Cantilever Beam with Load at Any Point Calculator
Find the slope and deflection of a cantilever beam loaded at an arbitrary point. Useful for irregular load cases in real-world structural applications.
Analyze Cantilever Deflection with Point Load
Cantilever Beam with Arbitrary Point Load Formula
$$\text{Deflection} = \frac{P \cdot x^2 (3a – x)}{6 \cdot E \cdot I}$$
$$\text{Deflection} = \frac{P \cdot a^2 (3x – a)}{6 \cdot E \cdot I}$$
Where
- $$P$$ – the externally applied load,
- $$E$$ – the elastic modulus,
- $$I$$ – the area moment of inertia,
- $$L$$ – the length of the beam and
- $$x$$ – the position of the load
- $$a$$ – the distance of the load from one end of the support
Use this calculator when the load is not at the beam end. It supports any position a, letting you model scenarios like equipment mounted mid-span or external loads.