What is a Moment?

An Example of Moment Force
Cantilevers often cause high moment forces to occur (Photo: rusty_dragonfly)

A moment (aka torque?) is a slightly more difficult concept to explain than a force. While a force is seen everyday (how much do you weigh, is it safe to stand on that, I can't lift this t.v. up the stairs), a moment is a more unseen force (although I bet you've known how to use it for quite some time). Remember when you were young, and destructive, and you found that it was easier to break certain objects by bending them vs trying to rip it apart. A moment is the force that gives a numerical value to the amount of bending in an object. It is an integral part of calculating the bending stress acting on a member.

The actual definition is: The moment of a force is a measure of its tendency to rotate an object about some point.

The moment of a system (M) for a force about a point (a) is the cross product of the force (F) and the distance from a to the perpendicular intersection of the force line (call it d). In short,

M_a = F*d

If r is provided as the vector between the point the moment is taken about, a, and the point the force is applied to then d = r*sin {\theta} \hbox{ for }\theta < 180^\circ .

As I alluded to above, the moment acting on an object is important to calculate because it is integral to finding the bending stress acting on a member (bending stress is one of the main forces that needs to be calculated along with shear and axial to name a few). You can see how to calculate the Moment (usually donated as M) in a few different beam types here. Also it is important to know can be found by integrating your shear force.

To clarify it's place in the world of structural engineering:

Force ↔ Shear Force ↔ Moment Force

through differentiation and integration of each other.

Don't you love when it all starts to come together!

Here are a couple important rules when it comes to moments:

  1. A moment force can transfer along the length of a beam a beam
  2. When the line of action of the force travels through the center of rotation a moment will be zero. To simplify this a moment is defined as the rotational force about a designated point. If you were to apply a force that also passed through that designated point then the moment of the system would be zero.
  3. At a pinned connection, the moment is zero. Only a fixed or continuous member will allow moments to travel through the supports.

Enough Background, How do I find it?

To get started understanding the moment force, and how it's calculated, try the following.

  1. A Simple Moment Calculation
  2. A Medium Difficulty Moment Calculation

A Simple Moment Force Calculation

Take the above photo and find the maximum moment force acting on the diving board. You have a penguin standing at the free edge of a diving board. Assume the board is fixed at one end, and cantilevers out 6'-0". Also, the penguin weighs 20 lbs and the diving board weighs 5 lbs/ft. Graphically the system looks something like this:

An example of a moment force calculation
Fig 2: Moment Force Calculation

Using your Moment Diagrams and the superposition of loads? you can find that:

M = \frac{wl^2}{2} + Pl = \frac{5 plf * (6 ft)^2}{2} + 20 lbs * 6 ft = 210 lb-ft

Note: The units for moment are force-length (ex: lb-in, lb-ft, kip-ft, etc.)

A Medium Difficulty Moment Calculation



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