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# Two way slab on grade analysis

## Two way slab on grade analysis

(OP)
i have to analyze whether a two way slab can take the weight of 115 kip crane outrigger reaction load. i graduated in May and really have no clue where to even start. ive looked up aciR, and other resources. any help is greatly apprciated

### RE: Two way slab on grade analysis

I'd make it a punching shear problem. Supplying punching resistance concrete on grade is cheaper than loading it with bending moment bars. Keep it a 100% shear load and there is no bending moment in the slab.

Find out how much soil area you need to support 115 Kips + slab weight. Is that the maximum load. No wind ... etc? Or with wind? No overturning moments, etc?

Make the slab thick enough over that area to stay below the concrete's punching shear allowable stress (without using any bars). Then just add minimum shrinkage and thermal steel.

Sorry, I thought it is a new slab you were designing. It's an old slab you're checking.
Do the same to find out how much area you need to have adequate soil bearing.
Put your crane load in the middle of that area. Assume that there is a one way cantilever beam, 1ft wide fixed at the crane base, going from crane base to the edge of the calculated bearing area.
You will have that factored soil bearing load on the bottom face, weight of slab on top. (I'd use a 0.9 factor on that.) Calculate the resulting bending moment. Check if thebeam and steel in the slab is adequate for that moment. It's a Conservative approach, since the slab is actually 2-way, but you are considering only one way of steel and concrete action.

If it does not work. Come back and tell us and we might try considering it as a flat plate with 2-way bending action resistance. Roark's formulas can be helpfull.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Two way slab on grade analysis

(OP)
@1503-44
so i have a crane mat thats 5'*5'*1', i analyzed with the crane outrigger load and that should be fine. the slab on grade has w2.1 wwf, barely reinforced. senior colleague says tht means the slab doesnt take shear or bending. but how do i go about analyzing with mesh, never done that before, and how do i analyze if the crane mt will crack the slab on grade as well? can i check the punching shear of the critical area after the crane mat? i cant really read plans well as a just graduated, but their doesnt seem to be any control joints

### RE: Two way slab on grade analysis

Concrete will handle low shear stress by itself, such as in a beam not requiring stirrups, or in a thick slab where all steel is placed horizontally. The stress must be limited to <= the concrete shear allowable. If stress is less, no steel is needed and no cracks should occur.

WWF will provide at least some bending resistance. It might be small, but it is something.
It will not help in shear, because steel area is in the horizontal plane, but shear stress is vertical plane. That's why concrete thickness is important for handling shear stress.

We will take your colleague's advice and assume we can not develop beam bending.
Find the area of the slab needed to resist punching shear. The horizontal surface area of the slab with a perimeter large enough to provides enough vertical section area in the slab such that the shear load is less than the concrete shear allowable alone (no steel).

Then you will have to distribute the crane load over the area of the slab. I would try building a steel distribution mat above the slab, in which case the steel beams must be designed for the bending shear and moment, which allows the slab to provide for the punching shear only.

BTW, you don't say how thick the slab is.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Two way slab on grade analysis

(OP)
@1503
It’s 5, inches, it’s also rather wide. When I try to do punishing shear equation, because it’s based on width of slab and critical perimeter, the kips come out to a lot. Like 3600 kips. The equation I’m using is Vu=Pu*(w^2-b0^2)

### RE: Two way slab on grade analysis

What's the shear allowable stress of your concrete?

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Two way slab on grade analysis

(OP)

I calculated this

### RE: Two way slab on grade analysis

I don't know what dimensions are, or your assumptions of how the mechanics is supposed to work without some minimal explanation of what you are doing and a basic sketch showing what/where the dimensions represent. 5" isn't going to take a lot of bending moment, so how is the slab supposed to distribute the load to the soil.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

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