Sign convention for SFD & BMD?

Shear positive when left section tends to move upward. Moment positive when beam sags (compression on top).

Where does maximum moment occur?

At locations where shear force is zero (change of sign).

SFD & BMD Calculator

Generate accurate Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) for various beam types and loading conditions. Visualizes internal forces with sign convention.

Max Moment

25 kNm

Simply supported beam • 10 kN central point load • L=5 m

Shear Force & Bending Moment Diagrams

Purpose: Visualizes internal shear force and bending moment along the beam.

Beam Type

Beam Length L (m)

Point Load P (kN)

Point Load Position from Left (m)

Uniform Distributed Load w (kN/m)

Applied Moment M (kNm)

Moment Position from Left (m)

Shear Force Diagram (SFD)

Bending Moment Diagram (BMD)

Governing Relations

dV/dx = −w(x)

dM/dx = V(x)

Key Points:

Maximum bending moment occurs where shear force = 0
Discontinuities in SFD indicate point loads
Discontinuities in BMD indicate applied moments

Enter beam loading to generate diagrams

SFD & BMD Guidelines

Sign Convention

Shear Force: Positive when left section tends upward relative to right

Bending Moment: Positive when beam is in sagging (compression on top fibres)

Common Loading Cases

Simply Supported + UDL: Max M = wL²/8 at centre

Cantilever + End Load: Max M = PL at fixed end

Point Load: Jump in shear = magnitude of load