principle of assessing deflections rigorously involves assessing the curvatures induced by both load and shrinkage, adding them together and then the total curvature is translated into a deflection.
The Technical Report discusses the importance of construction events. Total deflection at the end of every event comprises:
- An instantaneous deflection which is influenced by the extent of cracking
- An additional accumulated creep deflection
- An additional accumulated shrinkage deflection.
Once these totals are known, differential deflections between any two events can be calculated.
The Technical Report gives detailed guidance on some very complex looking calculations - it all seems very “rigorous”. However, we must not lose sight that the material - Concrete is a very variable material. Furthermore, how accurately can we really predict input parameters such as event loads and timings? The report advises that deflection accuracy can only be considered an estimate in the range +15 to -30%.
In the US, the basic approach described in ACI 318 has a similar approach to cracking, interpolating between the fully cracked and the uncracked states, (although it doesn’t recognize the reduction in tension stiffening). For creep and shrinkage, in ACI 318 there is a single multiplier for the deflection calculated from the cracked flexural rigidity. There are additionally two ACI Committees 435 and 209 which go into more detail about creep and shrinkage calculations. The US user can therefore either adopt the basic ACI 318 approach, or, take on board the ACI Committee 435 & 209 guidance. In special situations the TR58 approach could even be considered.
Expectations - It is incorrect to think that rigorous methods will provide greater economy. i.e. by allowing the engineer to reduce slab thickness or the quantity of reinforcement. The end result is greatly influenced by the various input parameters which each can impact on the deflection.