×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*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.

# FREE BODY DIAGRAM

 Forum Search FAQs Links MVPs

## FREE BODY DIAGRAM

(OP)
Hey,
I have a conceptual design, and I need to first check its potential strength.
Here is a schematic picture of the conceptual design:

I have a lifting bridge for lifting the weight through its interface which has 2 Shear pins for taking the shear.
The Shaft/Hole fit (marked in purple in the picture below) is H7/g6, so there is a transition fit.

By the way, the thread is loose while the Shaft/Hole fit is tight, so theoretically the Shaft/Hole interface is the one to take the loads due to bending and not the thread, which is there only to axially secure the threaded pin in its place.
I tried to have a FBD (Free Body Diagram) of the threaded pin part, which I suppose is the critical one.
Here is a picture of my FBD:

Here I try to find the internal (in the critical cut) forces and moments by equilibrium:

After finding V and M I find the shear stress and the normal stress using V/A and (M/I)*R correspondingly, and using von mizes relation sqrt(sigma^2 +3*tau^2) brings me to 80 Mpa.

The problem is that in the analysis I get around 25 Mpa.
I have to point out that I already checked a configuration in which there isn't a thread at all (as in the picture below), and the results didn't change.

So I am interested to know which one might be mistaken - the calculation or the analysis?
I just hope you can help me by checking the calculation process I made.

Thanks

### RE: FREE BODY DIAGRAM

why have a thread if the blue shaft is a tight fit in the green socket ?

is the blue shaft adjustable ? within the tight fit of the green socket ??

are you taking care to leave a space at the vertical face of the blue shaft ?
if not, then ...
1) this face is another loadpath for moment, and
2) you'll end up stripping threads (if you keep turning after the vertical face has seated.

you could consider a "jam nut", on the OML of the blue shaft.

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

### RE: FREE BODY DIAGRAM

(OP)
rb1957
I am sorry but I don't understand your probably useful comments. What about the FBD? Any comments?

### RE: FREE BODY DIAGRAM

Any dimensions? Could be your first FBD is mostly correct. I think I would model it as a cantilever with a moment applied to the left end and R2 as shown.

### RE: FREE BODY DIAGRAM

before you worry about the FBD, you have to worry about real things.

how does the thread work if there is a tight fit between the blue shaft and the green socket ?

if the blue in green is a permanent install, then the tight fit would work (I'd go for thermal interference).
But then you don't need the thread ?

if the blue in green has to dismantle, then you Can't have a tight fit.
So you should look to mechanical restraints, like cross bolts.

describing the moment restraint within the socket as a couple is "simplistic", and I'd rather keep it as a moment.

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

### RE: FREE BODY DIAGRAM

(OP)
There is no interference, H7/g6 is a "sliding" fit, so dismantling shouldn't be a problem.
About moment instead of couple - I didn't say both reactions are identical, hence it's not a pure moment (a couple) but reaction forces as might be in the real case. In my opinion the bushing can't provide the pin with moment as suggested earlier, but only forces.
A moment as a reaction would be taken into account if, for example, the parts would be welded to each other.

### RE: FREE BODY DIAGRAM

One problem I see is if the lifting pins are round and locate in the lifting frame, then what stops the loads along with the pins rotating within the liftingframe, put another way what holds the load horizontal while it’s being lifted?

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: FREE BODY DIAGRAM

(OP)
desertfox
A good remark, and since I didn't model everything it seems missing. But in reality there is a plunger that does the work.

