By J.R. Calvert

ISBN-10: 0333516613

ISBN-13: 9780333516614

ISBN-10: 1349113107

ISBN-13: 9781349113101

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**Extra resources for An Engineering Data Book**

**Sample text**

R = 0, 1, ... 2 Probability Distributions for Continuous Random Variables Exponential Distribution f(x) =A-e-M: a'-= 1/A-2 probability density function p= 1/A. x~O. l = 0 and a= 1. z 2 ,P(z) = - - e 2 J2; z Its cumulative distribution function lP(z) = J~ e -t12 dt -oo is the probability that the random variable is observed to have a value s; z (the shaded area shown in the graph ofN(0,1) on page 4-3). l) "'s ~ , where f(x)dx = 1 = tP -00 4-2 l k (x-p) l u Its cumulative distribution F(x) = e -tr 2 dt = cP( x ~11 ) .

Etc) is rarely ax oy of interest in engineering. ±ox may be treated as a normally (b) Instrument 'rounding off error distributed error by the equivalence Sx ~ ~&. 4-4 5. 1 Second Moment ofArea Definition: lxx = JJ(y- Yt)2dxdy The double integral is taken over the whole area of the shape. Similar expressions apply to axes in other directions. Radius of gyration k is defined by I = A k 2 for a specified axis. 0 Parallel axis theorem: X lxx= Iaa + Ayo2 where A is the area of the shape and y 0 is the perpendicular distance between an axis through the centroid, GG, and another parallel axis XX.

IGG is the minimum second moment of area for all axes parallel to GG. E. E. E. = Q dt oiJ; oq; oq; oq; I i = 1,2,3 for a 3 degree of freedom system. E. are kinetic, potential and dissipative energy. 3 - - Moments of Inertia Definitions: Moment oflnertia: I xx = Jr dm 2 M r is the perpendicular distance of the element of mass dm from the axis XX; the integral is taken over the whole mass of the body. Radius of gyration k is defined by I= Mk 2, for a specified axis. Parallel axis theorem: Ixx= IGG + My02 M is the mass of the body, y 0 is the perpendicular distance between an axis GG through the centre of mass and another axis XX parallel to GG.

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