Accurately determine the maximum slope and deflection of a cantilever beam under a uniformly distributed load (UDL). This essential engineering calculator helps civil and structural engineers analyze beam performance, ensuring structural integrity and design compliance for various construction projects.
Formula:
For a cantilever beam with a uniformly distributed load (UDL) 'w' over its entire length 'L', the maximum slope (θmax) and maximum deflection (δmax) at the free end are calculated as follows:
- Maximum Slope: θmax = (w × L3) / (6 × E × I)
- Maximum Deflection: δmax = (w × L4) / (8 × E × I)
Where:
- w = Uniformly Distributed Load (e.g., N/m, lbf/ft)
- L = Beam Length (e.g., m, ft)
- E = Modulus of Elasticity of the beam material (e.g., Pa, psi)
- I = Area Moment of Inertia of the beam's cross-section (e.g., m4, in4)