Cantilever beam under uniformly distributed load

Formulas

Maximum deflection

$$\delta_{\mathrm{max}} = \frac{q\ L^4}{8\ E\ I}$$

Maximum bending moment

$$M_{\mathrm{max}} = \frac{q\ L^2}{2}$$

Maximum shear force

$$V_{\mathrm{max}} = q\ L$$

Notations

• $E$modulus of elasticity, in GPa
• $I$second moment of area of the cross-section, in cm⁴
• $L$effective span, in cm
• $q$uniformly distributed load, in kN/m