"When a beam with a straight longitudinal axis is loaded by lateral forces, the axis is deformed into a curve, called the deflection curve of the beam. In Chapter 5 we used the curvature of the deflection curve to determine the normal strains and stresses in a beam. However, we did not develop a method for finding the deflections themselves. In this chapter, we will determine the equation of the deflection curve and also find delections at specific points along the axis of the beam. The calculation of deflections is an important part of structural analysis and design. For example, finding deflections is an essential ingredient in the analysis of statically indeterminate structures. Deflections are also important in dynamic analysis, as when investigating the vibrations of aircraft or the response of buildings to earthquakes."

DEFLECTION
A BEND OR CURVING AWAY

DEFLECTION CURVE
A CURVE THAT DEVIATES FROM ITS EXPECTED PATH.

DIFFERENTIAL EQUATION
AN EQUATION THAT RELATES THE RATES OF CHANGE OF DIFFERENT PROCESSES OR PHYSICAL PARAMETERS.

EQUATION
A MATHEMATICAL EQUALITY RELATING PARAMETERS OR MEASUREMENTS

TOLERABLE LIMITS