Unless it is too early and I am not thinking clearly, isn't this just the punching shear capacity of the concrete?
This will be laid out in any concrete design textbook.
Are you dealing with RC concrete or just plain?
In doing a new spread footing design I usually select the depth of the footing based on punching or wide beam shear. When doing the initial design, I only use the plain concrete to calculate the shear capacity.
Agree with ToadJones. Typical method in North American codes of dealing with punching shear is to consider the concrete only unless shear reinforcement (studs, vertical ties, etc.) are provided. What country are you in?
it is plain, or only has very nominal. It is ground supported. The BS codes do not calculate just concrete, the allowable figures take into account the dowelling action of the steel. In the equation is an AS value. If this is 0 the answer is zero. You could size so that the entire footing is in compression but that is not the case. Can you give me your equation for calculating capacity of just concrete and I'll compare to what I've come up with? Or teh theory behind it?
Since you are assuming an un-reinforced this generic unverified example I found with a quick Google search seems to make sense....usually we calculate punching at a distance that is related to the depth of the reinforcing "d", but with no steel you must use plain concrete provisions.
...in short, it is basically the strength of a 4-side shear plain through the concrete at some distance around the column.
But....what you would use for you distance and concrete shear strength is up to you or your code.
Here in the US, the punching shear capacity of reinforced concrete is much higher than for unreinforced concrete--even though you are only considering the concrete.
The ACI318 for punching shear do not ignore the normal reinforcing. It is an empirical method that requires that the flexural reinforcing required for ultimate strength be supplied and detailed as per the detailing rules of the code.
The BS8110 method is more closely dependant on the area of steel and uses a beam shear type flexural shear strength calculation.
But both require the tension face reinforcement.
Personally, I have never designed unreinforced sections for punching shear, never having believed in the concept but some codes do allow it. Make sure it cannot fall anywhere!
