Geokon 4425, Instruction Manual, Page: 19 / 27

13
For example:
Consider a horizontal convergence meter consisting of 60 ft. of graphite rods with spring
constant of 17 lb. per inch.
L = length of rods = 60 ft. (The distance over which the measurement is being made.)
W = weight of 60 ft. of graphite rods = 2 lb.
P
0
= 47 lb. and P
1
= 30 lb. (These values are obtained from a knowledge of the spring tension at
various extensions, and that an apparent measured convergence of 1.000 inch has taken place.)
The correction to L for sag initially is -60 x 4 / 24 x 47 x 47 = - 0.0045 ft. = - 0.054 inches
The correction for sag at T
1
is - 60 x 4 / 24 x 30 x 30 = - 0.0111 f.t = - 0.133 inches
So after correction for sag the true convergence is 1 – (0.133 – 0.054) = 0.921 inches
Summing all the various effects:
Dcorrected = Duncor Dtempe Drods Dsag
Equation 9 - Corrected Deformation
Again, consider the following example from a Model 4425-12 Convergence Meter attached to 30
meters of 1/4 inch diameter graphite rod.
R
0
= 4919 digits
R
1
= 6820 digits
T
0
= 15.3° C
T
1
= 32.8° C
(T
1
– T
0
) = + 17.5 °C
G = 0.002402 mm/digit
L = 30 meters = 30,000 mm
S = 5.95 N/mm
a = 31.67 sq. mm
E = 0.117 × 10
6
MPa
ω = 0 .049 Kgm/m = 0.481 N/m (0.033 lb./ft.)
P
0
= 133 N
P
1
= 163 N
From Equation 4:
K = ((6820 × 0.000375) + 1.08) × 0.002402 = 0.0087 mm
From Equation 2:
Duncorrected = (6820 - 4919) × 0.002402 = + 4.566 mm
(The plus sign indicates an extension.)