Net Section Modulus of Plate with holes

[jseng9]

Hi,

Would anyone be able to help me determine the formula for the net section plastic section modulus (Znet) of a plate with holes in it as in the attached. I understand the section modulus is simply (tp* dp^2 )/4 and thought I could simply use the same formula and sub in the hole diameter then subtract the hole sections modulus from the plate plastic section modulus but I wasn't succesful. See the photo of the plate I am trying to calculate. Bolts are 0.75" and holes are increased 1/8". Plate in question:

https://imgur.com/gallery/CFKRsmX

Risa calculated Znet = 9.56 in^3

Thanks!

 

[JStephen]

Top section above the bolt hole is 1.0625" wide, next section between bolt holes is 2.125" wide, middle section is 2.125" wide.
Assume top half has full yield stress over the whole area, reversed on the bottom half, calculate the moment.
So 1.0625"tSy(5.46875") + 2.125"tSy(3")+2.125"/2*tSy(0.53125") = 12.75tSY for the top half, or 25.5tSy for the whole plate.
So take Z = M/Sy = 25.5t. If t=0.375", Z = 9.5625. I don't see thickness stated, but assumed that to match your answer.

This is adding up the positive areas, you could take the total moment and subtract the contribution at the holes and should got the same thing- not the same as subtracting the Z's about centroid of each area, though.

 

[jseng9]

Hi there, yes the thickness of the plate is 0.375"! Thank you very much for the thorough response.

 

[jseng9]

Hi, sorry to bother you. Could you just tell me how you got Sy?

 

[jseng9]

Thanks JAE. I will look for posts I can contribute to

 

[jseng9]

JAE Are you able to help me find Sy or are you also unable to do your workflow/job?

 

[r13]

jseng9,

I hope you really learn the concept here, rather than just hoping to get the solutions. Once you are solid on the theories, and concepts, then given some time, you will develop the critical skill of parallel thinking and engineering judgement.

 

[jseng9]

Hi retired13, I appreciate your post. I’m going to work out the problem by hand and will share with you. Thanks for your help

 

[jseng9]

JAE please do not comment on any of my posts going forward. I find your behavior very hostile and you contradict the spirit of Eng-Tips.
Instead of trying to help people you consistently shoot them down. I do not want to associate with such foul people. Thank you kindly

 

[JStephen]

The Sy cancels out, so it doesn't matter what it is, just a means of visualizing what the Z is.