0

I am calculating the shear and moment for a combined foundation with bi-axial moments on each columns. I got the pressure at 4 corners under the foundation. in order to be able to calculate the sheer and moment, I would like to know how to calculate the volume of pressures under foundation. pressures look like below photo.

If I will be able to calculate the volume of below prism, then things will be easy. The top side is NOT planar enter image description here

Xin Lok
  • 103
  • 1
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Mar 10 '23 at 13:17
  • 1
    The question already seems to have an answer here: https://math.stackexchange.com/questions/438766/volume-of-irregular-solid – Martin Westin Mar 10 '23 at 13:44
  • 1
    The first thing to do is to decide how your upper surface looks like. As you say, it may not be planar indeed: just imagine a square on the ground, and on three of the four edges, the height is 10. But on the fourth edge the height is 1. There are multiple ways to create a surface, fitting in that, but which one will you choose for simulating your situation? – Dominique Mar 10 '23 at 14:31
  • 1
    @MartinWestin: I believe the question you refer to mentions a situation where the upper part is a plane, which is not the case here. – Dominique Mar 10 '23 at 14:33
  • Thanks @MartinWestin yes, the upper part is not plan – Xin Lok Mar 10 '23 at 15:31
  • @MartinWestin thanks for the link, I am reading the answer of Mark Davich – Xin Lok Mar 10 '23 at 15:41
  • You can find the answer in reply of Mark davish https://math.stackexchange.com/questions/438766/volume-of-irregular-solid thanks to @MartinWestin for posting the answer. – Xin Lok Mar 10 '23 at 16:25
  • 1
    I’m voting to close this question because as noted in the comments, it already has an answer here https://math.stackexchange.com/questions/438766/volume-of-irregular-solid – postmortes Mar 20 '23 at 07:28

1 Answers1

1

If the top is not planar, then the best we can do without a decent bit more of information is estimate. As is noted by Martin Westin, this has been answered already.

But to quickly summarize, we basically just average the heights: $h = \frac{h_1+h_2+h_3+h_4}{4}$ and use that as the height of a box. So the volume is: $$V = a\cdot b\cdot h$$ It is a rather good estimate if the top is close to planar. And without doing lots of measuring, I doubt you will be able to get closer to the real value.

N. Owad
  • 6,822
  • The top part might not be close to the planar. Its all depend on the forces and moment applied to the pedestals. I cannot use an average otherwise the result will not be accurate. – Xin Lok Mar 10 '23 at 15:28
  • your answer is correct, even if it is planar, the volume will be as you said, can anyone confirm before accepting the answer please? – Xin Lok Mar 10 '23 at 16:28
  • @XinLok It is the same answer as worked out in detail in the linked post by Martin Westin. Look there for the full explanation. – N. Owad Mar 10 '23 at 17:31
  • Full explanation is available in the linked posted by Martin – Xin Lok Mar 10 '23 at 18:41