# How can the shear capacity of a concrete slab be determined for effective depths under 200mm? [Eurocodes]

All,

I'm designing a minor slab to Eurocode 2. It's purpose is more for show than any real structural purpose however I need to justify it's ability to resist it's own self weight and possibly the accidental loading of a person climbing upon it.

The slab itself is 680mm wide, 160mm deep (100mm effective depth to rebar) and has a maximum span of 1200mm, so there is little room for shear reinforcement. Ideally, this slab should be kept as small and simple as possible.

This is a small slab and acts as a cope for a sheepile wall and so spans between the 'zig-zag' of the piles.

Eurocode 2 states the following:

As can be seen, for slabs with an effective depth (d) of less than 200mm, the equations do not hold up as the inequality K <= 2.0 must be satisfied.

There is very little explanatory text around these clauses and I am looking for guidance. Does this mean that a solution is impossible using these equations? If so, what other guidance can I refer too?

If not, what significance does the k value have? Does a k value > 2.0 give me a conservative result that I can continue to use?

Ultimately; How can the shear capacity of a concrete slab be determined for effective depths under 200mm within Eurocode 2?

• My understanding of the $k$ inequality is that the maximum adopted value must be less than or equal to 2. If you have $d<200$, you'll calculate a value for $k$ which is greater than 2, therefore you must ignore your calculation and adopt 2. That being said, I have no reference to back this up. – Wasabi May 12 '17 at 14:32
• @Wasabi is correct. I have no reference either (I can't find anything in EC0 to confirm it). I have plenty of experience with Eurocodes and know that you find this nomenclature throughout them. – AndyT May 12 '17 at 15:30

As @Wasabi and @AndyT mentioned in the comments, this means the maximum value $k$ can have is $2$, so if $d<200$ then $k=2$. This can be confirmed in the section on shear design for slabs from the document 'How to Design Concrete Structures to Eurocode 2'. Table 7 from this document shows:
which has $V_{Rd,c}$ unchanged for effective depths $d<200$ and $k=2$ at the bottom of the $d\leq 200$ column. You can confirm this by doing the calculation by hand. Using $k>2$ would be non-conservative as it would predict a higher shear capacity than allowed by the code.