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Strength of Materials: Discontinuity Functions

Another method that can be used to determine the deflection is to use the discontinuity functions; also known as the Macaulay Functions. The discontinuity functions are used to bypass the step of making a moment diagram to determine the moment. It does this by using the equations found in the table below and taking in consideration that the forces placed on the beam can be related to the deflection of the beam through calculus, as well as the shear forces. Refer to equation 1.

Beam Deflection forces and shear relation thru calculus (1)

Macaulay / Discontinuity Functions

An example of how to use the discontinuity functions to determine the deflection of a beam is shown below.

Deflection using Macaulay Functions example

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