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Mechanics of Materials CIVL 3322 / MECH 3322

Strain

Homework Issues

1) One problem per page 2) FBD or sketch 3) STAPLE! 4) Engineering paper 5) Indicate (C) or (T) No up or down arrows. 6) Write on one side of the paper only 7) Box or underline or highlight final answers 8) Follow the homework format 9) Homework must be readable by the teaching assistant

Axial Strain 2

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Strain

¢ We have considered stresses which are a force applied over a cross section

¢ Stresses acting on deformable materials produce changes in the materials they are acting on

¢ These changes can be displacements and/or deformations depending on how they act

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Strain

¢  If the deformation is along a loading axis, we talk about an normal or axial deformation

¢ A normal deformation accompanies a normal stress

¢ The deformation will be either an elongation or a compression

Axial Strain 4

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Strain

¢ An elongation will be considered positive and a compression negative

¢ This follows the sign convention for stresses

¢ The amount of deformation is given by the symbol δ (delta) and has units of length

Axial Strain 5

Strain

¢  If we start with an object loaded axially as shown below

Axial Strain 6

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Strain

¢ Without the stress applied, the axial length of the object is L

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Strain

¢ With the stress applied, the length of the object is L+δ

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Strain

¢ So the deformation of the object is δ, which is the change in length in the axial direction

Axial Strain 9

Strain

¢  If we take the ratio of this change in length to the original length, we have the strain in the object under this loading condition

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Strain

¢ The axial strain in this object is the ratio of the axial deformation to the original axial length

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Strain

¢ The units of axial strain (normal strain) will be length per length

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Strain

¢ Strains can produce stresses and stresses can produce strains

¢ Typically they occur together in a deformable material

¢ How much will be determined based on the material

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Strain

¢ Strain is denoted by the symbol ε (epsilon) ¢ Mathematically, strain is given by

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ε = δL

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Strain

¢ Units of strain are units of length/length and therefore appear dimensionless

¢ Special units of strain are µε, which is units of 10-6 times strain (this is called microstrain)

¢ You may also see strain given as a percent

Axial Strain 15

ε = δL

Strain

¢ The axial strain problems in the early part of this book are more trig/geometry problems than typical materials problems.

Axial Strain 16

ε = δL

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Problem P2.2

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Homework

¢ P 2.1 ¢ P 2.3 ¢ P 2.5

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