Understanding Beam Deflection
Beam deflection analysis is essential for serviceability and structural integrity of cantilever structures.
- Deflection Formulas Point load: δ = PL³/3EI. Uniform load: δ = wL⁴/8EI. Moment load: δ = ML²/2EI. Combined loads use superposition principle.
- Material Effects Elastic modulus (E) directly affects deflection. Creep factors: 1.5-2.0 for wood, 2.0-3.0 for concrete. Temperature effects: ±1/8" per 100ft per 100°F.
- Section Properties Moment of inertia (I) crucial - doubles depth increases I by 8×. Composite sections need transformed area method. Consider effective width for wide flanges.
- Load Duration Short-term loads use elastic analysis. Long-term loads need creep consideration. Cyclic loads may need fatigue analysis. Impact loads use dynamic factors.
Design Considerations
Serviceability Limits
Residential: L/180-L/360. Commercial: L/240-L/480. Special equipment may need L/720 or better. Visual impact important for exposed structures.
Load Combinations
Dead load + Live load most common. Snow/Wind loads where applicable. Consider pattern loading for multiple spans. Include construction loads.
Support Conditions
Fixed end reduces deflection vs. pinned. Support settlement affects deflection. Consider foundation flexibility. Account for connection rotational stiffness.
Mitigation Methods
Pre-cambering: typically L/300-L/500. Composite action can reduce deflection 30-50%. Stiffeners effective for local deflection. Consider haunched sections.
Analysis Guide
- Load Analysis Force distribution.
- Moment Calculation Bending effects.
- Deflection Check Serviceability limits.
- Stress Verification Material limits.