Page 866 - Mechanical Engineers' Handbook (Volume 2)

8 Sensors 857

F = 5 lbs.
L L
2 = 1 in. 2 = 1 in.
1
8 in. = h
b = 1 in.

Figure 46 Strain gauge example.

Stress Modulus
E stress (modulus of elasticity)(strain) (64)
MC (bending moment)(distance from neutral axis)
bending bending stress (65)
I (moment of inertia)
6
2
E Al 10
10 lb/in. (psi) modulus of elasticity for aluminum (66)
L length
M F (5 lbs)(1 in.) 5 in. lb bending moment force (67)
2 2
1
c –– in. (68)
16
1 1 1 3 1
I bh 1 1.6
10 4 in. (base)(height) 3 (69)
3
4
12 12 8 12
(5 in. lb
0.0625 in.)/1.6
10 4 in. 4
.000192
6
10
10 lb/in. 2
192
(unitless) (70)
Strain 1.92
(71)
R/R
Gauge factor Z (72)
axial
R RFE (120)(2)(0.000192) 0.046 (73)
This change in resistance is very small. It must be amplified in some way to be able to
practically measure the change. If the above strain gauge is used in a voltage divider, (1)

F

F
F
M M

F
Figure 47 Free-body diagram.