### RE: FREE BODY DIAGRAM

a real world problem with a two point lift.

as to fits ... I read this "By the way, the thread is loose while the Shaft/Hole fit is tight".

can you expand this comment ... "After finding V and M I find the shear stress and the normal stress using V/A and (M/I)*R correspondingly, and using von mizes relation sqrt(sigma^2 +3*tau^2) brings me to 80 Mpa. The problem is that in the analysis I get around 25 Mpa."

are you saying a hand calc gets you 80MPa but FEA gets you 25 MPa ?
or worse are you saying the "answer" is 25 MPa ?? (if so the direction about homework)

what do you mean with "since I didn't model everything it seems missing" ?

relevant to your FBD ... what's the distance between R1 and R2 ?
a) the width of the blue/green overlap (as though the blue shaft has "cocked" in the (large) green socket hole, and is contacting at the extreme ends) ? or
b) 1/3 of the width ? (why would I think this ??)

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

### RE: FREE BODY DIAGRAM

Hi well if there is a plunger supporting the load then the load weight is not necessarily a two point lift, can you show the plunger on the model please.

Further we can’t check the 25Mpa without knowing size of pins etc, in principle the FBD a appears correct however the practicality of the lift frame and pins isn’t the best way forward. For example the concentricity of the thread to the
the toleranced pin diameter is critical because if the thread concentricity is out by more than the clearance between the bore and the pin then you won’t be able to assembly the pins to lift it. This statement also holds true for the tapped hole and the bore on load you are trying to lift.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: FREE BODY DIAGRAM

That free-body diagram - the one that shows reaction loads where gaps will be?

### RE: FREE BODY DIAGRAM

What “analysis” was used to get 25 MPa?

### RE: FREE BODY DIAGRAM

(OP)
Here are some photos of the design.
You can see that the lifting pin has a supporting flange with bolts.
But the Engineer who is in charge of the safety required calculating it as if there are no bolts and there is no support by the flange.
The motivation is making sure that improper use of the device may not immediately lead to a failure.

Here is a calculation of the stress in the critical cut under the assumptions above (reauired by safety).

### RE: FREE BODY DIAGRAM

It would all workout better if you used a taper fit rather than a clearance fit, with a straight start and hole.

### RE: FREE BODY DIAGRAM

(OP)
Compositepro, why?

### RE: FREE BODY DIAGRAM

Since the bolts are on the neutral axis they don't help much. The thread is shown in bending, unlike the original problem statement; not an ideal condition as it creates a stress concentration, possibly 5 to 10 times the expected stress.

It looks to me like this arrangement will twist the ring and then the pin will sit at a substantial angle in the cradle.

Is this a copy of an existing product?

### RE: FREE BODY DIAGRAM

yes, it looks sort of magical, but then I don't think we're seeing the complete story.

ok, your calc is 84 MPa, looks reasonable. why do you "think" the answer is 25 MPa ?

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

### RE: FREE BODY DIAGRAM

I think you're close enough for a bush job on this one already but for the sake of debate I think your reaction will actually occur on the 'face' of the pin which mates with the outer ring diameter. I would treat the spigot end as a fail-safe should the 4? external fasteners fail to hold that joint tight.

This approach makes no difference to your hand calc which seems correct enough to me although I'd probably set my inital free-body diagram up a little differently as a result. It does make a difference to how tight the spigot fit needs to be (not very) and whether you develop concerning stress concentrations at the section step.

Why is the socket bushed? Curiousity only.

### RE: FREE BODY DIAGRAM

Well it appears we agree with the analysis, however I still don’t understand how the whole bottom ring doesn’t rotate along with the flanged pins, sorry for my ignorance.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: FREE BODY DIAGRAM

The pins are held in place by 4 SHCS (two each side) to the ring so the ring can't rotate relative to the pins. The pin in turn is restrained from rotation by the torque arm (clamped to the pin just inboard of the hook) which can be fixed in what appears to be two positions 180 degrees apart by the index plunger on the hook.

### RE: FREE BODY DIAGRAM

Thanks, I get it now 😀👍

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: FREE BODY DIAGRAM

The index plunger doesn't stop the torque arm from rotating away from the bridge frame. If the load is high enough the ring will twist taking the pivot pin with it and move the torque arm out of engagement with the index plunger.

