Simply Supported Beam Reactions (Point Load)
Simply Supported Beam Reactions (Point Load)
Before any beam can be sized, the support reactions must be found — they are the starting point for the shear, moment and deflection diagrams.
By static equilibrium, taking moments about each support gives R_a = F·b/L and R_b = F·a/L. where F is the point load, a and b its distances from the left and right supports, and L = a + b the span.
Inputs
F := 20 kN=20000 N
a := 2 m=2 m
b := 4 m=4 m
The span is the sum of the two load distances.
L := a + b=6 m
Taking moments about the right support isolates the left reaction.
R_a := F·b/L=13333.33 N
The right reaction follows from vertical equilibrium (or moments about the left support).
R_b := F·a/L=6666.67 N
Results
The two reactions sum to the applied load, a quick equilibrium check. The larger reaction occurs at the support nearer the load and governs the bearing and connection design there.
Assumptions & limitations
- Statically determinate, simply supported span.
- Self-weight neglected — add it as a UDL if needed.
- Rigid supports, small deflections.