The Effect of Gravitational Elongation on a Vertical Tape
The construction of a truly tall tower presents the opportunity to encounter one of the singularly unique situations in surveying; gravitational elongation.
The completion or “topping out” of the tower will inevitably require the establishment of the towers true height and consequently the establishment of a mark or marks to determine the future vertical movement of the tower. Tall towers are subject to axial shortening which is remediated during construction by super-elevation of critical structural members. This shortening does not cease upon the completion of construction and a long term monitoring program is to be expected.
During the initial and subsequent determinations of elevations on these marks vastly differing observation conditions are likely to be encountered. The “topping out euphoria” will in all likelihood require that the initial observations be carried out before the entire tower is enclosed and climate controlled. Openings in the towers base and top will undoubtedly result in a chimney effect causing air currents in the shafts and stairways which must be countered in the observation program and temperatures will not be consistent.
While little can be done to control the conditions encountered by the surveyor, corrections can and must be applied to produce the truest values possible.
Determining the elevation of the base and top of a tall tower for monitoring purposes demands the utmost in both accuracy and precision. Because of these demands only a calibrated and corrected taped distance will suffice. It takes an educated and experienced surveyor to name the standard corrections applied to a taped distance. Few have ever actually applied them in practice. And of those, but one known to the author has ever applied the correction for gravitational elongation.
Gravitational elongation is a tensile effect produced upon the tape through its employment in a vertical plane, various known specifications of the individual tape, and the use of an additional weight to still its oscillation. Because varying weights may be used under differing conditions and different lengths of tape observed due to obstructions, combined with the great height being measured, the gravitational elongation will produce a significant effect upon the results of the observation which would result in erroneous determinations of elevations in the monitoring program.
Taking WTC1 as the perfect example, we can extrapolate several scenarios which may be encountered. We can assume the height measured by a single 200 foot long tape in seven sections. The effects of varying weights upon this tape will produce significant differences in the determination of the towers true height and introduce errors into the subsequent monitoring program. Considering the specifications of our standard tape, which is calibrated to be 200 feet in length under a 23.1 pound tension with a cross section of 0.003 square inches, unit weight of 0.0102 pounds, and a modulus of elasticity of 29,700 KSI, we can evaluate the effects of varying weights upon the true length of our tape.
By addition of a five pound “stilling mass” weight the effect of elongation has stretched the tape by 0.031 feet. A ten pound weight, 0.061 feet and twenty pounds, 0.121 feet. These are not insignificant numbers when considered against the demands of a monitoring program. Even without the addition of a “stilling mass” our tape will have elongated 0.002 of a foot per two hundred foot section. Were subsequent measurements carried out with a different tape of unknown specification, differing stilling masses and standardized length the results might be incomprehensible.
The formula for the correction of gravitational acceleration upon a tape of known specification and calibrated length;
s = gx/AE [ M + m/2 ( 2l – x ) – P/g ]
g = latitudinally varying gravitational acceleration (32.174 ft/s/s at our latitude)
x = measured length (ft)
A = cross sectional area of tape (in²)
E = modulus of elasticity (KSI)
M = stilling mass added to tape (lbs)
m = mass of the tape per unit length (lbs/ft)
l = nominal length of tape (ft)
P = calibrated standard tension (lbs)
1. The answer will be returned in decimal inches and is converted to decimal feet by dividing by 12.
2. The certificate of calibration of our standard and field tapes was provided by Cooper Hand Tools, in a comparison with N.I.S.T. traceable standard tape 14757.
3. The specifications of our tapes, composed of a SAE1095 tool steel, were provided by the Apex Tool Group, the manufacturer of Lufkin steel tapes.
4. A temperature correction must also be applied.
Log in to reply.