Jib Crane: Boom Combined Stress 1

[yikes]

I was wondering if any of you folks could help me out.

I have a jib crane consisting of:

-A vertical column, pinned at top (to main structure) and bottom (to footing/foundation)

-A horizontal beam acting as the "boom" of the crane (basically a wide flange beam bending about its strong axis) that is connected to the column at, say, midheight.

-A tension rod, fastened to the column at its high end and fastened to the horizontal beam at its low end (at about beam midspan). The angle measured from horizontal at which the tie rod extends up from the beam midspan to the column is about 25 degrees.

-Both the horizontal beam AND the tie rod have connections at the column that allow the boom portion to "swing", or "sweep" over about a 90 degree area, obviously with the column remaining stationary.

My question is this:

If load is applied to the end of the horizontal beam, there occurs combined stress (bending+axial) in the portion of the beam between its support at the column and the location of its connection to the tie rod. What value for Ky (effective length factor for buckling about weak axis) should be used when checking axial loading in this segment? Use 2.0 for a fix-free configuration, or use a K with a lower magnitude, because it's not truly "fixed" at the column (remember, it can actually pivot)? Can we depend on any resistance to weak axis buckling from the tie rod (two 1 1/8" rods)? I wouldn't think so.

Please help! I hate to be too conservative and use nothing less than Ky=2.0, but I'm not really comfortable using anything less.

 

[ishvaaag]

Then you can use the P-Delta approach and forfeit the Ks. Include some initial imperfection even, and model the beam with segments, ore even made of plates. If you find an stable solution at the factored level then you need not care at all by the Ks, but look you have used the proper bending axial and bending stiffnesses appropriate for the loads.

In any case, you have basically a column pinned at both support ends, that is, where rods meet the beam and at the connection between the beam and column. Other thing is that there maybe some torsion applied at the rods' support end, and the effect of this torsion need be accounted for the then eccentrical support delivered by the rods and the vertical hinge axis at the column. Likely the eccentrical response of the rods will be canceling any significant torsional action from the tip load.

As you see the hinge condition at rod support and column support enforce for both xx and yy bendings single halfwave bending (except you want allocate some vertical on strong axis bending stiffness to the column support connection) for the compressed region, hence K=1 for L between rods and column support. Moments of bending and of eccentrical input of the rod action need then be considered, and for the resultant forces use equations for flexocompression of say LRFD code.

 

Think about it practically..the use of anything less than 2 may result in a minor saving which is not worth it if lateral torsional buckling occurs in that cantilever.
I have seen failed jib cranes because the designer used less than 2.
From a design point of view, some people use even 3 depending on the details of the joints. Don't think that 2 is over the top. You don't wanna have a failed jib crane attached to your name.
hope that helps

 

[ishvaaag]

Well, one can argue that the failed cases may be due to other thing, say bad consideration of the loads in design or excess of load in practice.

K=1 for the axial load between rod support and inner hinge since buckle is single wave and compression limited to this extent.

Other thing is what the unbraced length is for flexure. You go to Galambos V table 5.11 and for 1 flange restrained laterally where the beam is continuous beyond the cantilever you have to take effective lenght 2.7 times that of cantilever. For the part between rod support and hinge support unbraced length by the definition in LRFD might be the actual length since laterally restrained at the compression flange by the rods. This lateral support is somewhat doubtful but still marks the end of the single half wave, that continues to be for such segment of the jib crane the way of failure. Hence since the formulation of the critical moment is based on the single half wave the equations in the check should still be conservative.

In any case it is not a design case in which I would feel much cozy with only with what in LRFD indicated. So the direct modelization with initial imperfections for P-Delta and short segments or evne plates would give further assurance of standing the wanted loads safely at some proper safety factor.