# Stability

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Even before the creation of the beautiful and complex structures of today, the most important and fundamental concept behind structural engineering has always been stability.  When a simple shelter needs to be built, even a bundle of sticks propped up to shield against the wind, the preliminary concern lies in keeping the house upright.  For the most part, that is simply what the word stability means.  If a structure has the capacity to bear the forces applied to it without tipping over or sliding, then it is stable.

Figure 1.1

For example, if a pencil stands upright on its pointed end, it will very quickly fall over.  If a hand is placed at the top holding the eraser end, it will remain in place.  Figure 1.1 demonstrates a steel column with similar constraints. However, fasteners such as tape, glue, or modeling clay could be used in conjunction with several pencils to construct a model fort.  This model would be a rigid or stable structure.

Figure 1.2

Certain machines that are designed to move are not classifiable as stable structures.  For example, the pendulum in a grandfather clock swings back and forth due to the force of gravity and the counterweights that keep the motion going.  The pendulum is connected to the clock by what is known as a pin joint.  This joint does not support a moment; that means that it can freely turn around its axis.  There is no twisting resistance in the joint.  By itself, a pin joint cannot be a support for a stable structure.  However with the right combination and linking of these joints, a stable structure is possible.  A square frame composed of three members pinned together would be unstable.  See Figure 1.2.

Figure 1.3

Any lateral force applied would cause the structure to fold flat.  However, if a fourth member is pinned across opposite corners of the square, the shape would become rigid.  Any force applied to it would have to snap one of the beams in order for anything to move.  Because it does not freely rotate about any of the joints, it achieves the status of a stable structure.  See Figure 1.3.

A common way of describing this definition of stability is with degrees of freedom.  A degree of freedom is the ability to move linearly in one of the three spatial dimensions and the ability to rotate on an axis.  If an object is constrained so that it cannot translate in the x, y, or z dimensions and is incapable of rotation about any axis, it is considered stable.  A detailed explanation of the lateral forces referenced in this section can be found in Unit 2: Lateral Loads.

One concern of structural engineering involves designing and building components and members that fit together to form stable structures.  However, the materials and geometries of these members must be able to withstand all the loads applied to them.  Apart from simple stability, engineers are also interested in preventing breaking or failure of a structure.  To reference the pencil fort example, the model needs to be stable enough to remain rigid, but the wood in the pencil also needs to be strong enough to prevent snapping.  Using simple methods like mechanics of materials to analyze such properties is how engineers can analyze simple designs.  However, it is extremely rare that buildings are designed with such simplicity.  Almost all structures today require significantly more calculations to analyze.  It is with more complex material, and more diverse building plans, that FEA software has proven to be an empowering asset.