Support Reaction — Simple Beam, Off-Centre Point Load

Reactions come straight from statics, and the lever-arm logic is worth internalising rather than memorising: each support takes the fraction of the load proportional to its distance from the opposite end. A 40 kN load 2 m along a 6 m span puts $40 \times 4/6 = 26.7$ kN on the near support and $40 \times 2/6 = 13.3$ kN on the far one. The two sum to 40 kN, as they must, and the near support — the one the load is closer to — takes the larger share.

The "opposite end" part is where people go wrong, and it is worth a sanity check every time: slide the load right up against a support and that support should take essentially all of it. This crossed relationship is why an off-centre load punishes one support badly. Park a crane outrigger at the quarter point of a beam and that support carries 75% of the load, not half, and the beam-to-column connection, the bearing plate and the column below all have to be checked for that number rather than for the average.

Two practical follow-ons. Reactions are what the supporting structure has to carry, so this is the number that migrates down into the column, the wall, the footing and eventually the soil — and it is also what a scaffold, shoring tower or crane mat gets sized on. And for a run of loads, superposition works: compute each load's contribution to each reaction and add. It is exact, unlike most rules of thumb, because reactions on a determinate beam come from equilibrium alone and never depend on the beam's stiffness or material at all.