BMBeamMaster Pro
A comprehensive, interactive guide to understanding internal forces, statics, and the calculus of structural engineering.
1. The Physical Intuition: What are Internal Forces?
Shear Force ()
Imagine trying to slice a loaf of bread or snap a carrot by sliding your hands in opposite vertical directions. Shear force is the internal vertical sliding force that tries to cut the beam perpendicular to its longitudinal axis.
Bending Moment ()
Imagine holding a plastic ruler and bending it into a U-shape. The top fibers crush together (compression), and the bottom fibers stretch apart (tension). Bending moment is the internal rotational force fighting to keep the beam straight against applied bending.
2. The Mathematical Mechanics
✓ The Graphical Rules
Cause an instant vertical "jump" in the Shear diagram. Moment diagram changes slope (creates a peak or valley).
Create a sloped, straight line in the Shear diagram. Create a curved parabola in the Moment diagram.
The Absolute Maximum Bending Moment always occurs at the exact location where the Shear Force diagram crosses zero ().
The Calculus Equations
Because loads dictate shear, and shear dictates moment, we evaluate beams by integrating from left to right.
The change in Shear equals the Area under the Load diagram.
The change in Moment equals the Area under the Shear diagram.
Guided Masterclasses
Master structural engineering fundamentals with these step-by-step interactive breakdowns.
Shear Force Diagram (V)
Bending Moment Diagram (M)
Step 1: Free Body Diagram
Interactive Sandbox
Design your own beam. Adjust dimensions and drag loads to watch the calculus execute in perfectly smooth real-time.
Point Loads (Max 5)
Uniform Loads (Max 3)
No uniform loads applied.