Fixed-pinned beam under uniformly distributed load

Formulas

Maximum deflection

$$\delta_{\mathrm{max}} = \frac{q\ L^4}{185\ E\ I}$$

Maximum bending moment

$$M_{\mathrm{max}} = \frac{q\ L^2}{8}$$

Minimum bending moment

$$M_{\mathrm{min}} = - \frac{9\ q\ L^2}{128}$$

Maximum shear force

$$V_{\mathrm{max}} = \frac{5\ q\ L}{8}$$

Minimum shear force

$$V_{\mathrm{min}} = - \frac{3\ q\ L}{8}$$

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