L8%20Mechanics

# L8%20Mechanics - Agenda \$ Stress Strain \$ Thermal Expansion...

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1 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Mechanics ! Senturia, Ch. 8, Ch. 9 " HW9 # Agenda \$ Stress & Strain \$ Thermal Expansion \$ Residual Stress \$ Simple Structures \$ Beams \$ Plates

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2 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold % Microsystems are comprised of different types of structural elements . Ref. ADI Ref. Young, et al., HH98 Motivation Point Load Axial loading Torsion Distributed Load
3 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Simple Physics: “Two-types of forces may act on a solid body” 1. is distributed over the volume of a body, Ex: gravity 2. is distributed over the surface of a body % Normal component, Ex: hydrostatic pressure % Tangential component, Ex: shear stress Ref. Cook & Young, “Advanced Mechanics of Materials”, pg 2. Forces

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4 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold % Stress : Force per unit area acting on the surface of a differential surface element. Normal Stress : Shear Stress : Ref. Senturia, pg 184. Stress Note: positive stress = “tensile” and negative stress = “compressive”
5 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Ref. Hibbeler, “Mechanics of Materials”, pg 23. Stress

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6 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold To convert Into Multiply by Pa or N/m 2 atmosphere 9.869 x 10 -6 Pa or N/m 2 bar 1 x 10 -5 Pa or N/m 2 dynes/cm 2 10 Pa or N/m 2 kg/cm 2 1.020 x 10 -5 Pa or N/m 2 in. Hg 2.954 x 10 -4 Pa or N/m 2 in. water 4.018 x 10 -3 Pa or N/m 2 mbar 0.01 Pa or N/m 2 mtorr or micron Hg 7.5028 Pa or N/m 2 psi or lb/in 2 1.4508 x 10 -4 Pa or N/m 2 torr or mm Hg 7.5028 x 10 -3 Stress/Pressure Unit Conversion 1 atm ! 14.7 psi ! 101 kPa
7 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Decomposition of deformation : % Rigid body translation: “center of mass translation” % Rigid body rotation: “center of mass rotation” % Axial deformation: % Shear deformation: Ref. Senturia, p. 185. Deformation

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8 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Strain : differential change in length per unit length Uniaxial Normal Strain : Ref. Senturia, pg 186. Strain Note: tensile strain (and stress) results in elongation F F
9 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Strain % Pure Shear: Ref. Senturia, pg 186. F F

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10 Lecture 8 Mechanics EEL 5225, Fall 2010, David Arnold Ref. Cook & Young, “Advanced Mechanics of Materials”, pg 10. Stress-Strain Relationships Y = Yield strength F F