Balance a Loaded Beam on Two Supports

Move the supports and load. The reaction forces update automatically so that both translational and rotational equilibrium can be checked.

Reaction at A350 N
Reaction at B350 N
Total downward load700 N
ΣFᵧ0.00 N
Στ about A0.00 N·m

Beam setup

1.00 m
Measured from the left end.
5.00 m
Measured from the left end.
3.00 m
Drag the load anywhere along the beam.
500 N
Downward concentrated force.
200 N
Uniform beam weight acts at the beam center.
ΣFy = 0:   RA + RB = P + W
ΣτA = 0:   RB(xB-xA) = P(xP-xA) + W(3-xA)
Balanced beam: The upward reactions equal the total downward load, and the clockwise and counterclockwise moments cancel.

Free-body diagram

Rₐ = 350 N Rᵦ = 350 N P = 500 N W = 200 N beam center
reaction Rₐ reaction Rᵦ point load P beam weight W
Vertical-force check Rₐ + Rᵦ − P − W = 0.00 N
Moment check about A Στₐ = 0.00 N·m
CCW from Rᵦ
1400 N·m
CW from loads
1400 N·m
Predict before moving the load

Move P toward support A. Which reaction increases, and which reaction decreases?