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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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- Subject: RE: Lateral Stability of a Box Beam ? (Bracing two independent beams by turning into single box beam)
- From: "Conrad Harrison" <sch.tectonic(--nospam--at)bigpond.com>
- Date: Thu, 22 Jan 2009 10:34:11 +1030
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 ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) or UnSubscribe, please go to: * * http://www.seaint.org/sealist1.asp * * Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you * send to the list is public domain and may be re-posted * without your permission. Make sure you visit our web * site at: http://www.seaint.org ******* ****** ****** ****** ******* ****** ****** ********
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