Normal Strain/Shear Strain



Key Concepts:  Normal strain is typically measured as the change in length of a structural

element divided by its original length and is called engineering strain.  On the other

hand "true strain" is defined by sums of changes in length at any time divided by its

length at the same time.  Shear strain is the change in angle (distortion) between any

any two intersecting lines at a section of the structural element resulting from applied loads.



In a Nut Shell:  Imagine an arbitrary structural member say in the shape of a flat ovular plate. 

See the figure below.  Before loading let an arbitrary material segment, AB, in the plate be of

length L.  After loading the material segment may rotate and change length.  Let the length of

the same material segment become A*B*,  after loading be L*.  Then the normal strains are

defined as

                                           εengr  =  ( L*  -  L)/L  =  engineering strain


                                           εtrue  = ln ( L*/L )  =  true strain


Common units of strain are in  inches/inch,  millimeters/millimeter, or microstrain



Normal strain is considered to be positive when the material segment becomes

longer and negative if it shortens (sign convention).  Usually normal strains are

very small usually much less than 1.       | εengr  |   <<  1


Click here for an example of normal strain.      






In a Nut Shell:  Imagine the same arbitrary structural member.  Before loading let AB be

an arbitrary material segment and AC be a reference line.   Further let the angle between the

reference line and the material segment prior to loading be π/2  radians.  After loading the

material segment, AB, may change length and rotate relative to the reference line.  Let the

angle between the material segment and the reference line be   π/2 - γ  after loading. 

Then the shear strain is  γ .  Shear strain is the change in angle in radians.


Shear strains will become important when analyzing twisting of torsional members.




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