Fastener Loading question 3

[zonaguy920]

I have two bolts mounting a member to a fixed support (pictured in gray), where my load P is known. I'd like to use an "overhanging load" scenario where R_1 and R_ledge are my two reaction loads, except I have that 2nd bolt R_2 which complicates this a bit. I would assume that R_2 is going to be much less than R_1. Can anyone offer help in how in how I can solve R_2? Thanks in advance.

 

[desertfox]

Hi

Try this link

http://www.roymech.co.uk/Useful_Tables/Screws/Bolted_Joint.html

Look for strength of bolted joints withstanding bending forces

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

 

[DAVIDSTECKER]

R_2 will have the highest reactionary force as it is the closest to the fulcrum R_Ledge.

 

[klaus.]

No way !!!

 

[Tmoose]

I'd say it is an indeterminate problem using statics.

The stiffness of the green beam and the gray angle affect things hugely.
Once down to that level (reality) the conditions of the faying surface may come in to play. For instance, if the beam and angle are mighty stiff, but badly machined, or raw stock, there might be no reaction at Rledge. The attached image is obviously exaggerated, but with very stiff components 0.001" can make a significant difference.

 

[drawoh]

zonaguy920,

Torque each of your two bolts down to some force way in excess of P, say 10P. Select bolts big enough to do this. Each bolt will see a force of 10P as you apply and remove the force[ ]P. The only force that will vary will be the contact force between the two plates.

--
JHG

 

[klaus.]

Yes of course it is indeterminate.....

 

[drawoh]

klaus and Tmoose,

This is not an indeterminate problem, or at least, not a difficult one.
[ul]
[li]If the bolts are tightened as I noted above, you approximately have a cantilever beam fixed at one end.[/li]
[li]If the bolts are loose, the beam will pivot until it engages one of the bolts. All of the load will be on that bolt.[/li]
[li]If each bolt is tightened gently on top of a spring and you slowly increase P, the beam will start off equivalent to a fixed cantilever beam as noted above. When the spring clamping forces are exceeded, the beam will tilt and the springs will compress. The compression and the compression forces will be equivalent to the distances from the pivot. This is easily solvable if you assume the beam is infinitely rigid. This model is equivalent to you exceeding the clamping force of the bolts.[/li]
[/ul]

I have had trouble with this in the past. The model actually is easy to to understand. If the bolt is not being stretched (strained) by the beam, the force on the bolt does not change.

--
JHG

 

[zonaguy920]

Tmoose,

I see what you're saying, thanks for the response. As I've set it up, yes it's indeterminate with the three unknowns. I tried making a conservative assumption and say that R1 (bolt furthest from the ledge) will take all the load. This way, if my safety factors look good I don't need to worry about R2 since we know that the load on R1 > R2. This however didn't work, so I resorted to seeking help in figuring out R2.

Drawoh,

This is good advise. Just beef up the bolts and preload to 10x the applied load. This way I can say the ledge is a fixed point and solve as a cantilever beam. I was trying to avoid needing to use larger bolts as the gray angle I show represents a drawing that's already been released and I'll need to ream those through holes to make them larger. But hey, sometimes you gotta do what you gotta do.

Appreciate the help

 

[klaus.]

correct.,..but I did not say is difficult
it is a typical second semester student exam question

 

[drawoh]

zonaguy920,

It always is nice to simplify your calculations. It also is nice to design and build things that are over-designed and safe.

--
JHG

 

[desertfox]

Hi zonaguy920

This link shows a really good example of your problem:-

http://nptel.ac.in/courses/112105125/pdf/mod11les1.pdf

A word of caution when tightening the bolts, if you tighten the bolts to much then the material being clamped might well yield, outdoor this occur the bolts will not have the preload you think they have.

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

 

[Tmoose]

Hi zonaguy920,

So your analysis so far suggest that the bolt at R1 running solo ain't up to the task ?

What size, grade, installation torque were planned ?

 

[Tmoose]

I was thinking, depending on the width of the bars / straps, especially the green one, it may have surprisingly high stresses at R2, and a tendency to bend there.
Like this -

https://www.lowes.com/creative-idea...IC/metal-strap-tabletop-pumpkin-102191979.jpg

https://www.lowes.com/creative-idea...IC/metal-strap-tabletop-pumpkin-102191982.jpg