Cantilever Beam - Load at Free End Deflection Vertically with No Rotation
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Cantilever Beam - Load at Free End Deflection Vertically with No Rotation formulas
| \(\large{ R = V = P }\) | |
| \(\large{ M_{max} \; }\) (at both end) \(\large{ = \frac{P \;L}{2} }\) | |
| \(\large{ M_x = P \; \left( \frac{ L }{2} - x \right) }\) | |
| \(\large{ \Delta_{max} \; }\) (at free end) \(\large{ = \frac{P\; L^3}{12 \;\lambda\; I} }\) | |
| \(\large{ \Delta_x = \frac{P \; \left( L \;-\;x \right)^2 }{12\; \lambda\; I} \; \left( L + 2\;x \right) }\) |
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