×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Need Compressive Stress Equation Explained. Please Help!

Need Compressive Stress Equation Explained. Please Help!

Need Compressive Stress Equation Explained. Please Help!

(OP)
Ok, so I have a shaft and a hub that is connected with a solid dowel pin in double shear. I need to calculate the compressive stress in the shaft and in the hub under a torque load. I've found an equation that I believe may be my answer, but can someone please break the equation down for me so I can understand what's actually going on here? Stress is normally calculated by σ = P / A and I understand that T = P*D, but where does the Area fit into the equation below? Please see the attachments for further details. Thanks in advance for any help!



Pressure in Shaft:
- This equation can be rearranged to (6*P)/(d*D). (d*D) is the Area, but how does the multiplier 6 come into play?



Pressure in Hub:
- Totally lost on this equation. Please explain.



Site For Reference

RE: Need Compressive Stress Equation Explained. Please Help!

Hi

Can you explain why you think you have compressive stress in the shaft?

RE: Need Compressive Stress Equation Explained. Please Help!

I think that he is referring to the bearing stress that the pin is causing to the holes of the hub and shaft.

RE: Need Compressive Stress Equation Explained. Please Help!

(OP)
Yes, I do mean the bearing stress. Just can't figure out how the equations above are derived.

RE: Need Compressive Stress Equation Explained. Please Help!

Where "in the hub" do you think this "pressure stress" from the formula is being calculated with the formula?

RE: Need Compressive Stress Equation Explained. Please Help!

(OP)
At the contact surface between the pin-hub or pin-shaft. The formula was actually found on mitcalc.com.

RE: Need Compressive Stress Equation Explained. Please Help!

Hi jus2sho

I've tried to find a proof for the formula's you posted with no luck, other than working through them myself which I haven't got time to do, however I believe the formula's to be correct if that helps.

RE: Need Compressive Stress Equation Explained. Please Help!

(OP)
I believe they're correct as well. I'd just like help if someone could explain how they're derived.

RE: Need Compressive Stress Equation Explained. Please Help!

"how does the multiplier 6 come into play?"
from bending of a rectangular section ... stress = My/I = M(d/2)/(b*d^3/12) = 6M/(b*d^2)
so p1 is the bending stress on the inner shaft as the shaft applies the torque to the pin.

the pin takes the torque from the inner shaft to the outer, as a couple. the pin is not in double shear; yes, there are two faces in shear, but this is not double shear.

see if you can take my description of p1 and figure out p2. hint, the outer shaft isn't a rectangle, but two rectangles.

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

RE: Need Compressive Stress Equation Explained. Please Help!

no, double shear means two shear faces are reacting the same load, so a fastener can rect something like double the single shear allowable.

this fastener the shear faces are reacting a couple; not double shear.

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

RE: Need Compressive Stress Equation Explained. Please Help!

Where did the 6 come from? Imagine force distribution on the pin rectangular area within the shaft diameter D. That force distribution is triangular with the largest value at the shaft diameter and zero at the shaft center. The resultant force of this triangle is applied at a distance of D*2/3 from the shaft center. That distance is D/2 * 2/3 = D/3. The resultant force is T/(D/3), torque divided by the moment arm of the resultant force. The shear produced by that force is tau*d*D/2 = T*3/D. tau = 6*T/(d*D^2).

Ted

RE: Need Compressive Stress Equation Explained. Please Help!

sure, there's more than one way to malipulate the math to get "6" ...
"triangular distribution of stress/pressure" = elastic bending distribution.

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

RE: Need Compressive Stress Equation Explained. Please Help!

(OP)
rb1957 nailed it. Thanks! It makes perfect sense where the "6" comes from. Now I just have to figure out the second equation...

RE: Need Compressive Stress Equation Explained. Please Help!

Hi

Here is an example showing the formula the op originally posted

https://books.google.co.uk/books?id=kfHD1ess3kMC&a...

Not though again the author states the pin is in double shear.

RB1957

The reason I believe the pin is in double shear is that when the pin passes through both sides of the shaft, it only takes half of the total load due to the total torque at each interface, now if the pin did not pass right through the shaft, ie a blind pin, then the force at the single interface due to the applied torque would be double that of the pin passing through both sides of the shaft.

