Cantilever Beam - Concentrated Load at Free End
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Cantilever Beam - Concentrated Load at Free End formulas
| \(\large{ R = V = P }\) | |
| \(\large{ M_{max} \; }\) (at fixed end) \(\large{ = P\;L }\) | |
| \(\large{ M_x = P\;x }\) | |
| \(\large{ \Delta_{max} \; }\) (at free end) \(\large{ = \frac {P\; L^3} {3\; \lambda\; I} }\) | |
| \(\large{ \Delta_x = \frac {P} {6\; \lambda\; I} \; \left( 2\;L^3 - 3\;L^2\;x + x^3 \right) }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ P }\) = total concentrated load
\(\large{ R }\) = reaction load at bearing point
\(\large{ V }\) = shear force
\(\large{ w }\) = load per unit length
\(\large{ W }\) = total load from a uniform distribution
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ \Delta }\) = deflection or deformation