Stresses in hollow pins 2

[Albie2]

Will someone please tell me the formulae for calculating shear and bending stresses in hollow pins. My old textbooks only discuss solid pins. Can you suggest a good reference book?

Thanks

Albie2

 

[wes616]

for a solid pin

S = F/A = F/(PI * r^2)

for a hollow pin

S = F/A = F(PI * (ro - ri)^2

not much to it...

Wes C.
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[wes616]

Try STRENGTH OF MATERIALS; by J. P. Den Hartog, Dover Publications (June 1, 1961);ISBN: 0486607550

Wes C.
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No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[rb1957]

for bending stresses, there's only a change in I ... if you can calculate this for a solid bar, you should be able to do it for a tube.

for shear stresses, the same formulae applies for solid bars and tubes (VQ/It) ...

 

[chicopee]

RB57 has the rigth approach for bending stress calculation.

 

[dimjim]

for a hollow pin

S = F/A = F(PI * (ro^2 - ri^2))

essentially you are subtracting the area of the hole
from the area of the solid pin to get the rim
area as the above formula indicates.

 

[Gulban]

for a solid pin

S = F/A = F/(PI * r^2)

for a hollow pin

S = F/A = F(PI * (ro - ri)^2

I agree to wes the formulas are listed above

 

[gearguru]

Why are you multiplying the force with the area?

S = F/A
For a hollow pin:
A = PI*ro^2-PI *ri^2 = PI *(ro^2-ri^2)
(NOT PI * (ro - ri)^2)

and

S=F/(PI*(ro^2-ri^2))

 

[dimjim]

That slipped by me too.
Thanks gearguru!

 

[swearingen]

The shear resistance of a tubular member not subject to other modes of failure actually approaches half of the value stated, i.e., S=2F/A.

I've always understood this as the near-vertical side walls taking the shear (as in the web(s) of an I or box beam), where the top and bottom portions do most of the work in bending.

 

[dimjim]

Swearingen,
Could you give the resource for that conclusion?
Interesting!
It does seem that there would be some difference
as to whether it was a thin vs heavy cross section
and/or rim thickness vs diameter.

 

[swearingen]

I've been using that equation for years and once saw the derivation, but a quick look in my library found this one:

AISC Steel Construction Manual, 13th Edition, Spec. Chapter G6, Round HSS.

"The nominal shear strength, Vn, of round HSS, according to the limit states of shear yielding and shear buckling, is
Vn = FcrAg/2 "

Fcr is the critical buckling stress and depends on D/t ratio, Ag is the gross area, and HSS stands for Hollow Structural Section which pertains to a specific type of pipe used in structures.

Note that the AISC spec is not intended to design watchband pins and the like, but I've used it for hollow pins as small as 1/2".

My first post alluded to other failure modes such as local buckling; this equation and the ones further along in the text take those issues into account. However, if you have a good feel for the material and proportions of the pin and know it won't fail in those modes, I think the S=2F/A number is a good one to compare to the yield stress.

 

[dimjim]

Swearingen
Thanks!

 

[gearguru]

It depends in how many places on the pin is the shear applied.
If in 2, then the swearingen's formula is what I would use also. If in one location only, then I'd prefer to use mine formula.