Help With Bending Stress Calculation 1

[MarkJ_]

I am trying to perform a simple bending stress calculation on a bolted flange interface but keep calculating a huge bending stress and can’t see where I am going wrong. Please can someone help?

I have a tool that is 2.9 metres long and weighs 250Kg. This has a bolted flange interface at the far end and I want to verify that the bolts can take the weight when I lift the tool from horizontal to vertical from the other end by crane via a lifting point. The bolted flange interface is is 4 x 8mm bolts all spaced equally 80mm apart.

So I am using the basic equation, Stress = (M*y)/I

M = 1778 Nm (I calculated this as being the weight is divided equally between all 4 bolts so 613N per bolt x 2.9m).
y = .004m
I = 2.0106e-10 m^4 calculated using: ((pi*d^4)/64 where d = .008m)
Stress = (1778*.004)/2.0106e-10 = 35372.5 MPa

This is a huge stress and I can’t help thinking I’m going wrong somewhere. Can anyone help?
Thanks
Mark

 

[3DDave]

You have calculated taking the bending with the bolts alone, lined up side by side like a tear-off strip. No wonder the stress is high.

Make a drawing with top, front, side views showing all the parts and where the load is applied.

 

[GregLocock]

I suggest you post a diagram of your model of this, it makes no sense to me as written.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[bcd]

Looks like you have not factored in the distance between the bolts or spacing of the bolts in your I calculation.

 

[Scuka]

The stress formula you used is meant to calculate stresses due to bending in a beam, where M is the bending moment in the beam at the point of interest.
You used the formula as if you had a beam that's 8mm in diameter, 2.9 meter long and has 250 kg hanging off of it. That's why you get huge stresses. Of course an 8 mm thick, 3 meter long rod can't hold 250 kg at its end.

Bolts are not part of the beam per se. They are in a flange are not subject to bending as the beam is.

Make a free body diagram to figure out the forces acting on a bolt (direction and magnitude), and use the appropriate formula from there.

Basically, you have one of these two cases (your description doesn't specify which, but hopefully, you know)

https://mechanicalc.com/reference/bolt-pattern-force-distribution

Google or look up in a textbook "bolt pattern load" for more information.

 

[rb1957]

you do know you aren't calculating the bending in the flange ? this would need the thickness of the flange.
Let's look at the load in the bolts

the offset moment (I don't follow your calc, so my calc would be (250*9.81)*2.9/2 = 3556Nm ... your tool weighs 250kgf = 250*9.81N.
is reacted by the four bolts ... don't know the size of the flange, 100mm ?, so I'll use the bolt centers (80mm) ...
P = 3556/2/0.08 = 22228N ... boy, that doesn't seem right ...

250kg = 550 lbs
2.9m = 114in
moment = 31400 in.lbs
80mm = 3.15in
P = 31400/2/3.15 = 5000 lbs = 22700N ...

well, there's your problem ... you need 3/8" or 1/2" (10mm - 12.7mm) bolts

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

 

[MarkJ_]

Thanks a lot for the great advice. I see that it makes sense now that I was using the incorrect formula and treating the bolt like it was an 8mm beam. I have attached a sketch to better illustrate the lifting scenario. Basically the tool is third party and there is no option to change from the 4 x M8 bolts at the interface in question. So firstly I want to determine if these bolts are sufficiently strong to take the weight of the tool (250Kg weight and 2.9m long) when lowering it from vertical to horizontal via a single lift point at the top.

I would also add that my calculation skills are rather rusty!
Thanks again for the support.
Mark

 

[rb1957]

how did the 3rd party approve the tool ?

but then your sketch is not the problem you asked.

the "lifting point" at the far end of the beam is supporting something like 1/2 the weight of the beam,
and (critically) changes the end from a moment resisting cantilever to a simple support.

now your 4 8mm bolts are resisting approximately 125kg of shear load (* whatever safety factors you need)
this is a "trivial" 570/4 = 143N per fastener (* whatever safety factors you need).

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

 

[Scuka]

I would also add that my calculation skills are rather rusty!

As I said, do a free body diagram of the tool.

In the horizontal position, you've got force of the crane rope pointing up on the far left, you've got mass of the tool pointing down at the center of gravity, and you've got reaction at the bolted joint pointing vertically (horizontal reaction is approximately zero since there are no active horizontal forces).

So, back of the envelope calculation (i.e. assuming center of gravity is half way between the crane and the bolted joint), lift point sees a 125 kg of load, and bolted joint sees the other 125 kg of load that tries to shear it apart.
Reality is very close to this approximation so you don't even have to bother calculating it more accurately.

 

[rb1957]

yes, we're all looking at a pretty simple sketch. I took it as an overhead crane with a vertical lift (traversing as the tool is lowered) ... makes it very simple.

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

 

[MarkJ_]

Thanks again for your help with this. So if I understand correctly I can just treat this as a simply supported beam. The crane is one support and the contact at the other end with the ground is the other support. Because the bolted interface is so close to the support any bending moment is negligible and I can just treat this as a straight shear force acting on the bolts. Based on that the shear stress is small and bolts as is aren't an issue.
Thanks again
Mark