first of all I would like to thank you/you for the explanation and for the time spent.
as you wrote, the carello has a size of supports (seat area) between 200/250 mm.
to be more precise and to have a clearer idea I posted the 3d of the structure, to better understand the knots.
the heb140 beam is the central one at the top, welded on the wings to the structure made with hea120.
to me they asked, in order to put a tag, the max flow of the heb140 where the hoist should be mounted regardless of the scope of the hoist.
Thank you
the type of structure sees the connection of the central putrella directly on the shorter side ones. In fact, the torsion deformation of the lateral putrelles is such as to move the behaviour of the central beam more towards that of an uncertain beam (although the beam was perfectly stuck on the putrelles) in terms of flender moment diagram.
therefore it is definitely correct the calculation made with p*l/4 to evaluate the time of calculation.
I admit I was too much in limiting the collaborative width to just 200mm. probably you could consider a width of about 330mm (always in the hypothesis of a 45° spread).
instead it is the arrow the problem because the central beam behaves more like a hinged beam and therefore the most correct arrow is that with the coefficient 48 that leads to a value of 8,5mm.
Considering that it is a hoist and that it does not have the necessary precision request of a road of a carriage probably it is still acceptable not to descend under l/300=4000/300=13mm as in the normal calculations of the beams under variable loads. even if it seems so much we say it is acceptable.
as far as total flow is concerned, it is only necessary to make mrd/med reports and to take the smallest and multiply it for 20 kn.
then recalculates the strong moment of local verification:
mrd = 330x12^2/4x235/1,25x10^-6 = 2,23 knm
therefore the maximum load for global verification is: 20 x 54,92/30 = 36,61 kn
maximum for local verification: 20 x 2,23 / 1,19 = 37,47 kn
therefore we say that it is possible to carry the load to about 36 kn without particular problems.
What happens to the arrow? grows in the ratio 36/20 x 8,5 = ~ 15mm
actually is too high value. We reduce the maximum load in the 13/15 ratio and then the actual maximum load is: 36x13/15 = ~ 31 kn with 13mm arrow.
therefore if the maximum to 31 kn is limited the resistances of the material and the maximum deformation. as we have seen the structure can bear up to 36 kn but the risk is the development of the movement when it exceeds 31 kn (obviously in the hypothesis that l/300 is acceptable for this problem).
it could be worth making a more accurate calculation with a program.
