1. Jul 10, 2008

### capterdi

Hi,

It´s been quite a while since the last time that I had to solve a classic statics load problem (about 20 years ago).

Here is my problem:

I have a simple "C" type hook (please refer to attachment "Gancho.jpg") made of 25.4 (1 inch) diameter commercial steel (for example cold rolled steel)

And I need to know which would be the maximum load that the hook can withstand.

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• ###### Gancho.JPG
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2. Jul 11, 2008

### justin0741

Maybe I am late with this response, but I learned an analytical technique last year for finding the stresses in curved members.

Its called the "Winkler-Bach Method". It is based on the assumption that transverse planar sections in the curved parts of the member are do not deform. "plane sections remain plane".

If you still want to know about it let me know and I will show a quick analysis for one of the curved parts. With that, you should be able to do it for the rest of the curved parts.

Heres what you need to know first:

1) What is the radius of curvature of each of the bends. The drawing attached does not indicate this. THIS TECHNIQUE IS WORTHWHILE ONLY IF THE CURVATURE OF THE MEMBER IS COMPARABLE TO ITS CROSS-SECTIONAL DIAMETER

2) What is the maximum tensile strength the steel and safety factor in the design.

3) What failure criteria need to be considered for the material. I would probably put the maximum shear stress in the member at half the tensile strength of the material if cracks are not a concern.

4) Perform a static analysis to determine the forces and moments where the curved parts are tangent to the "straight" members. The forces and moments can be related to the applied load on the hook.

5) use My/I=-Ey/(r0-y)*r0*(1/r-1/r0)

M- moment acting on curved segment

Use principles from statics (Newtons 2nd law) to relate the applied load to 'M'

I- moment of inertia = pi*(1 inch)^4/32
y=d/2=0.5"
r0- distance from centroid of curved member to the location where the stress is to be determined
r- distance from center of curvature to location where stress is to be determined

I use this a lot with FEA to check the maximum stresses in a model (FEA results distribute stresses accurately, but the maximum values are often off by at least 10%, and usually 15% in my experience.)

If all you want to do is find the static loads and moments, you need to specify the location. My knowledge leads me to believe that the most stress will occur in one of the curved segments.

Justin
justin0741@msn.com

By the way, I am getting my masters next year (not related to materials though I've had quite a bit of training related to the subject), so if you're impressed tell your hiring manager.

3. Jul 11, 2008

### capterdi

Hi Justin,

Great! Thank you. I´m interested in the method, and would like to understand it so to solve my hook problem through calculus.

Regards,
Carlos

4. Jul 11, 2008

### capterdi

5. Jul 11, 2008

### capterdi

"THIS TECHNIQUE IS WORTHWHILE ONLY IF THE CURVATURE OF THE MEMBER IS COMPARABLE TO ITS CROSS-SECTIONAL DIAMETER..."

Ok..all radii involved are 20 mm (the inner curve of the material is 20 mm). So, I think it complies with this criterion...right?

6. Jul 11, 2008

### justin0741

Yes. it does. However, the bend at the top of the hook appears top have a significantly larger bend radius than the other ones. Are you sure they are all the same? If the drawing you provided has a uniform scale, they definitely are not all the same.

Confirm this, and we can continue.

once you know the bend radii you should first use geometry to find the length of the straight segments of the piece.

Then you can do a static analysis to relate each of the moments to the applied load.

7. Jul 11, 2008

### Mech_Engineer

Overall, this is not a very good design for a hook. The corners act as stress concentrators that subject several parts of the hook to large bending stresses. Additionally, the round cross-sectional geometry gives large stresses at the edges of the material.

I would recommend buying a hook from McMaster-Carr that suits your lifting requirements, rather than bending one out of 1" rod.

8. Jul 11, 2008

### capterdi

At the top of the hook the bend radius is 50 mm.

Mech Engineer: your recommendation sounds good. The problem is that someone came up with the idea of fabricating this hook as I show it in the sketch, and start using it. So I was asked to work out from a theoretical point what the "safe" maximum load is going to be, and may be to put a sticker on the hook stating something like "Caution - Max. load = ??? kg.

9. Jul 11, 2008

### capterdi

And now I will have to apologize to everyone. At this time I realize that it was not a good idea from my side to start such a thread precisely 2 days before going to vacations. I´m going to be one full month out of my workplace, and so not going to be able to go into more detail around this issue.

But I seriously promise that around August 14 I will resume follow-up on this thread.
Again, I feel sorry for any inconvenience.

10. Jul 16, 2008

### PERCINV1

Hi , Sorry For Getting In This Discussion Out Of Nowhere , I Need To Know If Anyone Can Help Me Here , I Am Making , Desing , Calculating To Build A C Type Hook . My Concern Is That I Need To Know What Are The Rules That You Or One Needs To Certify This Hook Ones Is Already Build . Let Me Explin Myself Better , There Is Rules That Can Make This Hook After Construction Be In Legal Status. In The Company Where I Work For Ther Has Been A Lot Of Accident And Recently One Hook C Type Broke In Half . If Anyone Can Hell Me I Will Really Appreciated , I Have Been Looking Everywhere In The Internet And Defferent Books.
percin@ualberta.ca

11. Jul 16, 2008

### Mech_Engineer

Just buy a hook from a manufacturer that is rated for the load you're working with. You won't save any money designing your own when you take into account the engineering costs; and judging by your post, you don't have enough experience to design such a safety-critical item.

Basically, the original poster (when he gets back) needs to realize that he CAN'T rate the hook he has shown because he knows nothing about the material used or if it was tested to any specifications. With the amount of time and money he will spend trying to analyze the thing he can easily purchase several hooks that have a rating already from a vendor that specializes in hook design.

As an engineer, I would not be comfortable signing off on any hook's load rating without:
• Very specific data about the material it is made out of with test specs (ASTM or other)
• Some robust analytical and/or FEA calculations for stresses in the hook
• Very specific knowledge about its intended use

Last edited: Jul 16, 2008
12. Aug 20, 2008

### capterdi

I have attached the solution that I could figure out. This is based on a cantilever beam analysis, but perhaps this simplification is very rudimentary. So, any comments and suggested solutions are welcomed!

Thanks,

capterdi

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13. Aug 20, 2008

### Mech_Engineer

The maximum stresses in the hook occur at the sharp corners, not at the long section you are trying to approximate as a cantilever (I'm not sure calling it a cantilever is a very good approximation anyway).

One way or another, like I said before you CAN'T rate the hook's strength, because you know nothing about the material it is made out of or how the hook has been used in the past. Giving a rating for the hook is a very dangerous prospect because if the hook fails while operating under your "rating" and the accident damages expensive equipment or injures/kills someone, YOU can probably be held responsible for it.

In my opinion, you need to tell your boss you cannot properly rate the hook for the reasons I have specified. Otherwise, you're jumping into a pool of water headfirst without first knowing how deep it is.

I have attached some simple ANSYS model pictures that qualitatively show where the maximum stress occurs in the hook. I have blanked out the numbers in the picture because the hook's exact material properties (which we don't know) will determine the stress.

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• ###### Hook 3.jpg
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14. Aug 20, 2008