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Normal force resolution - four point support

Normal force resolution - four point support

(OP)
Hi all, a quick question for you guys to help as a refresher.

Say for instance a round bar is seated in a VEE BLOCK with included angle in the VEE of 90 degrees. Assuming vertically downward force of 500N from the weight of the bar, then the Normal force onto each planer face of the VEE would be 353N (500 x cos(45)).

If this same set-up was placed on a support block that made contact in 4 positions rather than 2 - lets say P1@30degrees, P2@60degrees with P3 and P4 symmetrical to these about the vertical axis. Assuming geometry, pad stiffness etc ensured the load was equally shared between all four, then how do I resolve those same normal forces at each pad. I would end up with 2 equations and 4 unknowns - I assumed there is some symmetry I can take advantage of in that P1 = P4 and P2 = P3.

With that in mind I get sum of forces in
X=0, 0.86P1 + 0.50P2 - 0.50P3 - 0.86P4 = 0
Y=0, 0.50P1 + 0.86P2 + 0.86P3 + 0.50P4 = 500

Using symmetry to remove P3 and P4 from the equations, and simplifying I get P1=P3 = 216.5N and P2=P4 = 125N. Putting these back into the original equations seems to be correct, but just can't help feeling I've slipped up somewhere so would love to hear thoughts.

Thanks.

RE: Normal force resolution - four point support

Draw your force diagram, show the plan and elevation views of the four supports. It is not clear (to me at least) that you are as symmetric as you think.

RE: Normal force resolution - four point support

E240509,

A four point contact is not solvable by statics. The contact forces will be affected by the rigidity of your bar and your base.

--
JHG

RE: Normal force resolution - four point support

drawoh is correct, although a reasonable assumption may be equal reaction forces, or equal vertical components, or ...

another day in paradise, or is paradise one day closer ?

RE: Normal force resolution - four point support

If they're real machined parts then I would guess the part inaccuracies (roundness, bending, flatness, etc.) may be more significant than the relative stiffnesses of the part and v-block.

RE: Normal force resolution - four point support

Solution looks correct to me, assuming simple contact and rigid parts.

RE: Normal force resolution - four point support

if you could define the part inaccuracies (the real world problem that 4 points aren't going to line on the ideal curve) and the stiffness of the different loadpaths, then you could solve it.

Failing that you could assume (and, yes, I know what you get when you assume ...) something reasonable and get a result that may be somewhat reasonable (or it could be fiction).

another day in paradise, or is paradise one day closer ?

RE: Normal force resolution - four point support

Based on OP's description and problem statement, I interpreted this as an academic exercise, not an attempt at resolving forces on real parts with tolerances.

RE: Normal force resolution - four point support

E240509:
The above discussion and comments is why, in a situation like this, you usually make the blocks P1 - P4 out of some material which is allowed to yield a bit to try to achieve a more uniform bearing stress or set of reactions. This becomes a very difficult problem to solve, for the reasons mentioned above, but you can work to assure that the blocks yielding a bit, preventing damage to the primary/valuable part. For example, you might line the vee-block, or as in your sketch something approaching a saddle, with a material slightly softer than the round bar or vee-block so that this softer material could conform a bit to both outer pieces, as a function of the high bearing stresses, at high geometric spots. The other extreme is a large pressure vessel, in a shipping saddle, with oak 2x4's lining the curved surface btwn. the saddle and the vessel.

RE: Normal force resolution - four point support

(OP)
Hi all - purely for interest only and thanks for your views. I have seen large OD pipe sat on two point supports and also some on four point and just curious as to a potential method of knowing what each support may be loaded with. As with previous comments, the attachment of soft compliant lining or rubber coated rollers is often the 'real world' set-up.

RE: Normal force resolution - four point support

E240509,

You may not appreciate how resilient a four point support is with many tons of large diameter pipe sitting on it.

--
JHG

RE: Normal force resolution - four point support

so it'd head towards a equal reaction force (equal pressure in the resilient lining) solution ?

another day in paradise, or is paradise one day closer ?

RE: Normal force resolution - four point support

rb1957,

Here is a thought.

Could you arbitrarily define some reaction forces. Instead of making them equal, vary them by ±50%. Analyze your base for stress and deflection. You probably understand how out-of-round your pipe is. You know what sort of fabrication tolerances are feasible with your mount structure. Your analyzed deflections should reflect this, right?

--
JHG

RE: Normal force resolution - four point support

sure, or maybe bound the solution by using either the inner pair or the outer pair ?

another day in paradise, or is paradise one day closer ?

RE: Normal force resolution - four point support

"how do I resolve those same normal forces at each pad?"

If the purpose of the exercise is to "solve for normal force," you can't, as so many others said.

If however the purpose of the exercise is to use statics to evaluate the design for damage, etc, then the iterative method mentioned by Drawoh and probably others should suffice.
Similarly, codes that cover lifting with slings and cables wisely insist that any diagonal pair be sufficient by itself.

RE: Normal force resolution - four point support

E240509,
I didn't get past your second sentence.
I don't think the distribution of reaction forces is going to matter if you have P=W*cos(a) when you should actually have P=(1/2)W/cos(a).

STF

RE: Normal force resolution - four point support

Your system can be easily solved by the concept of statically indeterminate structures which incorporates strain as an additional equation under the flexibility and stiffness methods. A references into solving your problem is under Mechanics of Material authored by Gere and Timoshenko. A second reference being the Theory of structures by Timoshenko and Young primarily dealing with structural analysis but by extension of the subject matter presented in that book can also solve your problem. While books are expensive, you can find them from used book dealers found on the internet which in my case I'll first search Abe Books site.

RE: Normal force resolution - four point support

However, it does put you in the ball park.

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