Beam Deflection Calculator
Calculate maximum deflection and slope for simply supported and cantilever beams under various loads.
What Is the Beam Deflection Calculator?
The Beam Deflection Calculator computes the maximum deflection of structural beams under various loading conditions and support types. Enter beam length, cross-section properties, material modulus, and load to instantly determine deflection for cantilever and simply supported beams.
Formula
How to Use
Select the beam support type (cantilever, simply supported, fixed-fixed) and load type (point load, uniformly distributed load, or moment). Enter the beam length (L), elastic modulus (E), moment of inertia (I), and load magnitude. The calculator outputs maximum deflection and location.
Example Calculation
Steel cantilever beam (E = 200 GPa), 3m long, I = 8.33×10⁻⁶ m⁴ (100×100mm square section), point load P = 5 kN at tip: δ = (5000 × 3³) / (3 × 200×10⁹ × 8.33×10⁻⁶) = 135,000 / 4,998,000 = 0.027 m = 27 mm.
Understanding Beam Deflection
Beam deflection analysis is a cornerstone of structural engineering and mechanical design. When a beam is loaded, it bends, and the maximum deflection must be controlled to prevent structural failure, excessive vibration, and serviceability issues. Building codes specify maximum allowable deflections as fractions of the beam span (e.g., L/360 or L/240).
Deflection depends on four factors: the applied load, the beam span, the material stiffness (Young's modulus E), and the cross-sectional moment of inertia I. Deflection decreases with larger I and E values. This is why structural steel beams use I-sections (H-beams), which maximize I for a given amount of material.
The calculator covers the most common loading scenarios used in structural engineering practice: cantilever beams with point or distributed loads, and simply supported beams with central or uniformly distributed loads. For complex loading patterns, use the superposition principle and add deflections from individual load cases.
Frequently Asked Questions
What is beam deflection and why does it matter?
Beam deflection is the lateral displacement of a beam under load. Excessive deflection causes structural damage, cracking in attached elements, and occupant discomfort. Building codes set maximum deflection limits (e.g., L/360 for floors).
What is the moment of inertia (I) in beam calculations?
The second moment of area (I) measures a cross-section's resistance to bending. A larger I means less deflection. For a rectangle: I = bh³/12, where b is width and h is height in the direction of bending.
What is Young's modulus (E)?
Young's modulus (elastic modulus) is the stiffness of a material. Steel ≈ 200 GPa, aluminium ≈ 69 GPa, wood ≈ 10–14 GPa. Higher E means less deflection.
What is the difference between cantilever and simply supported beams?
A cantilever is fixed at one end and free at the other. A simply supported beam rests on two supports. Cantilevers deflect more (3× more for the same load, span, and section) because only one end resists rotation.
Is this calculator free?
Yes, completely free with no sign-up required.