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Simple Beam Reactions & Moments

Simply Supported · Uniform + Point Load · Deflection

When to use: Compute support reactions, maximum shear, maximum bending moment, and midspan deflection for a single-span simply supported beam carrying a uniform load w and an optional point load P at distance a. Results check against the L/360 (live load) and L/240 (total load) serviceability limits.

Beam & Loading
ft
kip/ft
kip
from left
ft
ksi
in⁴
Key Formulas
R = wL/2 (each support, UDL)
Mmax = wL²/8 (UDL, midspan)
Mmax = Pab/L (point load)
δ = 5wL⁴/384EI (UDL)
δ = PL³/48EI (central P)
Maximum Moment
125.00
kip·ft
Results
Left Reaction R₁20.00 kip
Right Reaction R₂20.00 kip
Max Shear Vmax20.00 kip
Max Moment Mmax125.00 kip·ft
Max Deflection δ0.952 in
✗ L/360
limit 0.667 in
✓ L/240
limit 1.000 in
References
Statics — equilibrium ΣM=0, ΣF=0
AISC Steel Construction Manual — beam diagrams
IBC Table 1604.3 — deflection limits L/360, L/240