Cantilever Beam - Load Increasing Uniformly to One End
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Cantilever Beam - Load Increasing Uniformly to One End formulas
| \(\large{ R = V = W }\) | |
| \(\large{ V_x = W\; \frac{x^2}{L^2} }\) | |
| \(\large{ M_{max} \; }\) (at fixed end) \(\large{ = \frac{W\; L}{3} }\) | |
| \(\large{ M_x = \frac{ W\;x^3 }{3\;L^2} }\) | |
| \(\large{ \Delta_{max} \; }\) (at free end) \(\large{ = \frac{W\; L^3}{15\; \lambda\; I} }\) | |
| \(\large{ \Delta_x = \frac{W\;x^2}{60\; \lambda \;I \;L^2} \; \left( x^5 + 5\;L^4 x + 4\;L^5 \right) }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ R }\) = 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