What Is a Bending Moment?

In order to understand how structures function as a whole, engineers must be able to calculate how the structure can resist the forces it may encounter without failing. In real-world terms, those forces include live load (the people or materials the building will store), dead load (the weight of the structure itself), and elemental considerations like snow load, wind load, and earthquake load. Building codes generally set the parameters for these design loads, but it is crucial to have an understanding of how and why those codes are set in the first place.

Both internal forces and external forces act on structures, affecting the way all their components work together. Therefore, engineers must consider both in designing a structure for maximum stability. 

When a load is applied to a column, it places the column in compression. The ability of the column to sustain that load (or compressive external forces pressing inward and shortening the particles that comprise that column) is a calculation that helps determine the structural integrity of the building as a whole. No material can sustain an infinite load, so when engineers consider external forces, they measure a reaction called the “bending moment.”

What is a bending moment?

As its name implies, the bending moment occurs when a force is applied to a structural element (such as a column or beam), and that external force causes the element to bend and ultimately fail. Consider a simply supported beam bearing a load: The maximum bending moment in the beam occurs at the point of maximum stress—the last moment before it fails. This principle is key in designing buildings for maximum structural integrity.

There are two types of bending moments, depending on which way the bending occurs: 

• Sagging or positive bending: The compression happens in the top fiber, which causes a tension (or pulling) reaction in the bottom fiber.
• Hogging or negative bending: The compression occurs in the bottom (for instance, a force pushes a horizontal beam perpendicularly from below), causing tension in the top.

Master builder Jordan Smith illustrates the bending moment in this way: 

“Your wood will encounter a bending moment when force is applied. For instance, as I walk across a floor, I’m pushing down—gravity’s pulling me down—and that bends the beam and puts the top member in compression, and the bottom member in tension.”  

How bending moment relates to other forces and stresses

Put most simply, structural design involves these four forces:

• Compression: Particles of a material are pushed against each other, causing them to shorten, or compress. In a building, compression usually comes from the top.
• Tension: The opposite of compression, in which a pulling force is working to lengthen the material. If a beam is being compressed from the top, it will be in tension at the bottom. 
• Torsion: A structural element is subject to torque—or a twisting force.
• Shear: Opposing structural forces cause slippage on a plane. In other words, a shearing force that causes layers to slide across each other in opposite directions. Buildings need shear walls to resist lateral, or shear, forces. 

You’ll always find these four stresses acting on a structure. Imagine: You’re walking across the second floor of a house. Your weight is applying compression to the beams holding up the floor, and as the beams compress at the top, they’re also stretched in tension at the bottom. This creates a bending moment. The beams are also held together in a web that is in shear. To maintain structural integrity, the home’s construction must be able to hold all of these forces in balance.  

Learn more about how forces and stresses act on structures and materials in MT Copeland’s Wood Materials class, taught by professional builder Jordan Smith.

Learn more about how forces and stresses act on structures and materials in MT Copeland’s Wood Materials class, taught by professional builder Jordan Smith. 

How is the bending moment calculated?

The concept of the bending moment is vital to engineering because it is used to calculate how much bending may occur when different forces are at work. Civil and structural engineers construct bending moment diagrams for a building based on the probable stresses or loads a building will experience. That diagram shows where an element will experience the maximum bending moment; in other words, where the element would most likely break from bending. They can then identify where the elements are weakest and provide the necessary reinforcement to resist bending. 

To calculate the bending moment of a certain point in an element, you would take the magnitude of the force and multiply it by the distance of the force from that point. The bending moment is usually measured as force x distance (kNm), and occurs as a result of external forces.

Because you are measuring either positive or negative bending—meaning the force is happening from above or below—the force must be perpendicular to the line between the point where the force is applied and the reference point.

MT Copeland offers video-based online classes that give you a foundation in construction fundamentals with real-world applications. Courses include professionally produced videos taught by practicing craftspeople, and supplementary downloads like quizzes, blueprints, and other materials to help you master the skills.