Calculation
RA = F·(L−a)/L; RB = F−RA
The closer the load sits to a support, the larger that support's reaction; a centred load splits the reaction exactly evenly.
Dubbel Mechanik B 1.6.1 Auflagerreaktionen in der Ebene (Freimachen, Gleichgewichtsbedingungen): RA = F·(L−a)/L
Support reactions under an eccentric point load
The closer the load sits to a support, the larger that support's reaction; a centred load splits the reaction exactly evenly.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Support reaction at A RA — Support reaction at the support from which load distance a is measured.
- Point load F — Vertical point load on the beam.
- Load distance from support A a — Distance of the load from support A along the beam axis.
- Span L — Total distance between supports A and B.
Example
F=1,000 N, a=3 m and L=5 m give RA=1000·(5−3)/5=400 N and RB=600 N.
Assumptions and limits
Rigid, weightless beam with two point supports and a single vertical point load; beam self-weight, distributed loads and multiple load cases must be superimposed separately.
Understand Support reactions under an eccentric point load
This calculator determines the reaction at one support of a simple beam carrying exactly one point load that need not be centred, a commonly needed basic statics case.
What does this quantity describe?
For a beam of length L on two supports with a point load F at distance a from support A, moment equilibrium about support B gives reaction RA=F·(L−a)/L; force balance gives RB=F−RA.
Formula and variables
RA = F·(L−a)/L; RB = F−RA
RA = F·(L−a)/LRB = F − RA
| Symbol / input | Meaning |
|---|---|
| Support reaction at A RA | Support reaction at the support from which load distance a is measured. |
| Point load F | Vertical point load on the beam. |
| Load distance from support A a | Distance of the load from support A along the beam axis. |
| Span L | Total distance between supports A and B. |
Choose the inputs correctly
F is the applied point load, a its distance from support A along the beam axis, L the total span between supports.
How to use the calculator
Measure a and L along the same axis from the same reference support; a=L/2 gives the familiar special case of equal reactions.
Worked example
F=1,000 N, a=3 m and L=5 m give RA=1000·(5−3)/5=400 N and RB=600 N.
Understand the result and units
The closer the load sits to a support, the larger that support's reaction; in the limit a→0, support A carries the entire load.
F is a force, a and L are lengths. RA is output as a force.
Typical applications
Hand-calculating support reactions for point loads in statics problems, crane runway and beam design, before deriving moment and deflection diagrams.
Assumptions, limits and common mistakes
Rigid, weightless beam with two point supports and exactly one vertical point load; beam self-weight, distributed loads, multiple point loads and angled loads must be superimposed separately.
Common mistake: Do not accidentally measure a from the wrong support; the formula assumes a is measured from support A, for which RA is calculated.
Frequently asked questions
What is “Support reactions under an eccentric point load” used for?
Hand-calculating support reactions for point loads in statics problems, crane runway and beam design, before deriving moment and deflection diagrams.
Where do the input values come from?
F is the applied point load, a its distance from support A along the beam axis, L the total span between supports.
What does the result not cover?
Rigid, weightless beam with two point supports and exactly one vertical point load; beam self-weight, distributed loads, multiple point loads and angled loads must be superimposed separately.