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Beam Calculator
Calculate deflections, moments, shear forces, and reactions for various beam configurations
Beam Configuration
Parameters
Beam Types
Simply Supported
Beam supported at both ends, free to rotate
Cantilever
Beam fixed at one end, free at the other
Fixed-Fixed
Beam fixed at both ends, no rotation allowed
Propped Cantilever
Cantilever with additional support at free end
Key Parameters
Young's Modulus (E): Material stiffness
Moment of Inertia (I): Cross-section resistance to bending
Deflection: Vertical displacement of beam
Bending Moment: Internal moment causing beam curvature
Shear Force: Internal force perpendicular to beam axis
Common Materials
Steel200 GPa
Aluminum69 GPa
Concrete30 GPa
Wood (Oak)11 GPa
Key Formulas
Simply Supported Beam
Center Point Load: δ = PL³/(48EI)
UDL: δ = 5wL⁴/(384EI)
Cantilever Beam
End Point Load: δ = PL³/(3EI)
UDL: δ = wL⁴/(8EI)
Fixed-Fixed Beam
Center Point Load: δ = PL³/(192EI)
UDL: δ = wL⁴/(384EI)
Sign Conventions
Deflection: Downward is positive
Moment: Sagging is positive