Transcript Old Lecture 20 sect ..

ME 221 Statics
Lecture #20
Sections 9.7 - 9.9
ME 221
Lecture 20
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 Wednesday, October 23
ME 221
Lecture 20
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 20
3
Exam #2 Results
Will be returned Wednesday
Scores will be posted on Blackboard
Solution will be posted on Blackboard
See syllabus for regrade policy
Last Lecture
Moments of Area
Moments of Basic Shapes
Polar Moments
Parallel Axis Theorem
Radius of Gyration
Principal Second Moments
• Definition of product of inertia
– Product of inertia axis theorem
• Definition of principal axes
• Mohr’s circle to find principal axes
• Example
ME 221
Lecture 20
6
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 20
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
CROSS SECTION!!!
ME 221
2b
IMIN
x
Ixx
IMAX
Ixx, Iyy
Iyy
x Ixy
+Ixy
Lecture 20
(Ixx+Iyy)/2
8
Example
ME 221
Lecture 20
9