16.6_M of I

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

This preview shows pages 1–6. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 I y dA k A = = 2 2 y y I x dA 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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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