huangyhg

a simple statics question
i would like your opinion on the following:
consider 2 ft. long outrigger 3x3 angles @ 24鈥?centers.
one end of the outriggers is fixed and the other end is free.
at the free end of all outriggers there is a continuous unistrut channel supporting a moving track with a hung load of 2 kips say.
assume the capacity of each outrigger is only 1 kip.
as the load moves directly under each outrigger tip, does failure occur in the outrigger or does some of the load distribute to the adjacent outriggers because of the continuous beam action of the unistrut?
thanks in advance for your comments.
dk
the unistrut channel is a beam with multiple elastic supports (since the 3x3 angles will deflect). if the unistrut is stiffer than the angle then the load will redsitribute to the adjacent angles quite easily. if the adjacent angles manage 500 lbs each, then the maximum moment in the unistrut will be the same as if the load was mid-bay and supported by two angles; so you might want to say something like 800 lbs goes down the central angle and 600 lbs at the adjacent two, this'll create a higher moment in the unistrut.
if you want to do some sums on this, assume a reaction in the central angle. as a cantilever the angle will deflect so much. now based on the original load assumption, the remainder of the load is reacted by the adjacent angles, causing the unistrut to deflect (as a beam, assume simply supported). compare the two deflections to see how close they are, how good is the original load distribution ?
yes, there is a redistribution; how much depends on the relative stiffness of the channel to that of the outriggers.
you can make an estimate by the formulae of beams on elastic foundations.
prex
i've run into this with stairsteps that were cantilevered at one end, connected by handrails at the far end. yes, the load gets distributed around some, and it can be difficult to figure exactly. the supports on the end may be the biggest problem in the design, because you can only spread the load in one direction from there.
by the way, this is not a statics problem, the situation is statically indeterminate, which puts it into the strength of materials classification.
i agree with prex and rb1957. you should do design the strut as a beam on an elastic foundation. this will also give you the reactions into the 3x3 angles. figure the results with the load in different positions to get the maximum effects for the strut and the angles.
the other option is to design the angles for 2 kips of load each and forget about it.
thanks everyone for all your responses - greatly appreciated.
prex, thanks for the link to xcalcs - good stuff on there.
daria

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