This document defines key concepts in mechanics of materials including stress, strain, shear stress, and torsion. It defines stress as the internal resistance to an externally applied load, and strain as the ratio of change in dimension to original dimension when a body is subjected to force. There are different types of strain including tensile, compressive, volumetric, and shear. Shear stress is defined similarly as the internal resistance to an applied shear load. The document also discusses Hooke's law and the linear relationship between shear stress and strain for elastic materials. Finally, it defines torsion as occurring when an external torque is applied, creating both an internal torque and shear stresses inside the material.

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3. Stress
This is a measure of the internal resistance in
a material to an externally applied load.
Stress is designated and is defined as:
stress
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load W
=
area A
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4. STRAIN
When a body is subjected to some external force, there is some
change of dimension of the body. The ratio of change of
dimension of the body to its original dimension is known as
strain.
Strain may be:- a) Tensile strain
b) Compressive strain
c) Volumetric strain d) Shear strain
Tensile strain- Ratio of increase in length to original length of
the body when it is subjected to a pull force
Compressive strain- Ratio of decrease in length to original
length of the body when it is subjected to a push force
Volumetric strain- Ratio of change of volume of the body to the
original volume
Shear strain-Strain due to shear stress`
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5. Concept of strain
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6. Sign convention for strain:
• Tensile strains are positive whereas
compressive strains are negative.
• The strain defined earlier was known as linear
strain or normal strain or the longitudinal
strain.
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7. Shear Stress
Similarly in shear the shear stress is a measure
of the internal resistance of a material to an
externally applied shear load.
shear stress
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load W
=
area resisting shear A
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8. Concept of Shear Stress
• Shear stress is defined a the component of
force that acts parallel to a surface area.
• Shear stress is a stress state where the shape
of a material tends to change (usually by
"sliding" forces – torque by transversely-acting
forces) without particular volume change.
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9. Shear stress and strain
Area resisting
shear
Shear displacement (x)
Shear Force
Shear force
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L
Shear strain is angle
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10. Shear Stress
Shear stress tends to change the shape of a body without changing its volume
Note: we apply shear force and shear stresses develop in the interior of the material
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11. Sign convention of shear stress
The sign convention for shear force and
stress is based on how it shears the materials
as shown below.
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12. Hooke’s Law for Shear
By conducting a similar material testing to normal stress (Section 2.4), there
is a linear
relationship (for most engineering materials) between the shear stress and
shear strain
Fig : Relationship of shear stress τ – shear strain γ for linear elastic material
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14. Torsion
Torsion occurs when an external torque is
applied and an internal torque, shear
stress, and deformation .
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15. Torsion and Shearing Stress
• There is also an internal shear stress which
develops inside the shaft.
• This shearing stress on the cross sectional area
varies from zero at the center of the shaft
linearly to a maximum at the outer edge.
• This may be thought of as being due to the
adjacent cross sectional areas of the shaft
trying to twist passed each other.
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