1
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Introduction to Solid Mechanics-Vm211
Chapter 15
STRESS AND STRAIN
TRANSFORMATION
Chapter 15
Stress and Strain
Transformation
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Introduction to Solid Mechanics-Vm211
CHAPTER OUTLINE
1.
Plane-Stress Transformation
2.
General Equations of Plane Stress Transformation
3.
Principal Stresses and Maximum In-Plane Shear Stress
4.
Mohr’s Circle – Plane Stress
5.
Absolute Maximum Shear Stress
6.
Plane Strain
7.
General Equations of Plane-Strain Transformation
8.
Mohr’s Circle
−
Plane Strain
9.
Strain Rosettes
10.
Material-Property Relationships
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Introduction to Solid Mechanics-Vm211
Stress state at a point
State of plane stress at a point on surface of airplane
fuselage.
SJTU
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Introduction to Solid Mechanics-Vm211
15.1
PLANE-STRESS
TRANSFORMATION
General state of stress at a point is characterized by
six independent normal and shear stress components.
In practice, approximations and simplifications are
done to reduce the stress components to a single
plane.
SJTU
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大
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Introduction to Solid Mechanics-Vm211
The material is then said to be
subjected to
plane stress
.
For general state of plane stress at a
point, we represent it via normal-stress
components,
σ
x
,
σ
y
and shear-stress
component
τ
xy
.
Thus, the state of plane stress at the point is
uniquely
represented by three
components acting on an element
that has a specific orientation at
that point.
15.1
PLANE-STRESS
TRANSFORMATION
SJTU
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Introduction to Solid Mechanics-Vm211
Transforming stress components from one
orientation to the other is similar in concept to how
we transform force components from one system of
axes to the other.
Note that for stress-component transformation, we
need to account for
the magnitude and direction of each stress
component, and
the orientation of the area
upon which each
component acts.
15.1
PLANE-STRESS
TRANSFORMATION

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