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# Re: cantilever T-beam

• To: seaint(--nospam--at)seaint.org
• Subject: Re: cantilever T-beam
• From: "Kevin Below" <kbofoz(--nospam--at)gmail.com>
• Date: Tue, 3 Apr 2007 22:46:01 -0400

Gary, this is getting serious and I would appreciate your comments as I am at the moment designing the 8 metre footbridge that I mentioned.   I think that  the  question of stability of the top flange of the guardrail-truss is very dependent on the position of the point of application of the load, as you said.

I have started by calculating the lateral force required for a lateral support to adequately restrain the compression chord, which is, by rule-of-thumb, 2% of the compression force in the chord.  (I used 5% to be a little conservative).  This lateral restraint is provided by the rigid joint with the cross-member between trusses at the deck level.  The vertical members of the trusses form a U with the cross-members.

So I am not actually relying on the fact that the position of the load may actually stabilise the trusses, but it sure increases my comfort level.

I suppose that the stability analysis would involve work-energy calculations.  Maybe someone can confirm or refute that.  The work done by the load(s) would be the product of the load(s) and the movement of the load(s) from the original position to the new position after lateral buckling (with the truss rotated and deflected down because of its reduced rigidity in the rotated position).  This would be compared to the work done to twist the truss from the restrained upright position at the supports to the rotated position at mid-span.  If the first is greater than the second, the truss would be unstable.

It is probably not very clear from my description, but maybe ...

Does that sound reasonable as far as a model goes ?  Of course, I'm not going to go that far, but if it's correct, then it helps understand why even loading on the bottom flange may not always be stable.  It still depends on the relative rigidities of the truss for the major and minor axes, but it is more stable than top-flange loading.

Kevin

On 3/31/07, Gary L. Hodgson and Assoc. <ghodgson(--nospam--at)bellnet.ca> wrote:
Kevin,
I was thinking only of a cantilever because the previous writer was
proposing to use K = 2.
As for your example, I often run into that on overhead cranes with
walkways.  I often use the guard-rail as an auxiliary truss, if I don't
want to, or can't, cantilever off the bridge girder.  The customer says
"what in H" is that HSS 8x4 or whatever top rail on the guard rail.
Fortunately, sometimes I can brace back laterally to the bottom flange
of the bridge girder at the centre or 1/3 points to reduce the
unsupported length.
Gary

Kevin Below wrote:
> Gary, does that mean that a bridge with side trusses which support the
> deck on the bottom member does not have a potential buckling problem
> of the top chords under the compression load ?  Your explanation is
> I'm thinking of a short steel footbridge I have to do soon.  I was
> concerned about buckling of the top chord (which is also the hand-rail).
>
> On 3/29/07, * Gary L. Hodgson and Assoc.* <ghodgson(--nospam--at)bellnet.ca
> <mailto:ghodgson(--nospam--at)bellnet.ca>> wrote:
>
>     Jason,
>     You might look at where the load is applied on the cantilever.
>     Nethercott in Britain then Galambos in the USA gave descriptions
>     of the
>     appropriate length factor for cantilevers.  If the load is applied
>     above
>     or below the neutral axis determines whether the beam can buckle
>     sideways.  For example, I get involved with a lot of crane
>     runways, e.g.
>     a single monorail beam cantilever,  loaded on the bottom flange,
>     cannot
>     buckle to the side as the vertical load is counteracting the
>     tendency to
>     buckle sideways. Hope this helps.
>     Gary
>
>

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