### RE: FREE BODY DIAGRAM

Does the pin thread into the ring?

### RE: FREE BODY DIAGRAM

@3DDave - one assumes that the ring is designed with sufficient stiffness to prevent a second order failure of that kind. Given the load is a whopping 100 kg total, it's an entirely plausible design.

### RE: FREE BODY DIAGRAM

"one assumes" isn't good engineering practice when "The motivation is making sure that improper use of the device may not immediately lead to a failure." which may mean this gets snagged and the load is 10,000N.

### RE: FREE BODY DIAGRAM

(OP)
Hey
rather_be_riding the bushing is for preventing cold welding of the metals (PH 15-5/AL 6061-T6).I think there is a little chance it may happen, but I don't want to take a chance.

3D Dave, the carried load CG is almost coincide with the ring symmetry axis, so the plunger is expected to endure a small shear force.

### RE: FREE BODY DIAGRAM

Does the pin thread into the ring?

You don't answer questions, but then question answers?

### RE: FREE BODY DIAGRAM

@3dDave

I don't think the remainder of the design was really the OPs question. They were specifically asking about the analysis of the pin.

If we really want to get into misuse cases, the only real solution is load limiting on the hoisting device. If this happens to be sitting under a 50 tonne crane for example, there's no reasonable way you're going to protect against all modes of load snag. The practical outcome in most facilities is just that operators have to not be zombies because SOMETHING somewhere has to fail if you snag. If it's not the lifting device, it'll be the hoist or the unfortunate item that gets snagged. Load limiting tends to be impractical for any system that hoists more than one load of course which is almost always the case where we see lifting points intended to be used with hooks (as this one is). If I want to limit the crane to match a lifting device, it's usually permanently close coupled without a hook.

If the OP is working to a lot of common standards, they probably have a factor of safety of 2 in that 100 kg load already. A lot of lifting devices are tested at twice the rated capacity prior to commissioning.

### RE: FREE BODY DIAGRAM

@rather - the OP has skipped answering a number of questions. I doubt that you have any answers.

### RE: FREE BODY DIAGRAM

OP ... please explain this comment in the OP ...
"The problem is that in the analysis I get around 25 Mpa."

Your analysis looks to be theoretically reasonable, but the design seems to have real world issues (mostly the very minimal support of the load).
Now, maybe there are good reasons for this, but we don't know your design decisions and limitations that led to this design.

You ask about your FBD. Sure, that is a solution, a fairly reasonable solution if a lot of assumptions are made. The question I think we have is does the FBD accurately reflect your specific design, given we can't see all of the design. And are you accepting of the (implicit) conservatisms within the FBD, or are you looking for something more accurate.

Are you saying that your hand calc gives 80MPa but an FEA gives you 25MPa ? Not very surprising if this is the case.

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

### RE: FREE BODY DIAGRAM

(OP)
Sorry for the delay in replying.
I don't have access to the computer most of the week, and it's very difficult to answer in detail through my mobile phone.

3DDave
"The thread is shown in bending, unlike the original problem statement; not an ideal condition as it creates a stress concentration, possibly 5 to 10 times the expected stress" - which thread do you mean? maybe you think the blue interface in the picture below is a thread? if you do, so it's not, it's just H7/g6 fit od the pin to the bushing. if you meant the thread that is marked with an arrow, so nothing is threaded into it at this stage.

"It looks to me like this arrangement will twist the ring and then the pin will sit at a substantial angle in the cradle" - why? 2 is secured to 1 through the bolts that aren't seen in this section view, 3 is secured to 2, and 5 locks 3 and located at 4. as a result there will be only negligible movement due to small clearances of mating surfaces.

"Does the pin thread into the ring?" - no, see my explanation above.

rather_be_riding
"external fasteners fail to hold that joint tight" - why? if they generage axial loads that lead to enough friction (coefficient of friction*total axial force) the pin/hole interface isn't theoretically needed, but is there only for a backup.
In addition I agree that analyzing this problem like I did is very far away from reality, but I should prove this device for the worst case scenario in which no bolts are tightened and no face to face tightening exists, and as a result all the load is carried by the pin.

