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RE: Lateral Stability of a Box Beam ? (Bracing two independent beams by turning into single box beam)

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Thanks Paul,

As you imply the published literature has extensive coverage of elastic
instability.

Not forgetting the original problem: two lightly loaded independent beams
with a concern that without lateral bracing the beams would be excessive in
size and possibly weight. The proposed solution was, given the two beams
were in close proximity, to turn them into a single box section, to increase
torsional resistance and therefore improve lateral stability. If the two
independent beams were further apart this would not be a very practical or
efficient solution.

Considering the box section. It principally consists of two pairs of
flanges. One pair to resist bending in the vertical plane and the other pair
to resist bending in the horizontal plane. Since the objective is to
constrain the size of the two beams, expect the box to be wider than it is
deep. Not very efficient to support the principal vertical loading. For
roughing out the size of the box the elastic section modulus Z for a pair of
flanges is approximately Z=DBT(approx). This is obtained by ignoring the
relatively insignificant contribution of Iy1+Iy2 when applying the parallel
axis theorem. D=depth between flanges, B=breadth, T=thickness. The two
proposed plywood covers, would provide the flanges for the vertical loading,
making the two original beams somewhat redundant. Being relatively broad
flanges and thin, the plywood may be prone to local buckling. In the
horizontal plane, the two proposed beams provide the flanges for a
relatively much deeper beam, with relatively more stable flanges. This deep
beam resists the pseudo horizontal displacing force, causing the buckling.
So potentially being much stronger in the horizontal plane than the vertical
plane, the lateral buckling problem has been reduced. But not very
efficiently.

Staying with the beam analogy for the assembly of the two beams. To provide
resistance to the lateral displacement: there is more than one way to create
such a beam in the horizontal plane. For example the two beams can be
considered the chords of a parallel chord triangulated truss, or a
Vierendeel girder. Offcuts from the section used for the two beams can be
used as perpendicular webs. These fastened top and bottom of the depth of
the beam to provide some torsional resistance to minimise twisting of the
two beams which are otherwise simple plate elements. Then continuing with
the beam/truss analogy, provide steel strap cross-bracing for the diagonal
webs (shear). Crossed because the pseudo displacing force could displace or
load in either direction.

However, returning to the original problem: it is not about forming a beam
in the horizontal plane: it is about changing the mode of buckling.
Independently the two beams (plates) will buckle their full span in a half
sine wave. If an offcut of the beam section is fastened at midspan: then for
displacement to occur at midspan either the offcut/bridge is placed in
tension as the beams displace away from each other, or the offcut/bridge is
placed in compression and buckles or crushes, as the beams displace towards
each other. With the bridge designed to have the appropriate stiffness, then
each individual beam/plate now buckles with a full sine wave, or a half sine
wave in half its length.

If not comfortable with such. Then as I first indicated calculate the axial
compression force causing the buckling, and treat the assembly as either
spaced columns, battened column or laced column. The differences are
described by Galambos. If adopt the laced column then effectively returning
to forming a truss in the horizontal plane.

Since the bending moment typically varies along the length of the beam, the
normal compressive forces/stresses on the section also vary. So primarily
trying to reduce the segment length of the most highly stressed portion of
the beam. So not entirely necessary to box up the entire span. And if
plywood is the preference then diaphragm bracing to one side may be more
practical then boxing.

After all are the plywood covers going to be installed in situ, whilst the
two beams are propped? If so how easy is it to install the lower plywood
cover? If the box is fabricated first, then may have transportation and
crane problems. For that matter are timbers 27ft long readily available?

Since the beams are lightly loaded: not much more than self-weight. Then can
probably load test during construction, and add additional restraint as
necessary to push member bending capacity closer to section bending
capacity.


But each to their own comfort zone.




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



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