Cantilever Calculator
Calculate cantilever beam deflection, stress, and moment with our comprehensive calculator. Perfect for engineers, architects, and construction professionals.
Step 1: Beam Properties
Understanding Cantilever Beams
A cantilever beam is fixed at one end and free at the other. The maximum deflection occurs at the free end and is calculated using beam theory formulas based on material properties and loading conditions.
Step 2: Material & Cross-Section
About Material Properties
The modulus of elasticity (E) determines how much a material deforms under load. Steel has high stiffness (200 GPa), while materials like wood are more flexible. The cross-section shape affects the moment of inertia (I), which significantly impacts deflection.
Cantilever Analysis Results
Maximum Deflection
Material Performance Comparison
| Material | Modulus (E) | Deflection | Stress | Safety Factor |
|---|
Cantilever Formulas
Deflection Formula
δ = (P × L³) / (3 × E × I)
Where: δ = Deflection, P = Load, L = Length, E = Modulus of Elasticity, I = Moment of Inertia
Bending Stress Formula
σ = (M × c) / I
Where: σ = Bending Stress, M = Bending Moment (P × L), c = Distance from neutral axis, I = Moment of Inertia
Moment of Inertia Formulas
Rectangular: I = (b × h³) / 12
Circular: I = (π × d⁴) / 64
Where: b = width, h = height, d = diameter
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