A new update - After reviewing my analysis with an expert we found a problem in some contacts in the analysis, something that led to distorted results, and after fixing it the results were quite close (+/- 10%) to the hand calc!!!

### RE: FREE BODY DIAGRAM

@elinah - I wasn't suggesting they wouldn't hold the joint tight; I more meant a fail safe in the event someone fails to tension them properly. We're in agreement. Glad your check matched up in the end.

### RE: FREE BODY DIAGRAM

Elinah34,

I suggest you reconsider your design if you have not done so. The lifting mass centre of gravity point should always lover than the handling shaft centreline. Otherwise there will always be a tendency of failure in the balance of lifting mass and lifting equipment. This should be a major point in the risk analysis for the entire lifting operation.

This may probably change your design slightly or substantially, you need to decide.

### RE: FREE BODY DIAGRAM

(OP)
saplanti, you are right.
As I mentioned earlier, you see only partial image of the entire assembly. In the reality the c.g should coincide with the axis of rotation.

### RE: FREE BODY DIAGRAM

Dear elinah34 ,

I did not read the previous posts but just screened. The FBD at your 4th post is OK but there are some errors at calculation . ..

I =( Π* R**4)/4 If D=18 mm r= 9 mm = 0.009 m.

I = ( Π* 0.009**4)/4=5.15 *E-09 or ( 5.15*10**(-9 )) M**4

σ = M*y/ I =( 48.2*0.009)/5.15*10**(-9) =84,233,009.71 N/m2 so, 84.2 MPa is OK.

The Von Misses stress calculation shall give the same result .

When you assume the section as a clock, the max bending stresses will develop at 6 and 12 hrs.
The max . shear stress will develop along the axis 9 to 3 .

So the max stress in this case at 6 and 12 aclock.

PS.
1- When you apply FS =4 , ( Common practice for lifting tools and eq.) that makes 337 MPa. what is the yield str. of the material?
2- I f i were, i would consider a different set up.( such as a cross piece lifting frame and four point lifting with cable etc )

### RE: FREE BODY DIAGRAM

as much as we look at the blue pins, we also should look at the yellow lifting beam in the 1st post.

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

### RE: FREE BODY DIAGRAM

(OP)
HTURKAK
Thanks for checking the calculation. There is a requirement of having the ability to rotate the lifted mass while it's lifted. That's why there is a 2 point (along an axis) connection.

rb1957
The yellow jig is an existing one that is proven to safely lift up to 300 kg mass.

### RE: FREE BODY DIAGRAM

I think the reason you're seeing such a discrepancy between your hand calculations and the FEA results are because you're using σ = M*y/ I to determine bending stress.

Beam bending is only really valid when the span/depth ratio is around 8 (according to Roark)... It appears you have a span/depth ratio less than 1 (L=17.1mm and D=18mm). As such your pin will not act like a beam.

### RE: FREE BODY DIAGRAM

(OP)
_eh-ngineer
Thank you. Which formula is relevant for hand calculation in such cases ("short beam")?

### RE: FREE BODY DIAGRAM

elinah34
There really aren't any relevant hand calculation formulas for a short beam. The closest you're going to get is something akin to stress on a gear tooth, and even this likely won't give you reasonable results for hand calcs.

FYI, this is all reviewable in Roark's Formulas for Stress and Strain section 8.10.

In this application you could consider only shear with a significant stress concentration at the shoulder.

### RE: FREE BODY DIAGRAM

(OP)
Thanks, I will take a look at it.

#### 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.

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

Click Here to join Eng-Tips and talk with other members! Already a Member? Login

#### Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Design for Additive Manufacturing (DfAM)
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a partâ€™s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!