Solving a Connection Problem: Bolted Joint Stress Analysis

[Mustard Dijon]

Hi dear friends. I have a big problem and I need your help, I've realized that the joint connection I've drawn (and it is made already) was (most probably) wrong. There is a plate that is bolted to two U beams and the plate is welded to a horizontal I beam at the top. Please take a look at the picture link below. Three of the bolts are for a U beam and three for the other (they are diagonal), top "dot" is the centroid of the welded I beam (there is the same plate at the other side of the I beam, so the system is symmetric wrt the I beam).

I don't have many tools at work, so I manually investigated the joint stresses at the top I beam (can anyone comment on the suitability of this method, what I did is I isolated the top beam in a complicated system because the program I use doesn't give joint stresses, then I found the joint stress and I assume this is the joint stress in the system).

Anyways, my main question is about bolts.To cut it short I'll try to show what I did for bending moment My only and for one of the bolts at the top. I found My as approx. +4500000Nmm. Then I've found the centroid of the bolted joint as (200,100). Now the tensile force due to My on the top bolt should be ((bending moment)*(distance from bolt to the y-axis ))/(sum of all bolt distances to the y-axis squared) which is
((4500000)*(50))/(50^2+0^2+100^2+50^2+100^2+0^2)=9000 N

Then the stress is 9000/144(bolt area)=62.5 mpa due to My.

But I didn't consider (where I did wrong) that the centroid of the I beam (where moments are applied to the plate) is not coincident with the bolt centroid. I don't know how this comes into play. There is a 180 mm distance between the bolt centroid and the I beam centroid. Frankly how does the moment from weld joint affects the bolts I can't really physically understand in my mind. Can anyone help? Thanks in advance.

http://i.imgur.com/SzgtYxy.png

 

[PhanthomJay]

It is hard to understand the problem without looking at the entire system and loading. You might not even have a moment on the bolts of significance, like if were a truss. Even though the joint is not a true pin, many trusses have large gusset plates at the joints, which may be treated as a pinned joint with small error, and you just get axial forces in the members and the bolts ate designed to resist the shear from the axial loads. The diagonal bolt line of action should line up with the I beam centroid more or less. But I'm only guessing what the system may look like.

 

[Mustard Dijon]

Yeah it is difficut to describe the problem without pics so I've drawn a representative version of the system. The I beam is welded from the top, the plates with the holes are attached to diagonal beams with bolts. I isolated the I beam from the system and found its support stresses. Then calculated the bolt stresses but I don't know what would be the effect of the distance between the I beam and the bolt centroids. The lines of action points to the I beam centroid.

http://i.imgur.com/CgLnM78.png

 

[PhanthomJay]

You want to calculate the support forces and moments, not the support stresses. Depending on what loading arrangement is applied to the system, the bolt pattern could be subject to forces and moments in all directions. Be sure to consider the forces as well as moments acting on the bolts. If there is a moment acting on the bolts, it doesn't matter if it is eccentric to the cg of the bolt pattern.

 

[Mustard Dijon]

Thank you Sir. It is just my bad wording, I meant support forces and moments. Thanks a lot.