Deflection of Slab with step 1

[SteynvW]

Hi all

Me and a couple of engineering friends were arguing about the deflection
of a slab with a step in it compared to one without a step. (See attached sketch).

My gut feeling is that it will create extra stiffness and reduce the deflection if
it has a step. I will however never take this into consideration if I designed such a
slab.

What are your thoughts?

 

[AnimusVox]

Wow, KootK's breaking out the straight edge and upgrading from a napkin? Must have struck a chord.

 

[KootK]

Sketch quality ebbs and flows as you're about to see.

I messed around with some models over the weekend and came up
with some qualitative conclusions that I find pretty interesting. I wanted to make a comprehensive spreadsheet to study individual parameters in more detail but, as it turns out, that's hard. Here's what I've got:

1) A first order elastic analysis with lateral restraint at the supports will indeed yield two mechanisms of load resistance, one of which will involve axial load in the slab and shear across the step (henceforth known as the Bookowski effect). See the crude sketch below.

2) with the step at midspan, the Bookowski effect yields upper and lower slab moments that sort of oppose one another and produce no net vertical displacement at midspan.

3) we've been contemplating a step shifted towards the higher slab which produces tension reaction on the slab. If you shift the step towards the low slab (right of centre here), I think that you actually get compression reactions acting on the slab. This surprised me. In both cases, the lateral reactions on the slab produce an upwards deflection at midspan that will oppose the displacement induced by the imposed load.

4) in cases where the slab height is small in proportion to the span, I expect that the Bookowsi effect would be small. With deep steps, it seems to have a pronounced effect on bending moments.

5) since the two load paths share in resisting the applied loads, I believe that it would remain safe, in all cases, to reinforce stepped slabs ignoring the Bookowski effect and designing to the conventional moment diagram proposed at the top of this thread. In this respect, a shear failure across the step may actually serve to hasten the redistribution of moments to match the conventional load path. That said, I'm now considering using at least minimum shear reinforcement across my deeper steps to keep any shear cracks reasonably small.

Item number five involves quite a bit of judgement/conjecture on my part. I welcome any debate and/or dissenting opinions.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.