CVE 220 Mechanics of Material Lecture No' 6 S' 2002

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CVE 220 Mechanics of MaterialLecture No. 6 (S.
2002)

• Gere Section 2.6-2.7
• James Hu

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Reading

• pp. 105-127

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Prismatic Bar in Tension
axially loaded
cross section (plane mn) perpendicular to the x
axis
(uniform distribution)
2-D view
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Inclined Section
inclined section pq
P total axial force
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Stress on the Inclined Plane
Stress on the inclined plane is to be calculated
using the forces in the normal and shear
components of the force and the inclined area.
force components
A1 the area of the inclined section
Normal force N P cos q
Shear force V P sin q
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Stress on the Inclined Plane (contd.)
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Orientation of the Inclined Section
The orientation of the inclined section
specifying the angle q between x axis
and the normal n to the section.
positive angle q is measured counterclockwise
from the x axis
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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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Standardized Notation and Sign Convention
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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Standardized Notation and Sign Convention (contd.)
(with negative sign)
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Alternative Forms
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Stresses vs. Angle
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Shear Failure
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Problem 2.6-3
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Work
Static load The load is applied slowly.
It gradually increase from zero to its maximum
value P.
The work done by the load is equal to the area
below the load-displacement curve.
unit joule (J) 1 J 1 N-m
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Strain Energy
Strain energy (U) the energy absorbed by the
bar during the
loading process
Conservation of energy
Strain energy (U) external work done (W)
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Elastic and Inelastic Strain Energy
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Linearly Elastic Behavior
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Non-uniform Bars
All loads must act simultaneously
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Homework Assignment 3

• Problem 2.4-3 (page 164)
• Problem 2.4-14 (page 167)
• Problem 2.5-3 (page 168)
• Problem 2.5-6 (page 169)
• Problem 2.6-8 (page 173)
• Problem 2.6-16 (page 175)
• Problem 2.7-1 (page 175)
• Problem 2.7-5 (page 176)

Due 2/14/2002
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Read Ahead

• Section 3.1-3.3 (pp. 187-203)