ME 221Lecture 191 ME 221 Statics Lecture #19 Sections

ME 221Lecture 192 Homework #7 Chapter 4 problems: –52, 53 & 54 Chapter 9 problems: –2, 3, 4, 11, 23, 29 & 32 –Use double integration for 2, 3, 4 & 11 Due Friday

ME 221Lecture 193 Homework #8 Chapter 9 problems: –42, 43, 50 & 55 Chapter 5 problems: –11, 13, 16, 20, 24 & 25 –Additional information to be on Angel Due Friday, October 24

Last Lecture Principal Second Moments Product Moment of Inertia Principal Axes Mohr’s Circle

Mechanics Nomenclature Polar Moment of Inertia = Torsional Stiffness Second Moment of Area = Bending Stiffness

ME 221Lecture 196 Product Moment of Inertia Basic section with two axes of symmetry x y Composite sections - product parallel axis theorem

ME 221Lecture 197 Mohr’s Circle for Principal Inertia +I xy -I xy I xx, I yy I yy x I xx I xy x draw point (I xx, I xy ) and the circle (I xx +I yy )/2 draw circle center (I xx + I yy )/2 x I MAX I MIN 22 use geometry to find I MAX, I MIN and  Angles in Mohr’s circle are twice those in the section analyzed.

ME 221Lecture 198 Chapter 9 Example