Cantilever beam under point load

Formulas

Maximum deflection

$$\delta_{\mathrm{max}} = \frac{P\ \alpha^2\ (3\ L - \alpha)}{6\ E\ I}$$

Maximum bending moment

$$M_{\mathrm{max}} = P\ \alpha$$

Maximum shear force

$$V_{\mathrm{max}} = P$$

Notations

• $E$modulus of elasticity, in GPa
• $I$second moment of area of the cross-section, in cm⁴
• $L$effective span, in cm
• $\alpha$position of the point load, in cm
• $P$point load, in kN