Analytical Bolt Calculation 2

[Sjqlund]

Hi eng-tips engineers!

I'm designing a bolted connection for a construction.


I'm quite unsure how to handle this statically indeterminate system shown on the picture below:

http://imgur.com/GNlr2G6

I know how to approach single bolt groups which are eccentrically loaded. This i usually do by moving the force to the center of the bolt group, and adding a moment.

However in the situation depicted on the image i dont know how to do this. One idea i had was to model the beam as being fixed in both ends (shown below), and then find the reaction forces at each end to the bolt group.

http://imgur.com/tcK9wYG

Would my idea work, or do you have other suggestions?

 

[PicoStruc]

Give your mandate to a structural engineer !

 

[Sjqlund]

Well.. i am a structural engineer..

 

[oldestguy]

My structural engineering professor claimed that all bolt and rivet shear resistance is due to the friction between the plates, not the shearing resistance of the bolts or rivets. Take that and run with it.

 

[Sjqlund]

Actually the loads are so large that i might not be able to pretension the bolts enough to carry in friction.

However, lets say that i do carry all the load in friction. And lets call the load P, pretension per bolt N, number of bolts n.

I could find an estimated required pretension by simply taking P=n*µ*N, i.e. N=P/(n*µ).

This is what i've done so far. However, i think that the friction also needs to overcome the moment. And then there's also the fact that due to the statically indeterminate nature of the problem, the inner bolts will carry a larger fraction of the load than the outer bolts and will hence need more pretension...

Am i making this more complicated than needed?

 

[rb1957]

i thought we didn't rely on friction for shear. yes, practically, there is but how consistent is the cof ? and the idea of preloading to generate the shear reaction as f*N seems ... nuts?

one approximation would be to say this is a fixed cantilevered beam, so the fasteners react the end moments (=PL/8) and the direct shear ... an easy enough calc. this is one extreme of the support reactions.

the other extreme is to consider this a pinned beam, so the fasteners react only the direct shear.

possibly the real answer is between these extremes.

Quando Omni Flunkus Moritati

 

[Sjqlund]

I'm not sure i quite understand your points on friction rb1957.

I agree that it can be difficult to calculate precisely how much friction you have - but as in most other complicated situations that just mean you choose your unknowns conservatively - i.e. a low coefficient of friction.

However, and note that i'm no expert, i've been taught to never let the bolts carry in shear, and always make sure that shear is carried by the friction.

 

[paddingtongreen]

I know of no bolt where the friction resistance exceeds the bolt shear resistance. I do know of cases where the the bearing surface (plate thickness or lack of thickness) is the control.

If this was an usual structural connection, the bolts would be assumed to carry equal loads, some aid from yielding is assumed. All this assumes that the bar is sufficiently sized for stability.

If you want real help, give more detail, loads size and type of bolt etc. and some evidence that you are indeed a structural engineer (think through what information people need to give an intelligent reply).

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[Sjqlund]

Thank you paddingtongreen. And sorry for asking my question in a bad way.

I think the keywords i needed to hear was yielding and thereby load redistribution.

The reason i haven't provided much detail about the problem, is that the design is really still up for discussion. However i know i'll be having a load situation as the one depicted.

To clarify which orders of magnitude we're in, the load in this situation will be ~600 kN, and the bolts will be somewhere between M30 and M40. The distance between the two bolted connections is ~2 meters.

 

[TLHS]

I'd keep this relatively simple.

I'd probably say that it's fixed for connection design, analyze the beam to the centre of the bolt group, then take the moment into the couples formed in each of the two orthagonal directions. I'd spread the vertical load evenly across all four bolts in the connection. Then I'd add all the vertical components and then take the sum of the squares to add in the horizontal components from one of the couples. Then I'd design the bolts to take the force in shear.

If you actually want to take it in friction the code way to do it would be to designate the connection slip critical and use the capacities given for the different faying surface conditions. You would then have to specify that the contractor is to pretension the bolts and prepare the faying surface as per whatever assumptions you made.

 

[paddingtongreen]

Nothing wrong with TLHS's solution but remember it is always an idealized solution. The positions of the holes are punched or drilled to within tolerances, there will be some yielding.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[Sjqlund]

So if i understand you correctly TLHS, you'd say that (denoting the load P, length between the two bolt connections L, and distance between bolts d):

vertical shear on each bolt: V_vert=P/8

and approximating moment in each of the two connections: M=PL/8

which gives horizontal forces: V_horz=M*d

and then design again the force of V_resultant = sqrt(V_vert^2+V_horz^2) ?

 

[johnbridge231]

Don't forget to check the bearing resistance of the plates as well.

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

http://www.engissol.com/cross-section-analysis-design.html

 

[rb1957]

i'd react the moment with tangental forces (ie inclined 45deg) rather than assuming horizontal. this gives components in two directions, combine with the direct shear (vertical) to get the resultants.

you should notice that each fastener sees very different loads. if you're Sure about the load direction you can "optimise" the fasteners, so long as you re-do the bolt group ... making the less loaded bolts smaller increases the load on the more highly loaded bolts, so you probably won't gain much doing this.

reacting the moment equally at the four fasteners implies perfect placement, or in the real world a small amount of redistribution (imagine the moment is reacted by only two fasteners, 'cause the other two are slightly misplaced and don't bear up as the ideal design suggests).

fastener shear and plate bearing are most likely failures. the stresses in the plate need to be looked at too.

Quando Omni Flunkus Moritati

 

[Sjqlund]

Thank you for pointing those things out rb1957.

Right now i find the components from the moment as Rx = M*y/I_p and Ry = M*x/I_p.

With regards to optimising bolt placement and size, i cannot change these parameters unfortunately.

And you're spot on, on the perfect placement requirement. This is why i'd prefer to carry in friction. However it seems that friction is not viable, and hence the question is how many bolts will in reality carry the load. What does one usually estimate wrt this?

 

[rb1957]

i think the reality is that small scale yielding and redistribution allow the theoretical calc to work.

do the bolt group, find the loads on the fasteners, figure out the size of fastener required (from shear and bearing).

i realise your inexperience (which is fine, we all had to start sometime) ... but this is about a 1/2 hr calc.

Quando Omni Flunkus Moritati

 

[ul92]

"Steel structures design and behaviour" by Salmon fifth edition is the best solution for you.

 

[engsteeldesign]

Once you find out the required bolt shear, you can use the iPhone app "Bolt Design" to check the bolt and the bearing capacity. It is a handy app. This is the only iPhone app that I know that does that.

 

[Sjqlund]

Seems like an excellent reference ul92, thank you.

 

[gobsmacked]

Without reference to any code, it looks as if friction should be a working load criterion and bolt shear and bearing should be ultimate load criteria.