MECH466-Lecture-6

# MECH466-Lecture-6 - MECH 466 Microelectromechanical Systems...

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1 MECH 466 Microelectromechanical Systems University of Victoria Dept. of Mechanical Engineering Lecture 6: Mechanics of Beams Electrostatic Sensors and Actuators May 28th, 2007 Mech 466, N. Dechev, UVic 2 Stress within Beams Moment of Inertia Beam Stiffness Beam Torsion Introduction to Electrostatics Overview of Electrostatic Actuators and Sensors Parallel Plate Capacitors Overview Mech 466, N. Dechev, UVic

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3 Deﬁnition of Beam Parameters Mech 466, N. Dechev, UVic We will consider simple beams that have: - A straight shape - A vertical axis of symmetry Examples of vertical symmetry include: y z x w h l t Neutral Axis Cross-Sections of Various Beams [image from Mechanics of Materials, E. P. Popov] 4 Pure Bending of Beams Mech 466, N. Dechev, UVic These are cases where a beam is subjected to a bending moment where we assume: - Deflection as a result of bending is less than 5% of beam length - All plane cross-sections of the beam before bending remain as straight planes after bending y x +M +M Tension Neutral Axis Compression Plane Cross-Sections
5 Pure Bending of Beams Mech 466, N. Dechev, UVic Consider some ‘infinitesimal’ cubes of material in the beam: y x t Point of Interest Maximum Compression Zero Stress Maximum Tension define ‘c’ 6 Deﬁnition of Beam Bending Stress Mech 466, N. Dechev, UVic The beam stress formula is given by: - where: Applies to all beams in a state of ‘pure bending’. Derivation is available in textbooks on solid mechanics.

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7 Moment of Inertia Mech 466, N. Dechev, UVic The moment of inertia, I , of a beam depends on the geometrical
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## This note was uploaded on 02/02/2010 for the course MECH 466 taught by Professor Dechev during the Summer '07 term at University of Victoria.

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MECH466-Lecture-6 - MECH 466 Microelectromechanical Systems...

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