# How do I calculate the volume of concrete needed for a particular force?

I am working on a city permit for a shade sail structure. The structure is two rectangular shade sails, 16x20, and 12x20, on six wooden 6x6x10 beams. Beams are installed in concrete slabs in the ground.

I am working with a (obviously inexperienced) civil engineer to make this permit. We have a disagreement, and I don't know how to resolve it, because I am not a civil engineer but whatever I am being told makes no sense.

The broad process seems straightforward: You calculate the force that the wind exerts on each sail, and then calculate whether the volume of concrete is sufficient for that force (I guess we assume that the beams and the tension hardware can withstand all of that - fine, I am now aware that there are two methods, MWFRS and C&C, and we are skipping over C&C for now, ok)

So, how to calculate the force on the sails makes sense to me: calculate the wind pressure (take the highest wind speed you want to protect against, square that, multiply by some empirically established constants), multiply wind pressure by area of sails to get force, divide by 4 to get force that each beam has to withstand.

The current plan claims to calculate the volume of concrete needed to resist that force in a way that makes no sense. The current plan says that the density of concrete is 150lb/ft^3 (ok so far, that seems standard), then multiplies that by volume, and gets the force. That can't possibly be right - that's the gravitational force that is exerted on the concrete block, not the amount of force that the concrete block can withstand.

So, how do you calculate the volume of concrete needed?

• I think I agree that these calculations don't make much sense. What they end up telling you is what mass of concrete would prevent the sails from lifting the concrete up out of the ground - but I can't see how that would correlate to preventing the sail and posts from being pushed over without being lifted. Imo the question which needs answering is what kind of structure in the ground would prevent lateral forces from the sail onto the post from pushing the post over - and the answer is not just "use more concrete", it's the shape of the poured concrete and how it's reinforced at the post. Aug 15, 2022 at 0:37
• I've been working on this on my own, and now I am wondering if the following is correct: The posts will be 36 inches deep into the concrete, and the beams are 6 inches across. The concrete is rated for 3000 PSI if it's 2 inches or more. So, does that mean that one of the sides is 6 * 36 = 216 in^2, and then 216 * 3000 = 648,000 LB, which is multiple orders of magnitude more, so maybe we are arguing over nothing. Aug 15, 2022 at 0:57
• My concern is more along the line of - what prevents the big lump of concrete from simply rotating in the ground? Aug 15, 2022 at 1:03
• 3000 psi is the compressive strength, so probably not relevant. Aug 15, 2022 at 1:24
• You might also need fancy (overbuilt) hardware connecting the post to the concrete... Aug 15, 2022 at 1:26