Page 46 - Aircraft Stuctures for Engineering Student

1.1 6 Experimental measurement of surface strains 3 1

Also

cII = OC - radius of circle
i.e.

(1.59)

Finally the angle 8 is given by

i.e.

2Eb - E, - E,
tan28 = ( 1.60)
Ea -E,
A similar approach may be adopted for a 60” rosette.

Example 1.4
A bar of solid circular cross-section has a diameter of 50 mm and carries a torque, T,
together with an axial tensile load, P. A rectangular strain gauge rosette attached to
the surface of the bar gave the following strain readings: E, = 1000 x 1K6,
Eb = -200 x and E, = -300 x where the gauges ‘a’ and ‘cy are in line
with, and perpendicular to, the axis of the bar respectively. If Young’s modulus, E,
for the bar is 70 000 N/mm2 and Poisson’s ratio, v, is 0.3, calculate the values of T
and P.

Substituting the values of E,, &b and c, in Eq. (1.58)

€1 = -(lo00 - 300) +- J( 1000 + 200)2 + (-200 + 300)’
2 Jz
which gives

E1 = 1202 x
Similarly, from Eq. (1.59)
EII = -502 x
Now substituting for and sI1 in Eq. (1.56)

70 000 x
CTI = (-502 + 0.3 x 1202) = -80.9N/mm2
1 - (0.3)2
Similarly, from Eq. (1.57)

cII = - 10.9 N/m2
Since Q, = 0, Eqs (1.1 1) and (1.12) reduce to