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Outline

Outline. Force, vectors Units Normal, shear components Pressure Lithostatic Stress Stress Tensor Resolving stress on a plane. Dynamic Analysis Stress. Force is mass * acceleration. Units? kg m/s 2 =Newton Mass is in kg “weight” is your force on Earth (mass * g). y. A. x.

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Outline

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  1. Outline • Force, vectors • Units • Normal, shear components • Pressure • Lithostatic Stress • Stress Tensor • Resolving stress on a plane

  2. Dynamic AnalysisStress

  3. Force is mass * acceleration • Units? kg m/s2=Newton Mass is in kg “weight” is your force on Earth (mass * g)

  4. y A x Force is a vector Normal F Fy= F . SinA Fx= F . CosA Shear

  5. F F Does applied force alone control deformation? Land’O Lakes

  6. Stress Stress = force / area Units = Pascals = mass * acceleration = N/m2 =kg/(m . s2)

  7. How much is 1 Pascal? • 1 Pa= 0.00014 psi • Car tire ~200,000 Pa • 1 Megapascal (1 Mpa) = 1 million Pa

  8. Normal and shear components

  9. szz szx sxz sxz sxx sxx szx szz Stress Components z x

  10. s1 Most compressive s3 s3 Least compressive s1 Principal Stress Components You always can find an orientation of the reference cube where there won’t be any resolved shear stresses z x

  11. s1 Magnitude of Normal and Shear Stresses Normal s3 Shear

  12. In Lithostatic Stress, 1=2=3 • Similar to hydrostatic pressure • P =  g h • Units are in MPa • Be sure to work in meters • 1 g/cm3 = 1000 kg/m3

  13. Mohr Circle of Stress Mohr Circle of Stress sn= ½ (s1 +s3) + ½(s1-s3) cos 2Q ss= ½(s1-s3) sin 2Q Mean Stress Deviatoric Stress

  14. Common States of Stress Triaxial Biaxial Hydrostatic Uniaxial

  15. World Stress Map World Stress

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