Circular plate segment/bending

[bangerjoe]

Hi

i have a circular plate (annulus) in which i propose to drill a hole and suspend a load through an eye bolt.

the plate is connected via full penetration weld to a shell of the same thickness on the inner side of the annulus.

just wanting to know what section property i should check for in bending?

i tried taking the bolt width as the 'b' value of section modulus, but get an astronomically high bending stress which i just don't believe. someone suggested taking 45 degrees projection onto the annulus and use that as the section. (i've treid to explain via the attacehd image - sorry i don't have CAD).



Thank you in advance.


i will also take checking for punching shear of the washer thru the steel, bearing stress of the washer on the steel, and assess the weld against the shear and bending combination.

 

[bangerjoe]

oopsy attached.

 

[prex]

Check Timoshenko's Theory of Plates and Shells 2nd Ed. page 211, there you'll find the justification of the 45 deg.rule: for a conc.load at the free edge of an infinetely wide cantilever, the peak bending moment per unit length is close to P/2.
When the load is inside the plate, the peak bending moment decreases very roughly in proportion to the distance from the built in edge: you could check this with this tool (from the first site below): with the load in the middle the max b.moment is 0.655 times with respect to the load being at the edge. This is higher than a simple linear decrease, but as you could also average the bending moment over a width of the plate, taking a linear decrease should be still safe.

prex
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