Accurately calculate the deflection of solid rectangular beams under various loading conditions. Our easy-to-use online calculator helps engineers and students determine maximum deflection for simply supported or cantilever beams with point or uniformly distributed loads, vital for structural analysis and design.
Formula:
Understanding Beam Deflection Formulas
The deflection (δ) of a solid rectangular beam depends on its material properties (Modulus of Elasticity), geometric properties (Moment of Inertia, Length, Width, Height), and the applied load. The Moment of Inertia (I) for a solid rectangular cross-section is calculated as:
I = (b × h3) / 12
Where:
- I = Moment of Inertia (m4)
- b = Beam Width (m)
- h = Beam Height (m)
Common beam deflection formulas for maximum deflection (δmax):
1. Simply Supported Beam with Point Load (P) at Center:
δmax = (P × L3) / (48 × E × I)
2. Cantilever Beam with Point Load (P) at Free End:
δmax = (P × L3) / (3 × E × I)
3. Simply Supported Beam with Uniformly Distributed Load (w):
δmax = (5 × w × L4) / (384 × E × I)
4. Cantilever Beam with Uniformly Distributed Load (w):
δmax = (w × L4) / (8 × E × I)
Where:
- δmax = Maximum Deflection (m)
- P = Point Load (N)
- w = Uniformly Distributed Load (N/m)
- L = Beam Length (m)
- E = Modulus of Elasticity (Pa)
- I = Moment of Inertia (m4)