# Varignon’s I-Beam

### Model Description

Introduce Varignon’s theorem to students as a simple way to determine the moment about a point. This demonstration should take 5-7 minutes.

### Engineering Principle

Varignon’s Theorem states that the moment of a force is equal to the sum of the moments of that force’s components about the same point.

$M_{PT} = F_x \times d_{\perp y} + F_y \times d_{\perp x}$

where $d_{\perp}$ is the perpendicular distance from the Force’s Line of Action to the point.

### What You Need

Item Quantity Description/Clarification
Force Vectors 3 One vector represents the total Force Vector.  The other two should be smaller and represent the components of the force in each orthogonal direction.  The force vectors should have magnets taped to their backs.
I-Beam 1 The I-Beam should be made of durable material, then fastened to another piece of poster board with a light, large headed bolt.  This allows the I-beam to rotate when fixed to the board.

### How It’s Done

In Class: Introduce the problem of determining how much moment this force acting on a lifting eyelet on an I-beam will cause about the point O.  Show how the complex geometry can complicate this calculation.  Now Introduce Varignon’s theorem as a simple way to avoid this problem.  After stating the theorem, put it into practice on the I-beam.  Break the force into it’s orthogonal components.  After doing so calculate the combined moment of the force’s components about point O.  Show how each component can cause either positive or negative moment, so students must pay attention to the direction that each force causes rotation in.

### Cite this work as:

Jason Evers (2019), "Varignon's I-Beam," https://www.handsonmechanics.org/statics/467.

## 2 thoughts on “Varignon’s I-Beam”

1. Daniel Baker

Is there any way to enlarge the images in the activity? The description is not sufficient for me to be able to understand the activity. Thanks!

1. homadmin Post author

Daniel, good suggestion! I’ve made the image a little larger and also linked it to the full size image file.