RE: Need Compressive Stress Equation Explained. Please Help!

rb1957, I don't understand your using a rectangular cross section beam equation for a round pin. It seems that a better choice would be that for a round cross section beam.

The pin is in double shear.

Ted

RE: Need Compressive Stress Equation Explained. Please Help!

the rectangle is the section through the pin, reacting the torque with a linear stress field (aka bending stress), just like you proposed.

the pin is not in double shear ... the two active shear faces are reacting a couple; for me that is not double shear. for me double shear is when a pin has a load of 2P applied and reacts P on two faces.

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

RE: Need Compressive Stress Equation Explained. Please Help!

Hi RB1957

Well effectively that's what happens, if the pin is blind and only through one side it see's twice the force that it would see than if it were through both sides.
Another way of defining single and double shear is the number of pieces the pin break into on failure, so in single shear it would break in two pieces and in double shear it would break in three, now if the pin is through both sides of the shaft then clearly it would break into three pieces, would you agree?

RE: Need Compressive Stress Equation Explained. Please Help!

what are you trying to express when you say "double shear" ?

to me it's saying that the pin has two faces resisting the same load (2P applied, P reacted on 2 faces) so that the pin can support twice(ish) the usual load (ie 2*the single shear allowable).

i would not call this application double shear.

"if the pin is blind and only through one side" ... IMHO, no ... now you have two studs (as near as i can understand your description) each supporting 1/2 of the couple ... in single shear. I'm understanding the loading as torque coming down the shaft, and the pin takes the torque from the shaft to the cylinder.

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

RE: Need Compressive Stress Equation Explained. Please Help!

What is a couple? Two forces acting at some distance apart. Those two forces each act on the pin, lets say at the shaft/collar interface, creating shear loads on the pin where it crosses that interface twice. I see then double shear, one pin with two shear loads.

Ted

RE: Need Compressive Stress Equation Explained. Please Help!

sure, one pin with two loads ... call that double shear if you like, clearly you do; i won't.

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

RE: Need Compressive Stress Equation Explained. Please Help!

Hi RB1957

I can't post a sketch at present however let me try and describe what I believe,
Assume a torque of 100Nmm acting on a shaft of say 10mm diameter which is sleeved and pinned on one side only,so the pin can only transmit the torque through one interface, take moments to calculate the load on the pin at the interface and we obtain

100Nmm = 5mm * unknown force

Force = 100/5. ...... 20N

Now consider the pin passes through the shaft and creates two interfaces the reaction at each intersection becomes

Force= 100/10 ......... 10N

So we could increase the torque to 200Nmm to achieve a reaction of 20N at each interface thus increasing the capacity of the pin to transmit torque.

Now if the pin in the latter example fails and produces three pieces what failure mode would you call it, if it isn't double shear?

RE: Need Compressive Stress Equation Explained. Please Help!

no, i do not call a pin reacting a couple "double shear". i can see how you'd define double shear by the number of pieces the pin would break into, but i don't.

can we just agree to disagree ?

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

RE: Need Compressive Stress Equation Explained. Please Help!

Pressure in the hub.
The force on the pin in the hub acts at the mid-point in the hub thickness at diameter (D1 + D)/2. That force x (D1+d)/2 = T, or that force = 2T/(D1+D)

The pressure p2 = that force divided by the pin projected area(d*(D1-D)/2) or
p2 = (2T/(D1+D))/(d*(D1-D)/2) = 4T/(D1+D)*d*(D1-D) = 4T/(d*(D1^2 - D^2))

remember (D1+D)*(D1-D) = D1^2 - D^2

Ted

RE: Need Compressive Stress Equation Explained. Please Help!

Hi rb1957

Yes no problem. We can agree to disagree!

Regards

Desertfox

RE: Need Compressive Stress Equation Explained. Please Help!

i think you can get the same result using bending stresses, like i did for p1.

more than one way to skin a cat (but cats like none of them)

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

RE: Need Compressive Stress Equation Explained. Please Help!

rb1957, the OP asked for compression/pin bearing stresses, not pin bending stress.

Ted

RE: Need Compressive Stress Equation Explained. Please Help!

i'm tired ... yes, dear ...

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

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources