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RE: Lateral Stability of a Box Beam ?

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Thanks Paul,

What you say makes sense. But I have to think about it, something seems odd.
Coldformed C/Z are braced by bridging, normally a channel section fastened
to the web above and below the neutral axis. The bridging provides both
lateral and torsional restraint: that is Ly, and Lz are reduced.

The two beams when they kick laterally: could both kick towards each other,
away from each other or in the same direction. If the beams attempt to twist
they place the bridging in bending.

Ignoring the complexities of the stress gradient from compression to tension
which causes the twisting. Then simply have elements in compression (F=M/d),
which will buckle about their weak axis. Which suggests either a battened
column (steel structures code) or spaced column (timber structures code). A
quick look at timber structures code (AS1720) indicates a modified
slenderness, or modified effective length for the spaced column.

Also what is the difference between a floor joist crossing the members, or a
floor deck? Lateral displacement of one beam will cause displacement of the
others crossed by the joist or deck. So if we only have two beams do we
ignore the restraint provided by the joist?

Or the chords of a truss, effective length between webs. For parallel chord
truss, top chord effectively bridged against bottom chord. The whole truss
can buckle out of plane but the chords are braced in one direction. For a
bridge two trusses braced against each other. The CSI steel designers manual
has an article on U-shaped bridges, and the effectiveness of the horizontal
framing (bottom) to provide restraint to top chord of vertical trusses.

So it just seems like it needs closer inspection.

As for a box section. The boxed section has higher torsional resistance, and
generally higher resistance: no change to effective lengths with that
analogy so benefit probably not as great.

The plywood would be forming the flanges, which is unusual the plywood
normally forms the web. And again in simple terms force in flange is F=M/d:
flange needs appropriate area and appropriate spacing between fasteners to
reduce buckling of compression flange between fasteners. Checking fasteners
for shear flow will probably provide for such. See Gere and Timoshenko for
shear flow and examples for timber boxed sections. Also timber structures
code (AS1702) gives formula for fastening of built up sections. I guess NDS
doesn't.

In any case boxing up the beams, some what makes the beams redundant, since
they become the webs of a single section, resisting shear, and the plywood
the flange taking the normal stresses. The built up beam now having to carry
twice the load: the overall benefit is probably small.

Refer ASCE guide to bracing cold-formed steel structures which contains
George Winters original research paper and his use of corrugated cardboard
to provide lateral restraint.

Steel structures codes seem to have rules requiring the restraining force to
be between 2% and 2.5% of the flange force. This is a simplification to
avoid calculating the stiffness, the ASCE guide has theory and examples
calculating stiffness.

Not really about two tied beams. The bridging reduces the half-wavelength of
the buckle in the thin plate. The theory mainly assumes the buckle is
sinusoidal in nature, a half sine wave is the length of the buckle. Two
plates bridged together have smaller buckles between each bridging member,
and therefore overall potentially less kick sideways.

Needs closer inspection.


Regards
Conrad Harrison
B.Tech (mfg & mech), MIIE, gradTIEAust
mailto:sch.tectonic(--nospam--at)bigpond.com
Adelaide
South Australia


-----Original Message-----
From: Paul Ransom [mailto:ad026(--nospam--at)hwcn.org] 
Sent: Sunday, 18 January 2009 06:54
To: seaint(--nospam--at)seaint.org
Subject: Re: Lateral Stability of a Box Beam ?

If the 2 beams are identical with identical loading, there is no benefit to
simple ties. Unless there is some shear resistance mechanism between the
brace points, the unbraced length for lateral buckling is not reduced and
the ladder simply behaves like 2 tied beams (e.g. Iy1 + Iy2) and they just
displace in unison.

Regards
Paul
-- 
Paul Ransom, P.Eng.
ph 905 639-9628
fax 905 639-3866
ad026(--nospam--at)hwcn.org




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