# Static Balance: Definition & Examples

Instructor: Jennifer Perone

Ms. Perone has taught College Engineering, Ethics, Psychology, Perception, Statistics, Experimental Design & Analysis, Physics and secondary STEM topics for more than 15 years!

Statics is the analysis and study of objects in equilibrium, from bicycles to skyscrapers. The ability to balance all forces is very important to the stability of our world. When static balances fail, it can cause a structural collapse and catastrophe!

## Static Balance

Imagine you're out riding a bicycle, enjoying a beautiful day, and suddenly your front tire begins to experience momentum around its axis. It wobbles to the point that the wheel falls off, spilling you onto the pavement. Ouch! You wouldn't want to use that bike again until you figured out what caused the mechanical failure. Or much scarier - let's say you're up in the top of the Hancock tower in Chicago and it starts to sway from the winds off of Lake Michigan to the point that you're unsure of your safety if you remain in the building.

This is why understanding statics is fundamental to the successful practice of structural engineering. Ignoring the rules of statics is just asking for catastrophe.

Statics is the study and analysis of objects in equilibrium. It is important in all engineering projects because it allows us to balance forces and keep structures from accelerating from external forces, internal forces, and moments. Think of the Golden Gate Bridge, the Empire State Building, a bicycle, a pair of scissors or any other structure that needs to deal with all those forces, but also remain structurally sound enough to keep in equilibrium to perform the job for which it was designed. How do engineers do it? It's not easy, but it involves using engineering principles to figure out systems of forces and momentum acting on objects.

### Newton's Laws of Motion

Every element of a mechanical system must satisfy Newton's Second Law of Motion: The resultant force (f) acting on the element is related to the acceleration (a) of the elements by f = ma, where m equals mass.

While Newton's Second Law of Motion is important here, equilibrium of structures and objects is also about Newton's Third Law of Motion. This law states that the force exerted on a body I by a body J must be in equilibrium, or balanced with one another.

A system in static equilibrium is in balance and will experience no acceleration from outside forces. Newton's laws also require that the resultant moment of these forces about any point must be zero.

## The Equilibrium Equations

In static systems, there are two conditions that must be satisfied:

1) The sum of all forces in all directions must equal zero.

2) The sum of all moments around a point are also zero.

This means that the sum of all external forces on an object must equal zero, and that all moments around all points of this object must also be zero. If they are not, then you're dealing with a dynamic mechanical situation instead!

There are generally two types of support systems in mechanical engineering static systems: two-dimensional and three-dimensional.

### Two-dimensional application of supports

There are several types of 2-D applications of supports in static systems in mechanical engineering, including rope/cable/spring, contact with smooth surface, contact with rough surface, pin supports, roller supports, constrained pin/slider and built-in (fixed) supports. You can see these in common objects like scissors and staplers, or even truss bridges.

### Three-dimensional application of supports

There are also several types of 3-D applications of supports in static systems; among these are the ball-and-socket, roller support, the hinge, the bearing and the built-in support. The only difference from the 2-D applications are that we've added a dimension. In other words, the rules are the same as in the 2-D system, except that there is another dimension.

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