## Probabilistic mechanical design |

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### Contents

SUPPORTING MATHEMATICS | 16 |

LOADING RANDOM VARIABLES | 77 |

DESCRIBING COMPONENT GEOMETRY WITH RANDOM | 125 |

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AISI amplitude Appendix applied stress approximately assumed beam bending calculated central limit theorem Chapter coefficient of variation confidence interval considered constant constant-amplitude correlated cross section curve cycles to failure deflection determined deterministic diameter dimensional Distributions and Parameters dynamic loading element endurance limit engineering estimate the statistics Example factor Fatigue Strength Distributions follows force frequency fully reversed gear geometric given lognormally distributed materials behavior maximum mean value mechanical components moment-generating function narrow-band random loading normally distributed notch partial derivatives plate probabilistic design probability density function radius random process random values reliability S-N envelope sample shaft shear stress Sheet shown in Figure sinusoidal specified specimen standard deviation static load statistically independent steel strain stress at failure stress concentration Substitution of equation Table theory thickness tolerance utilizing equations value and standard variance vector Yes Yes yield strength zero