Transcript Lecture 19 sect 9.8.ppt

ME 221 Statics
Lecture #19
Sections 9.7 - 9.9
ME 221
Lecture 19
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 Friday
ME 221
Lecture 19
2
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
ME 221
Lecture 19
3
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 19
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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 19
(Ixx+Iyy)/2
7
Chapter 9 Example
ME 221
Lecture 19
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