Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

1.16 Experimental Measurement of Surface Strains 39

TheradiusofthecircleisCQand

CQ=

√

CN^2 +QN^2

Hence,

CQ=

√[

1

2 (εa−εc)

] 2

+

[

εb−^12 (εa+εc)

] 2

whichsimplifiesto

CQ=

1

√

2

√

(εa−εb)^2 +(εc−εb)^2

Therefore,εIisgivenby

εI=OC+radiusofcircle

is

εI=^12 (εa+εc)+

1

√

2

√

(εa−εb)^2 +(εc−εb)^2 (1.69)

Also,

εII=OC−radiusofcircle

thatis,

εII=^12 (εa+εc)−

1

√

2

√

(εa−εb)^2 +(εc−εb)^2 (1.70)

Finally,theangleθisgivenby

tan2θ=

QN

CN

=

εb−^12 (εa+εc)

1

2 (εa−εc)

thatis,

tan2θ=

2 εb−εa−εc

εa−εc

(1.71)

Asimilarapproachmaybeadoptedfora60◦rosette.

Example 1.7
A bar of solid circular cross section has a diameter of 50mm and carries a torque, T, together
with an axial tensile load,P. A rectangular strain gauge rosette attached to the surface of the bar
gavethefollowingstrainreadings:εa= 1000 × 10 −^6 ,εb=− 200 × 10 −^6 ,andεc=− 300 × 10 −^6 ,where
the gauges ‘a’ and ‘c’ are in line with, and perpendicular to, the axis of the bar, respectively. If
Young’smodulus,E,forthebaris70000N/mm^2 andPoisson’sratio,ν,is0.3,calculatethevaluesof
TandP.