Check out Roark's Formula's for Stress & Strain by Warren C. Young. With some simplifying assumptions, you should be able to find a design case that meets your needs. In the 6th edition book, see Table 24 Formulas for flat circular plates of constant thickness.
You should be able to find a solution in Roark, "Formulas for Stress and Strain." In my edition, Table 24, Case 16 seems to apply.
Not to be picky, but the problem is incorrectly stated. You can't avoid bending in this situation, unless you have no load. The issue is to avoid material failure or excessive deflection.
If the deflection of the plates is small, it can be assumed that the bolts will only see tension loads. Large deflection of the plates will place bending loads in the bolts.
loafer09. Yes we are trying to maintain the least amount of deflection possible. Therefore we are trying to determine the thickness that will achieve this. We're not worrying about the bolts because since we don't want much deflection there won't be any relevant bending on the bolts. We just need to know how to design the circular plate so that we can achieve the desired load without going past the yield point.
The boundary condition of each plate is closer to clamped than simply supported, but the stretching of the bolts will put it somewhere between the two.
Providing enough pretension in the bolt such that there is residual compression at the interface at the given loading might not be a bad idea. Thoughts?
Yes, slickdeals. Pretensioning the bolts will provide a better clamped edge along the bolt circle.
Checking deflection can be done using Equation (88) from "Theory of Plates and Shells".
Checking bending moment in the vicinity of the clip is not quite so easy because of its rectangular cross section. The force P on the sketch must be pretty substantial if ten 1.5" diam. bolts are needed to resist it. Perhaps the force should be applied to the plate by a round hollow section welded all around its circumference to the plate. The clip could be welded to the inside of the cylinder.
Please note that with normal plates and the equations of Roarks and those in Timoshenko there is no large displacement allowed. If the plate deflection is more than 1/2 the thickness you've exceeded the elastic equation limits and the resulting stresses are conservative and unrealistic.
Regards,
Qshake
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If you are really interested in some meaningful comments and ideas on you problem, it would be interesting to know a bit more about what you are trying to accomplish or what’s driving the sketch you have shown. It’s good to have shown a sketch, but without more detail, one immediately begins to wonder, why is he trying so hard to make his problem difficult.
If you are concerned about circular plate stress and deflection, why on earth would you use a 60" bolt circle? Why not 24" or less? With 10 - 1.5" bolts, what is the load P? You will have multi-axial stress concentrations at the four corners of the pulling lugs, a tearing stress, as they are so unsymmetrical wrt the bolt circle and the rest of the lug connection. This is also an area on the lug/plate weld which is difficult to make and prone to stress raisers in the weld itself. BA’s idea of a large pipe welded to the circular plate at least gives you a symmetric and relatively uniform loading between the bolt circle and the pulling load. Then, as he suggests, you can detail the actual lifting lug inside the stiffening pipe. All of these connections and load paths are much more easily rationalized.
Why not make your lifting lug 20 or 24" long, weld it to the plate, and put 5 bolts equally spaced, on either side of the lug about 3" from the lug. Then you basically have a cantilever on each side of the pulling lug, and the rest of the plate can be any shape you want. You didn’t indicate that there is really anything going on out there at the 72" circle.
forget the circle; model it as a two-way square plate.
Mtotat = PL/4 then divide that by two for each direction.
pre-tension the bolts like other posts suggested
check min thickness for prying action
![[pipe]](/data/assets/smilies/pipe.gif "[pipe] [pipe]")
