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