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Unformatted text preview: Use of Singularity Functions for Beam Slope and Deflections (a simpler method to replace sections 5.5 and 9.6 in Beer and Johnston) A special family of math functions can be used to write a single M(x) equation, resulting in only two constants of integration C 1 and C 2 even for the most complicated beam. These functions (which well call singularity functions) are defined as follows: = 0 if x is less than a <x-a> n = (x-a) n if x is greater than or equal to a, where a is the distance from the left end of the beam. These functions can be multiplied by constants and can be integrated using simple power law integration. For example, the unit step function <x-a> = 0 or 1, depending on the value of x and C <x-a> = 0 or C, depending on the value of x. A single integration of C <x-a> 0 gives C <x-a> 1 , while a second integration gives C <x-a> 2 . 2 These properties make it possible to use singularity functions to describe the effects of the common simple loading components on a single M(x) equation valid over the whole length of the beam with...
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- Fall '08