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ENGR 220Section 10.1 - 10.3
Plane Strain
• Review of Strain– Deformation due to a stress is specified using
the concept of normal and shear strain.
Normal Strain
• Elongation or contraction of a line segment per unit of length.
s
ssavg
'
s
ssnAB
' lim
along
Shear Strain
• The change in angle the occurs between two line segments that were originally perpendicular.
' lim2
along along tACnAB
Volume and shape deformations
Plane Strain
Strain Gauges
Strain Gauge
Strain Gauge
http://www.youtube.com/watch?v=YBm_j232yUU&feature=related
• http://www.youtube.com/watch?v=TjY48vYMPxw
Strain Rosette
Generic Solution
Strain measured along three axes at angles a b c
Transform along x-y coordinates
Stain Transformation Equations.
ccxycycxc
bbxybybxb
aaxyayaxa
cossinsincos
cossinsincos
cossinsincos
22
22
22
45˚ Strain Rosette
)(2 cabxy
cy
ax
60˚ Strain Rosette
)(3
2
)22(3
1
cbxy
acby
ax
Principal Strains
yx
xyp
2tan
22
2,1 222
xyyxyx
Maximum In-Plane Shear Strain
xy
yxs
2tan
22
plane-inmax
222
xyyx
2yx
avg
Mohr’s Circle
Mohr’s Circle
22
2
22
22
2
22
xyyx
yxavg
xyyx
R
R
Problem 10-2: Determine the in-plane strains of an element orientated at θ=20° counter-clockwise from the original position.
)10(175
)10(650
)10(200
6
6
6
xy
y
x