CVE 220 Mechanics of Material Lecture No' 8 S' 2002

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CVE 220 Mechanics of MaterialLecture No. 8 (S.
2002)

• Gere Section 3.4-3.5
• James Hu

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Reading

• pp. 204-219

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Derivation of Force-Deformation Relation
d-P
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Torsion / Angle of Twist (review)
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Comparison Axial Force/Torsion (review)
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Non-uniform Bars (review)
N1 PC PD PB
N2 PC PD
N3 PD
Total change in the bar
dD d1 d2 d3
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Change in Lengths of Non-uniform Bars Procedure
Summary (review)

• Identify all segments of the bar
• Determine the internal axial force in each
  segment
• Determine the changes in the lengths of the
  segments
• Add all segment changes to obtain the total
  change in length

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Non-uniform Torsion
internal torques
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Total Angel of Twist
The total angle of twist between the ends of
the bar
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Continuously Varying Cross Sections
Internal torque is not varying
Internal torque is varying
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Example 3-4
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Example 3-4 (contd.)
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Pure Shear
does not contain normal stresses
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State of Pure Shear
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Stresses on Inclined Planes
Ao the area of the vertical face
Force equilibrium in the direction of sq
Force equilibrium in the direction of tq
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Normal and Shear Stresses
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Stresses at q45o and q135o
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Sign Conventions Shear Stresses (review)
A shear stress acting on a positive face of an
element is positive if it acts in the positive
direction of one of the coordinate axes.

A shear stress acting on a negative face of an
element is positive if it acts in the negative
direction of one of the coordinate axes.
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Notation and Sign Convention (review)
subscript q indicates that the stresses act on
a section inclined at an angle q
shear stresses are positive when they tend to
produce counterclockwise rotation
sing conventions

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Fail along a 45o Surface
bar in compression
bar in torsion
failure in shear
failure in tension
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Stresses vs. Angle (review)
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Maximum Normal Strain
normal strain in the 45o direction
from geometry (section 3-6)
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Homework Assignment 4

• Problem 3.2-1 (page 251)
• Problem 3.2-4 (page 251)
• Problem 3.3-4 (page 252)
• Problem 3.3-9 (page 253)
• Problem 3.4-4 (page 256)
• Problem 3.4-7 (page 257)
• Problem 3.5-3 (page 259)
• Problem 3.5-4 (page 260)

Due 2/21/2002
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Relationship Between E, G, and n