Call for Papers - Educational Administration: Theory and Practice, E-ISSN: 21...
3 strain transformations
1. Strain Transformations
BIOE 3200 - Fall 2015
Note: These slides were adapted from slides by Dr Abhay Kumar on
slideshare.com.
Image above from http://trilion.com/optical-strain-measurement-biomechanic/
2. Learning objectives
Calculate strains in multiple planes
(strain transformations) within a rigid
body
Describe the function, design, and
application of a strain gauge.
BIOE 3200 - Fall 2015
3. Plane Strain Loading
x
y
Consider the 2D case where all
elements of the body are
subjected to normal and shear
strains acting along a plane (x-y);
none perpendicular to the plane
(z-direction)
z = 0; xz = 0; zy = 0
4. x
y
x’
y’
A
State of Stress at A
x
y
xy
xy
’x=?
’xy=?
Plane Strain Transformations
Similar to derivation of equations for stress
transformation, replacing:
by , and
by /2
5. Plane Strain Transformations
Sign Convention:
Shear strain ( ): decreasing angle is positive
Normal strains (x and y): extension is positive
x
y
before
x
y
after
x positive
y negative
positive
7. Strain Gauges
Function: Measure normal strain ()
Design: Stretching of wires in gauge during
deformation results in a change in electrical
resistance
8. Strain Gauge Rosettes
• Function: Measure normal strain () in three
directions; use these to find x, y, and xy
• Design: Two or three arranged at known
angular positions
45° Strain Rosette
x
45
°
45
° 0
90
45
x = 0
y = 90
xy = 2 45 – (0 + 90)
measured
9. Strain gauge applications
Measuring strains in devices or
structures
◦ Strain gauges for snow board testing:
https://www.youtube.com/watch?v=h1CvL
ZQABjE
◦ Strain gauges in human motion research:
http://file.scirp.org/Html/7-
4000046_33327.htm
Validating computer models and
predicted strains
BIOE 3200 - Fall 2015
Editor's Notes
The strain measure xy is used in these equations, which is different from the engineering shear strain xy :
xy = xy + yx = 2xy
Engineering shear strain xy is a total measure of shear strain in the x-y plane. In contrast, the shear strain xy is the average of the shear strain on the x face along they direction, and on the y face along the x direction.
See http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/strain.cfm#engstrain for a full explanation and derivation of shear strain and engineering shear strain terms.