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A structure or mechanical element is said to be rigid when it does not bend, or deflect, or twist too much when an external force, moment, or torque is applied. But if the movement due to the external disturbance is large, the member is said to be flexible. The words rigidity and flexibility are qualitative terms which depend upon the situation. Thus the floor of a building which bonds only 0.1 in because of the weight of a machine placed upon it would be considered very rigid if the machine were heavy. But a surface plate which bends .01 in because of its own weight would be considered too flexible.
Deflection analysis enters into design situations in many ways. A snap ring, or retaining ring, must be flexible enough so that it can be bent, without permanent deformation, and assembled; and then it must be rigid enough to hold the assembled parts together. In a transmission the gears must be supported by a rigid shaft. If the shaft bends too much, that is, if it is too flexible, the teeth will not mesh properly, resulting in excessive impact, noise, wear, and early failure. In rolling sheet or strip steel to prescribed thicknesses, the rolls must be crowned, that is, curved, so that the finished product will be of uniform thickness. Thus, to design the rolls it is necessary to know exactly how much they will bend when a sheet of steel is rolled between them. Sometimes mechanical elements must be designed to have a particular force-deflection characteristic. The suspension system of an automobile, for example, must be designed within a very narrow range to achieve an optimum bouncing frequency for all conditions of vehicle loading because the human body is comfortable only within a limited range of frequencies.