## Analytical Details

The first of multiple articles reviewing some of the methods and calculations used in structural engineering.

## Atypical Philosophy

A moment of consciousness, a moment of silence, a moment in history. Great philosophical topics, but not very applicable in structural engineering. A better application of the term in this discipline is the moment of force, or the tendency of a force to cause a body or mass to rotate around a defined point or axis. A moment develops whenever a force vector does not pass through the centroid of a mass, which in practical consideration is the typical case for structural applications.

## Deceptively Simple

The general mathematical equation for a moment is:

Moment = distance x force

The distance is defined as the moment arm, or perpendicular distance between the line of force application and the defined point or axis of rotation, or center of moments. Typical units are inch-pounds, newton-meters, or any expression multiplying units of force with units of distance. Convention usually calls for potential clockwise rotation of the mass as being positive, while counterclockwise rotation is negative. A simple example given in many texts is the moment of force developed in a wrench being applied to a nut. Using the nut as the center of moments, a 30 pound force being applied perpendicular to the wrench handle one foot from the nut, yields a moment of 30 foot-pounds being developed. Or for another example, what is the moment that is developed when two different masses are applied at opposite ends of a beam supported at some mid-span point by a fulcrum?

## If It Was Easy, Anyone Could Do it

These examples are a good start to understanding moments, but practically unusable in actual application. Forces are rarely applied in neat perpendicular lines of action but rather with multiple vectors, and the most interesting center of moments is usually not the actual point or axis of rotation. For a more realistic structural engineering consideration the center of moments will be offset, at a location requiring load determinations needed to prevent material failure. For example, a common center of moments would be offset from the base of one or more supporting columns, and the applied forces are loads transmitted through one or more support beams at the top of the columns. These beams may be installed in more than one plane, supporting multiple loads at varying distances from the vertical axis of the columns. Determining the optimum supporting base material for the columns could be considered partly by minimizing the composite moment at the location of the offset.

## Not A Blink Of An Eye

Clearly the determination of moments in complex structural applications is not a trivial exercise. Fortunately many computational tools and models are available to assist with these types of engineering analyses, which may also be incorporated directly into architectural design software. Of course there are many other load and force considerations required to properly execute a structural engineering design, which works to yield ever safer and more architecturally astonishing structures. In this design and engineering process, the phrase “just a moment” takes on entirely new dimensions.