# Dependency between load capacity for reinforced concrete slab and thickness

How does the load capacity for a reinforced concrete slab depend on the thickness of the slab?

Example:

Let's suppose that we have the following constants:

• concrete quality (including the maximum compression resistance)
• same rebars (E.g.: mash of 4/100 mm)
• the rebars are at 35 mm from the bottom of the slab
• the load is constant in every point of the slab

Firstly let's suppose that the slab has a thickness of:

1. 100 mm and supports a constant load (permanent: screed, ceramic tiles + temporary: objects, people) of 250 kg/m^2 (2.5 N/m^2).

2. 150 mm

3. 200 mm

How to determine the load capacity for points 2 and 3 based on point 1?

P.S.: The example is just to emphasize the idea. I'd like to have a more general solution.

• Given the multiple questions you have posted around this topic, what research have you done to find out the answers? See engineering.stackexchange.com/q/29229/10902 and engineering.stackexchange.com/q/29227/10902 – Solar Mike Jul 18 '19 at 11:21
• The questions are on the same topic, but they are different. I'm asking them because I didn't find any trusted answer for them. I made a research on a lot of documents and this is why I have these questions. I can add references to the resources I found and some other details, but it won't help. I tried to leave the questions as light as possible. Do you have any suggestion about improving them? – Elrond_EGLDer Jul 18 '19 at 12:49
• If you’re planning to use the simpler capacity calculation methods outlined in design codes (like designing edge and interior strips) the capacity calculation should be repeatable via spreadsheet for any thickness/rebar/rebar cover you like. Then, in demand calcs, you’ll account for slab self-weight. I’ve never seen an equation that predicts Slab2 capacity based on Slab1 (possibly because directly calculating Slab2 capacity is pretty simple). An undergraduate concrete design textbook should discuss slab capacity in depth, as well as building design codes for your country. – CableStay Jul 18 '19 at 15:03
• One thing that also needs to be considered is the effect of boundary conditions. Cantilever slabs and those with two opposing free sides behave very similarly to beams. But any other boundary configuration leads to slabs which behave very differently. – Wasabi Jul 19 '19 at 1:50 Using conditions given in the sketch above, let's do a parameter study.

M = AsFy(d - a/2)

a = Asfy/0.85fc'b, note, since As, b, fc' and fy are constant throughout this exercise, "a" is constant as well. Let's assume a = 50mm.

1. d = 65, M1 = AsFy(65-50/2) = 40Asfy

2. d = 115, M2 = AsFy(115-50/2) = 90Asfy

3. d = 165, M3 = AsFy(165-50/2) = 140Asfy

M2/M1 = 90/40 = 2.25, and M3/M1 = 140/40 = 3.5

Note, in reality, the ratios will be smaller. Because while the moment arm has increased for the deeper beam, the self-weight increases as well, albeit the rate of increase of the latter has less impact than the former.

Please check the equations and calculations for mistakes.

A very rough estimate to start designing is this.

The changing of the depth of a concrete slab changes the resisting momen arm: $$d-\frac{a}{2}$$ of the slab. With d, being effective depth and a, the depth of concrete stress block in compression.

In simply supported non prestressed slabs this distance changes almost linearly, even though a, is not linear but the changes are within the estimate error tolerance.

So if you multiply the slab depth by 20 % you approximately have 20% more moment resisting given all other factors are the same. This is a rule of thumb tool to start estimating the first parameters of the slab design.