The document discusses different types of strain: normal strain, lateral strain, and shear strain, emphasizing their definitions and calculations based on deformation relative to the original length. It describes normal strain as elongation per unit length along the load and lateral strain as deformation perpendicular to the load. The document also illustrates shear strain and its relationship to shear stress through angle variations and geometry.

1. Strain
1. Strain
Goal
2. Normal & Lateral Strain
3. Shear Strain
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2. Which deformation is large？
100 mmOriginal
Length
60 mm
10 N
10 N
Total deformation depends on original length !
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→ characterize as material property

3. Strain
Elongation per unit length
[ non-dimensional quantity]
Normal Strain
Shear Strain
ε
γ
：
：
Lateral Strainε’：
epsilon
gamma
epsilon prime
Mode and Symbol
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4. Normal & Lateral Strain
l
d
PP
l ＋ Δl
d＋ Δd
ε ＝
Δl
l
Parallel to load
Normal Strain
ε’＝
Δd
d
Perpendicular to load
Lateral Strain
2D
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5. Shear Stress
P
P
l
γ ＝
l
Δl
Δl ＝ tanl ∠ c’b c
γ ＝
l
Δl ~−∠ c’b c
Δl ~− l ∠ c’b c
∠ c’b c 0∵(
)
~−
∠ a b cAngle variation ofShear Stress ＝
Δl
a
b c
d
c’
d’
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6. Summary
1. Normal Strain
2. Lateral Strain
3. Shear Strain
Elongation per Unit Length [ - ]
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