Transcript Lecture 10.ppt

ME 221 Statics
Lecture #10
Sections 9.7 - 9.9
ME221
Lecture 10
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Homework #4
• Chapter 4 problems:
– 52 & 54
• Chapter 9 problems
– 2, 11 & 32
– Due Monday, June 14
• MatLab Group Problems
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ME221
4.13 – plot as a function of R with 0º < α < 45º
4.51 – plot as a function of length “l”
4.60 – plot the equivalent force and point of action
Due Monday, June 14
Lecture 10
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Last Lecture
Principal Second Moments
Product Moment of Inertia
Principal Axes
Mohr’s Circle
ME221
Lecture 10
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Mechanics Nomenclature
Polar Moment of Inertia = Torsional Stiffness
Second Moment of Area = Bending Stiffness
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Lecture 10
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Product Moment of Inertia
(Product Moment of Area)
• 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
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Mohr’s Circle for Principal Inertia
(Second Moment of Area about any Axis)
-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.
ME221
2b
IMIN
x
Ixx
IMAX
Ixx, Iyy
Iyy
x Ixy
+Ixy
Lecture 10
(Ixx+Iyy)/2
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More Chapter 9 Examples
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Lecture 10
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