ME 221 Statics
Lecture #21
Sections 9.7 - 9.9
ME 221
Lecture 21
1
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 today
ME 221
Lecture 21
2
Homework #8
• Chapter 9 problems:
– 42, 43, 50 & 55
• Chapter 5 problems:
– 11, 13, 16, 20, 24 & 25
– See Blackboard for additional information
• Due Wednesday, October 30
ME 221
Lecture 21
3
Exam #2 Results
Average score = 81
Scores posted on Blackboard
Solution posted on Blackboard
See syllabus for regrade policy
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
Product Moment of Inertia
• Basic section with two axes of symmetry
A
I xy   xydA
y
x
• Composite sections - product parallel axis theorem
I xy  I xy  xo yo A
ME 221
Lecture 21
7
Mohr’s Circle for Principal Inertia
-Ixy
• draw circle center (Ixx + Iyy)/2
x
• draw point (Ixx , Ixy) and the circle
• use geometry to find IMAX , IMIN and b
Angles in Mohr’s circle are twice
those in the section analyzed.
ME 221
2b
IMIN
x
Ixx
IMAX
Ixx, Iyy
Iyy
x Ixy
+Ixy
Lecture 21
(Ixx+Iyy)/2
8
Chapter 9 Examples
ME 221
Lecture 21
9
Guest Speaker
Engineering Study Abroad Program
Dr. Darren Mason
Albion College (formerly at MSU)
Engineering in Russia
Summer 2003