Beam Load Calculator (Simple)
Estimate the bending moment, shear force and deflection of a simply supported beam under a uniformly distributed load, a central point load, or both. Enter the span and loads to get the peak bending moment at midspan, the maximum shear at the supports, and an approximate deflection.
Formula
M_udl = wL²/8; M_point = PL/4; Shear = wL/2 + P/2; Deflection assumes EI = 20,000 kN·m²
- Bending moment from a uniform load is wL²/8; from a central point load it is PL/4; the two add together.
- Maximum shear at the supports is wL/2 from the UDL plus P/2 from the point load.
- Deflection is approximated assuming a fixed stiffness EI = 20,000 kN·m² (5wL⁴/384EI for the UDL, PL³/48EI for the point load).
- Because EI is assumed, the deflection is indicative only — use the real section stiffness for design.
- Results apply to a single simply supported span; continuous or fixed beams behave differently.
4 m span, 5 kN/m UDL, no point load
Inputs
- Beam Span: 4 m
- Distributed Load (UDL): 5 kN/m
- Point Load at Midspan: 0 kN
Moment = 5 × 4² / 8 = 10 kN·m. Shear = 5 × 4 / 2 = 10 kN. With EI = 20,000 kN·m², deflection ≈ 5×5×4⁴ / (384×20000) × 1000 ≈ 0.8 mm.
Frequently asked questions
What loads does this handle?
A uniformly distributed load (UDL) along the span and a point load at midspan, separately or combined, on a simply supported beam.
How is the bending moment found?
The UDL contributes wL²/8 and a central point load contributes PL/4. The calculator adds them to give the total maximum moment at midspan.
Why is the deflection only approximate?
It assumes a fixed beam stiffness (EI = 20,000 kN·m²). Real deflection depends on the actual material and section, so treat this figure as indicative.
Where does the maximum shear occur?
At the supports. For this loading it equals wL/2 from the distributed load plus P/2 from the point load.