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Re: End Plate Moment Connection - Bolt Force Distribution

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> From: "Jeremy White" <jwhite(--nospam--at)holbertapple.com>

> When looking at bolts in an end plate, would one consider an elastic
> distribution of the stress such that the bolt farthest from the center
> of the beam (center about the x-axis) has the most force?  The stress
> would be multiplied by the trib area of the bolt to find the bolt force.
> This is the procedure outlined in the Salmon and Johnson Steel Structures
> book. They discuss this method in conjunction with pretensioning of the
> bolts.  My situation is a metal building frame which is most likely not
> pretensioned (I would assume), but the method should still apply.

All end plate connections are essentially plastic connections,
regardless of the verbage in the applicable design standard. Design
maximums are simply reduced to terms of elastic analysis for
convenience. Elastic distributions are conservative.

Additionally, the design standards ensure that the structure load
effects that theoretically get to the bolt are in a stress range below
bolt yield to "force" the "failure" to occur in more ductile members.
That's the theory at the limit. 

In general, when connecting a flanged member (e.g. W section or 3-plate)
with end plates, it is convenient and conservative to assume that the
"NA" for the bolts is either at the NA of the section or the centre of
the total bolt group. I make the distinction because the bolt group may
not be symmetric top/bottom and the NA is not easy to define.

> The only other way that I can think of looking at the distribution of
> forces to the bolts is just to assume all bolts take equal force (all
> other AISC info seems to imply this).  It seems more logical that the
> outer most bolt would see more of the stress, but I haven't found any
> other material that backs this up.  Could anyone shed some light on the
> issue of how to distribute forces to bolts in an end-plate moment
> connection?

Elastic conservative. Plastic complicated. Research improving. See
below.

> From: "Jeremy White" <jwhite(--nospam--at)holbertapple.com>

> I just found where AISC design guide 4 mentions assuming that the outer
> bolts yield and cause inner bolts to simultaneously reach full tension =
> and causing all bolts to share load equally (kind of).  But with more than
> 2 rows you may not be able to assume this.

It is common to assume that the group of bolts near the flange (possibly
3 or 4 rows) are all loaded equally (e.g. T=M/(n*d)). The assumption is
that the full member section near the bolts has achieved ideal yield and
therefore, it is conceivable that the load could be distributed to the
bolts equally. These are not bad assumptions but there are some issues
that you need to consider (e.g. can the forces actually get into the
bolts).

There will generally be more force/in along the flange than along the
web (T/(A*t) considered, only). Also, the web welds may not be adequate,
stiffeners may be required, etc.

This can get into some really complicated plastic rotation and yield
line analysis.

AISC design guide approach to moment end plates was developed with
research by MBMA. This is basically state-of-the-art for practical
design convenience.

So, assuming that all bolts are equally loaded is a good first pass
assumption and may be adeaquate for design.

Regards
Paul

-- 
R. Paul Ransom, P. Eng.
Civil/Structural/Project/International
Burlington, Ontario, Canada
<mailto:ado26(--nospam--at)hwcn.org> <http://www.hwcn.org/~ad026/civil.html>

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