Bending moment on shank of bolt

[vvzp]

Hi,
I am wondering if anyone could shed a light on the ways to calculate the bending moment due to shear, on the shank of a long bolt. More specifically, how to accurately determine the bending moment arm when the long bolt is subject to shear? Many thanks!

 

[desertfox]

Hi vvzp

Can you give more info on the bolt ie dia, length its application and torque loading.
Bolts to my knowledge are usually just calculated on tensile and shear loading for failure, bolts and screws don't normally fit into the normal formula's for bending
because the length to diameter ratio is to small.

regards desertfox

 

[vvzp]

Hi,

Thanks a lot for your reply. As I understand, bending of the shank may not be negligible if the bolt is of reasonable length. As an example, consider the case when the two end plates are 0.5" thick each, with a shim of 0.2" in between.

If the bolt is subjected to a shear, what would be the moment arm? Can I take the arm's length as the distance between the middle sufaces of two end plates? Or, could it simply be the thickness of the shim?

When you said 'length to diameter ratio is too small', what does the 'length' refer to here? The moment arm's length?

Thanks again.

 

[desertfox]

Hi vvzp

What I mean by "length" is the length of the bolt under the
head, if bending theory is to be used the length under the
head of the bolt should be at least 8 times the diameter of
the bolt.Conventional bending theory assumes that the span or length of beam is much longer than depth of beam otherwise the theory gives inaccurate results.
Secondly bending in your joint will only take place if any of the plates the bolt passes through touch the bolt, or the bolt works loose during its duty. Taking your example then,if the bolt passes through the plates and centrally through the holes so theres a gap all round the bolt and the bolt is correctly pre-tensioned then any shear forces acting at right angles to the bolt axis would be countered by the friction generated at the mating surfaces of the plate.
If both plates touch the bolt then (ignoring the spacer)and the plates are sliding over each other I would consider shear forces only and size my bolt on shearing strength accordingly. If the plates are trying to seperate then the pre-load should be greater than this to prevent seperation.
Can you give your proper joint details ie:- bolt diameter, length, application of external loads and magnitude, torque for the bolts and size of jointed components.

regards desertfox

 

[yates]

vvzp,
Your question is very complex. If the bolt/nut assembly is being used as a shear pin i.e. no bolt preload, then loads are primarily in shear, as desertfox points out, with only a very small bending moment in the shank due to the moment arm resulting from the thickness of the plates. If however you have a considerable amount of preload, then what may be the determining stress for rupture is not necessarily pure shear in the bolt shank. You will probably find that the point of highest stress is in fact in the bolt underhead radius due to the high bending moment resulting from the bolt head being cocked over. Use of an underhead washer virtually eliminates this problem by preventing the edge of the bolt head from 'digging in' to the substrate material when the whole bolt is being tipped over. The use of close-tolerance holes (close to bolt diameter) will also help to keep things in pure shear and will make your stress calculation more accurate.

 

[VoyageofDiscovery]

Hi vvzp,

If you're concerned about moment, fillet weld all around the shim or cheek plate to one of the sandwiching end plates. Mo more moment!

Regards

VOD

 

[vvzp]

Hi, desert fox, yates, and VoyageofDiscovery:

Thank you so much for your responses.

To make myself a little clearer, my question was in the context of a space application and the requirement dictates that we should not consider friction. I had encountered several cases of bolt bending, and here are the examples:

Example 1. - the one I gave yesterday: bolt diameter = .25", hole size = .3125", bolt preloaded to 95-110 lbf;

Example 2. Three plates are to be bolted together by several bolts. The top plate is .3" thick, middle one 2.4" thick and the bottom one with a coin insert of .375" deep. A washer is underneath each of the bolt heads. For
some reasons, shear pins cannot be used on the plates, and there have to be some bolt/joint designed to take shears. In this case, what'd be the best way to deal with the bending moment?

Thanks again. I really appreciate all your help.

