Shear Force and Bending Moment Calculator | Beam Analysis Tool

Shear Force and Bending Tool Formula:

For Point Load (P) at a Distance (a) from the Left Support:

• Shear Force (just left of load): \( V = \frac{P \times (L-a)}{L} \)
• Shear Force (just right of load): \( V = \frac{P \times (L-a)}{L} - P \)
• Bending Moment at load point: \( M = \frac{P \times (L-a)}{L} - a \)

For Uniformly Distributed Load (UDL) over Entire Length (L):

• Shear Force at any point (x): \( V = \frac{W \times L}{2} - W \times x \)
• Maximum Bending Moment: \( M = \frac{W \times L^{2}}{8} \)

**Note**: Use the angles and applied load to solve for member forces.

The Shear Force and Bending Moment Calculator will be used by engineers, students, and teachers to analyze a beam under different loading conditions. The bending moment and shear force play a vital role in the selection of beam strength, stability, and structural safety.

One can enter beam type (simply supported, cantilever, overhanging), span length, type of load (point, uniform distributed), and cross-sectional dimensions. The calculator will compute the shear force at any point of the beam, the maximum bending moment, and the optional bending stress. The equilibrium equations, shear force diagram (SFD), and bending moment diagram (BMD) is calculated step-by-step.

SI units are permitted: N, kN, m, mm, Pa/MPa. This instrument suits civil engineers, structural engineers, and mechanical engineers, students, and educators who are studying beam performance as an aspect of academic or professional work. The Optional diagrams assist in the visualization of the impact of loads on the shear and bending of the beam.