A lever, not a shared load
The hoist load on a gantry beam splits between the two end frames by the lever rule, and the lever rule is a straight line. All of the load goes to the frame the trolley is sitting against; none of it goes there when the trolley is at the far end; in between it is a simple proportion of the distance. The beam and trolley weight behaves differently — it is spread along the beam, so half of it goes to each frame regardless.
With the defaults, a 2,000 lb hook load with the trolley 3 ft along a 12 ft span puts 1,500 lb on the left frame and 500 lb on the right. Add 190 lb of beam to each side and the reactions are 1,690 lb and 690 lb. They add to 2,380 lb, which is the load plus the beam, and that addition is the check worth doing every time.
Three quarters on one frame at the quarter point
Three feet along twelve is the quarter point, and the near frame takes three quarters of the hook load there. That is the number people are surprised by. Halfway along is the only position where the two frames see the same thing, and nobody parks a trolley in the middle because the load is rarely in the middle of the bay.
The consequence lands on the casters. With 130 lb of frame added and two casters a side, the heaviest caster on the defaults carries 910 lb and the lightest carries 410 lb. On a 1.5 square inch contact patch that is 607 psi against 273 psi, over a floor that has an expansion joint in it somewhere.
Past the frame, the far end lifts
Set the trolley position below zero or beyond the span and the beam is cantilevering. The reaction at the far frame goes negative, and negative in a reaction is not a small force, it is a force pointing the other way — the beam is trying to lift that end off the ground. The page flags it rather than printing a quiet minus sign, because the arithmetic and the failure mode are different things and the failure mode is tipping.
What the static split leaves out
All of this is a still load on a level floor. A gantry being pushed with a load on it has a sideways force at the top and drag at the casters, which is a couple the static numbers do not contain. A hoist starting or stopping puts a dynamic load through the beam that is larger than the weight hanging on it. A floor with a slope turns the whole frame into a very slow lever. None of that is in the reactions above, and all of it is in the room.
Questions people ask
How does a gantry crane split the load between its two frames?
By the lever rule. A load at distance x along a span L puts a fraction (L minus x) over L on the near frame and x over L on the far one. The beam and trolley weight is different — it is distributed along the beam, so each frame takes half of it wherever the trolley is. The two reactions always add up to the load plus the beam, which is the arithmetic check.
Where does the trolley have to be for the frames to share equally?
Mid span, and only mid span. At the quarter point the near frame already has three quarters of the hook load. With the page defaults that is 1,500 lb on one frame and 500 lb on the other from a 2,000 lb load, before the beam weight is added to each side.
What load does each caster see?
The frame reaction plus that frame's share of the frame weight, divided by the number of casters under it. With the defaults the heaviest caster carries 910 lb and the lightest 410 lb, which on a 1.5 square inch contact patch is 607 psi against 273 psi. Whether the wheel and the floor are up to it is a question for the caster rating and whoever owns the slab.
What happens if the trolley goes past the end frame?
The beam cantilevers and the reaction at the far frame goes negative — the beam is trying to lift that end off the floor instead of pushing it down. The page calls that out rather than printing a minus sign quietly, because it is a change of direction and not a small number. Whether the frame stays down is not something arithmetic decides.
Does the beam weight move between the frames as the trolley moves?
No. It is spread along the beam, so each frame carries half of it in every trolley position. Only the hook load slides from one frame to the other. That is why the lighter frame never gets down to zero on a simply supported span.
Do these numbers account for pushing the gantry while it is loaded?
No. Everything here is a still load on a level floor. Pushing adds a sideways force at the top and drag at the casters, starting and stopping a hoist puts a dynamic load through the beam larger than the weight itself, and a sloped floor changes the problem completely. Those are the conditions that decide how a portable gantry behaves and none of them is in this arithmetic.