 

[desertfox]

Hi vvzp

For example 2 you fail to mention the bolt dia or torque and am I right in thinking that the length of the bolt in example 2 is 2.4" + 0.3" + 0.375".
As regards the bolt bending you have encountered were these
bolt failures?

regards desertfox

 

[diamondjim]

I would reduce the diameter of the thru holes
to 9/64. The .062 clearance seem much out of line
for these little bolts. .015 clearance may be too
little unless you are assured of very accurate
true position drilling. The smaller the clearance,
the less moment can occur if I understand your problem.
You also may be having a surface bearing failure with
these oversize clearance holes. If the moment that you
are speaking of is the result of having this excess
clearance and the rings are allowed to slip radially
I can see a moment being applied to the bolts.
Interesting problem!

 

[vvzp]

desertfox, diamondjim:

Thank you for your replies.

desearfox:

For example 2,
- bolt_diameter = 0.25",
- bolt_length = 2.4" + 0.3" + 0.375" + 0.05"(washer thickness),
- upper_plate_hole_diameter = 0.275",
- middle_plate_hole_diameter = 0.3125",
I'd also like to know what'd happen if the certain portion of the middle plate hole is given tighter tolerance to take shear.

diamondjim:

You suggested that a reduced tclearance could minimize the bending moment. But, how to model/calculate the bending_moment_arm/bending_moment after all?

Many thanks.

 

[desertfox]

Hi vvzp

I have tried in vain to find some way of modelling your problem,even asked the stress engineers at work and got the same response as I gave you, we have formula's for tension and shear and bolts don't fail in bending.
Anyway I have thought of a possible solution which may eliminate some of your problem and that is by using shoulder bolts.With shoulder bolts you need precision holes
with a small clearance which would then ensure the bolts were loaded in shear.

Hope this helps

regards desertfox

 

[diamondjim]

I would make the clearance holes only 1/64
greater than the bolt diameter unless you
are not capable of holding true position
accurately. I would make two of the hole
having the greatest distance apart only
a few thousandth over the bolt diameter and
let these act as dowels to prevent moment
load by the plates shifting. The tighter you
can control the true position and oversize
holes the less moment you will have developing
in the parts.

 

[tmschrader]

for anybody still interested in above.
a 1/4 bolt in a 2.4" plate will experience bending and should be thought of as a pin. The handbook of engimeering calculations says to uses a evenly distributed load distribution (in your free body) to calculate bendind moment, but this results in overly consevative designs.

I have modeled and tested pins under load that shows the load distribution trapezoiod being quite a bit higher at the edges of the plate. if you have Mech 6 autocad (or simple FEA) you can match the displacements of the contact surfaces in the bolt and plate material and get results that match the testing pretty close.

 

[unclesyd]

Try this website it’s in the UK but it’s a good one guidence:

http://www2.umist.ac.uk/construction/intranet/teaching/civil res/MScSteel/index.html

The file you want is the third one down; Design Philosophies......

They are several good .Pdf files on this site

 

[unclesyd]

I was told the Gerogia Tech Civil Engineering Deptartment has done a lot of work on shear bolts and connections.
Also check on work pretaining to the Northridge Ca. earthquake. They had some bolting problems and one report I saw had some bent shear bolts.

 

[unclesyd]

tmschrader,
Not being a structural engineer as all have noticed your post jogged a comatose neuron. At times I’ve been ask to evaluate failed fasteners from steel construction. Some of these fasteners investigated were noted as “shear bolts”. Early on I was looking up the design parameters used in selection of a set of failed fasteners. Again if I remember correctly when I compared the bolted connection to a riveted connection any mention of the bending moment in the rivit dropped out. The reason I looked a the riveted connection was that part of the building was riveted and the other bolted. The differences is the connections were obvious, the bolted connection had slotted holes and the riveted only round. Supposedly both connections had the performend the same function. They reference I checked treated the rivet as a simple pin in shear as you mention. Also in testing shear pins, both in single and double shear, the clearances and edge of the hole are very critical