Support Reaction — Simple Beam, Off-Centre Point Load

Also known as beam reaction off centre load · Pb over L reaction · simply supported beam reactions · support load from a point load · near support reaction

R_A = \frac{P (L - a)}{L}

Worked example: 40 kN at 2 m of a 6 m span → near reaction 26.67 kN — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Beam reactions →

UniversityEngineering Mechanics

Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning. Find 1 more lesson on this formula.

See your Report Card

Compete with your friends
share your results

Learning zone

Support Reaction — Simple Beam, Off-Centre Point Load explained

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.

Support Reaction — Simple Beam, Off-Centre Point Load formula

R_A = \frac{P (L - a)}{L}

Where

$R_A$ = Reaction at the near support (N)
$P$ = Point load (N)
$a$ = Distance from that support to the load (m)
$L$ = Span (m)

Missing one of these? Work it out first, then come back

Reaction at the near support — Beam Reaction by Moment Equilibrium — Two Point Loads, Support Reaction — Simple Beam, Uniform Load (R = wL/2)
Point load — Max Moment — Simple Beam, Off-Centre Point Load, Max Bending Moment — Centre Point Load
Distance from that support to the load — Max Moment — Simple Beam, Off-Centre Point Load, Beam Reaction by Moment Equilibrium — Two Point Loads
Span — Max Moment — Simple Beam, Off-Centre Point Load, Fixed-End Moment — Fixed-Fixed Beam, Uniform Load