16.6_M of I - ENGR 211 Lecture 16 Moments of Inertia Civil...

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ENGR 211 Lecture 16 Fall 2007 1 Civil Engineering Moments of Inertia Moments of Inertia Civil Engineering Moments of Inertia Moments of Inertia • Properties of the cross-section • They are inversely proportional to the stresses in beams that cause failure. • They are proportional to the stiffness of beams. • They are second moments of area.
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ENGR 211 Lecture 16 Fall 2007 2 Civil Engineering What are Moments of Inertia? What are Moments of Inertia? • They come out of the elastic flexure formula: σ x = - M y I • Where I is Moment of Intertia • and σ x is the stress in beams that causes failure. Civil Engineering Definitions Definitions 2 2 x x Iy d A k A == 22 yy I xdA k A •Where I is Moment of Intertia •And k is the radius of gyration Remember how we solved for the centroid of an Area much the same way.
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ENGR 211 Lecture 16 Fall 2007 3 Civil Engineering Example Example Moment of inertia around the horizontal axis passing through the centroid of a rectangle. b h Civil Engineering Example Example Moment of inertia around the horizontal axis passing through the base of a rectangle. b h
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ENGR 211 Lecture 16 Fall 2007 4 Civil Engineering Axis being used is Axis being used is important! important! Civil Engineering Polar Moment of Polar Moment of Intertia Intertia , J , J J = r 2 dA R By symmetry, I x = I y = J/2
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ENGR 211 Lecture 16 Fall 2007 5 Civil Engineering Definitions Definitions 2 2 x x Iy d A k A == 22 yy I xdA k A 00 px y IJ r d A I Ik A = + = xy I x ydA = Civil Engineering Moments of Inertia Moments of Inertia
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This note was uploaded on 03/15/2009 for the course ENGR 211 taught by Professor Tona during the Spring '09 term at Oregon State.

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16.6_M of I - ENGR 211 Lecture 16 Moments of Inertia Civil...

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