ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is...
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Transcript of ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is...
![Page 1: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/1.jpg)
ENGR 220Section 10.1 - 10.3
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Plane Strain
• Review of Strain– Deformation due to a stress is specified using
the concept of normal and shear strain.
![Page 3: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/3.jpg)
Normal Strain
• Elongation or contraction of a line segment per unit of length.
s
ssavg
'
s
ssnAB
' lim
along
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Shear Strain
• The change in angle the occurs between two line segments that were originally perpendicular.
' lim2
along along tACnAB
![Page 5: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/5.jpg)
Volume and shape deformations
![Page 6: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/6.jpg)
Plane Strain
![Page 7: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/7.jpg)
Strain Gauges
![Page 8: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/8.jpg)
Strain Gauge
![Page 9: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/9.jpg)
Strain Gauge
http://www.youtube.com/watch?v=YBm_j232yUU&feature=related
• http://www.youtube.com/watch?v=TjY48vYMPxw
![Page 10: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/10.jpg)
Strain Rosette
![Page 11: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/11.jpg)
Generic Solution
Strain measured along three axes at angles a b c
Transform along x-y coordinates
Stain Transformation Equations.
![Page 12: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/12.jpg)
ccxycycxc
bbxybybxb
aaxyayaxa
cossinsincos
cossinsincos
cossinsincos
22
22
22
![Page 13: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/13.jpg)
45˚ Strain Rosette
)(2 cabxy
cy
ax
![Page 14: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/14.jpg)
60˚ Strain Rosette
)(3
2
)22(3
1
cbxy
acby
ax
![Page 15: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/15.jpg)
Principal Strains
yx
xyp
2tan
22
2,1 222
xyyxyx
![Page 16: ENGR 220 Section 10.1 - 10.3. Plane Strain Review of Strain –Deformation due to a stress is specified using the concept of normal and shear strain.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d6b5503460f94a499d8/html5/thumbnails/16.jpg)
Maximum In-Plane Shear Strain
xy
yxs
2tan
22
plane-inmax
222
xyyx
2yx
avg
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Mohr’s Circle
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Mohr’s Circle
22
2
22
22
2
22
xyyx
yxavg
xyyx
R
R
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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