ME382+Databook

# ME382+Databook - ME 382 Data Book(Compiled by M.D Thouless...

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1 ME 382 Data Book (Compiled by M .D. Thouless) Important: The data and formulae in this book should not be used for any purpose other than home-work assignments and examinations in ME 382. You will be expected to bring an unmarked copy of this handout to ME 382 examinations. Any unauthorized notations in a copy of this handout used during examinations may be considered an infringement of the honor code. Contents Values of physical constants 2 Conversion of units 2 Beams of arbitrary cross section 3 Torsion of cylinders 4 Thin-walled pressure vessels 4 Beam deflection formulae 5 Properties of sections 6 Equations for multi-axial loading 7 Additional mechanics equations 8 Mohr’s circle for stress 9 Mohr’s circle for strain 10 Stress concentrations 11 Linear-elastic fracture mechanics 12-18 Physics of materials 19 Composites 20 Fatigue equations 20

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2 V ALUES OF PHYSICAL CONSTANTS Absolute zero: -273.2 ° C Avagadro’s number, N A : 6.022 x 10 23 mol -1 Boltzmann’s constant, k : 1.381 x 10 -23 J.K -1 Molar gas constant, R : 8.314 J.mol -1 .K -1 C ONVERSION OF UNITS Force: 1 kgf = 9.807 N 1 lbf = 4.448 N 1 dyn = 10 -5 N Length: 1 mile = 1.609 km 1 foot = 304.8 mm 1 inch = 25.4 mm (Angstron) 1 Å = 10 -10 m Mass: 1 ton (long) = 1.017 x 10 3 kg 1 tonne = 1.000 x 10 3 kg 1 ton (short) = 908 kg 1 lb mass = 0.454 kg Stress: 1 psi = 6.894 x 10 3 N ·m -2 1 ksi = 6.894 MN ·m -2 1 N ·m -2 = 1 Pa 1 N ·mm -2 = 1 MPa Stress intensity: 1 ksi in = 1.099 MPa m Surface energy: 1 erg ·cm -2 = 1 mJ ·m -2 Temperature: 1 ° F = 0.556 ° C Volume: 1 liter = 10 -3 m 3 1 US gallon = 4.546 x 10 -3 m 3
3 B EAMS OF ARBITRARY CROSS SECTION Axial tension: ! zz = N zz A zz Beam bending: zz = M xx y I xx " M yy x I yy Shear force: (these results are approximate for some sections) zx ( x ) = V zx Q ( x ) I xx t x ( ) zy ( y ) = V zy Q ( y ) I yy t y ( ) where Q x ( ) = x dA ( x ) * A *( x ) ! and Q y ( ) = y dA ( y ) * A *( y ) " or, Q x ( ) = x A * x ( ) , where x is the distance between the centroids of A zz and A *( x) Q y ( ) = y A * y ( ) , where y is the distance between the centroids of A zz and A *( y)

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4 T ORSION OF CYLINDERS z x y θ A B C D R o i r T zz τ z θ = T zz r J zz where J zz = π R o 4 R i 4 ( ) 2 For a thin walled tube: J zz = 2 R 3 t T HIN - WALLED PRESSURE VESSELS Cylinder Axial (longitudinal) stress: σ zz = PR 2 t Hoop (circumferential) stress: θθ = PR t Radial stress: rr 0 Sphere Hoop (circumferential) stress: = φφ = PR 2 t Radial stress: rr 0
5 B EAM DEFLECTION FORMULAE M l P l P l P l /2 l /2 P l P l /2 l /2 P l End deflection Ml 2 2 EI Pl 3 3 EI Pl 3 8 EI Central deflection Pl 3 48 EI 5 Pl 3 384 EI Pl 3 192 EI Pl 3 384

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## This note was uploaded on 09/08/2011 for the course MECHENG 382 taught by Professor Thouless during the Fall '08 term at University of Michigan.

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ME382+Databook - ME 382 Data Book(Compiled by M.D Thouless...

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