Beam Deflection Calculator
Calculate maximum deflection and bending stress for a simply supported beam with a single point load at midspan.
Enter your values
Load, span, material modulus, and section properties.
How this calculator works
For a simply supported beam with a single point load at midspan, maximum deflection occurs directly under the load:
P is the point load, L is the span, E is the modulus of elasticity, and I is the second moment of area of the cross-section. Maximum bending moment and stress at the same point are:
c is the distance from the beam's neutral axis to its outermost fiber — half the section depth for a symmetric section.
Typical modulus of elasticity
| Material | E (GPa) |
|---|---|
| Structural steel | 190 – 210 |
| Aluminum alloy | 68 – 72 |
| Cast iron | 100 – 120 |
| Timber (softwood) | 8 – 12 |
Frequently asked questions
Does this work for other load or support cases?
No — this covers the specific case of a simply supported beam with one point load at midspan. Distributed loads, cantilevers, and off-center loads use different deflection and moment formulas.
How do I get the second moment of area, I, for my section?
For a rectangular section, I = b·h³/12 (b = width, h = depth). For standard structural sections, I is published in the manufacturer's section property tables.