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 ]
Where,
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)Notes;
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.
- 15 Replies
um…yeah..that seems right…um…just don’t forget to carry the 1….lol:bye: :-$
I should emphasize that the specifications given apply only to my standard and field tape manufacturer and model.
And how does the uncertainty of this method compare to that of an optical EDM looking over the edge of the building at a reflector on the sidewalk, with appropriate temperature and pressure corrections as best measurable?
.Considering the construction section of our roof and parapet, that technique would be impossible.
> And how does the uncertainty of this method compare to that of an optical EDM looking over the edge of the building at a reflector on the sidewalk, with appropriate temperature and pressure corrections as best measurable?
Don’t forget the application of appropriate straps, harnesses, and life insurances when using said EDM and reflector.
so why cant a disto d8 follow the path of the tape measure, no discernable gravitational affect on the beam, and 1mm in 100 metres, measured in stages.
The pull on the tape is a given, its a similar formula to working kln imposition for point loads,but consider the mass of the tape and the gravitational tensile strectching.
Having done lots of highrise, it really isnt easily done, you get different equations with hypothetcial co-efficients which result in supposed finite formula results.The height of the building you are on, is just a multiplicaion of a formula which i am trying to find for you.
I got it from lufkin or tajima or someone years ago, it may be in my garage, its similar to a report i read last year about the accuacey of prism and reflectorless diamensions and compared like for like. The tape measure report gave the specs on all the good quality tapes at the time, and how the materials reacted under different load conditions.where you asking for ideas on how to do it, or are you ok with what you are going to do
The one in Dubai is being monitored as well, I shall try and find who was doing it, I had an email from them years ago when it startedI would work digitally with some edm device, at least for the establishment of the reference points. the germans have some great gear, which is sold through leica, but in the 100,000 and up price range
of all the buildings i have monitored, some moved way less than allowed for, others way more, but they were mostly concrete and not steel. I could never get a quantified answer from an engineer, they just said, ”according to our models it should have…………
Cheers
DavidScott
Thanks for bringing to mind things that some of us would never think of. We measure almost entirely horizontally and with (for the most part) electronic measurement devices. It’s great to know that there are those out there that deal quite effectively with problems that never even occur to me.
Andy
One of these days…
Can I come down and work with you on the tower….only kidding…well, half-kidding..OK i’m not!!
I’d love to see a day in the life of working on that.
I’ll buy lunch…lol.O 😉
Are there any other effects like wind or sway of the building caused by the wind?
:-S
Radar
I hope everyone has a great day; I know I will!If the location of the sun and the ambient temp are not exactly the same as a previous msmt the gravitational pull on the tape is useless info.
I ran one building up using a columnator (sp). I highly recommend them, esp if you can find one that looks both up and down. We made 1ft sq alum plates with a 1/32″ hole in the middle with < at the 1/2 way point on each side. When the plate was aligned over the can hole we then scribed the < and set l&tks so the contractor and us could pull the control point back in.I took over a building where the previous chief set pipe on c/l floor at ground level at the edge of the building on all 4 sides then set pipe further out to set the gun on to transfer the line up to the floor. We think some of his pipe got hit. Window guys found .15ft with their laser. No, the pipe further out were not on line to anything, hey wasn’t my idea.
I must admit I’m also puzzled by this post…
How can offsetting gravitational pull on a tape (which is NOT a precise measurement instrument, in any case, and with compounding error being introduced at every break) be so important…? Seems you’d get much better results from a long-term GPS observation at a controlled point on the top (even though I know you have a lot of sway due to wind).
I should have added that I set a IP on the building line and protected it with steel guard posts with a elevation on it. We chained (100ft tape only used for vertical) up the edge of the building for elevations. Always at the same time of the day, could not do much about the temp, doing a temp correction seemed to create more differences in EL than just chaining it.
Both the tape and the building steel expand with temperature, so you need to figure out what temperature your height is for.
.Scott,
Take a look at page 7 of 8 (V/273) at this link
CONTROL SURVEYS FOR UNDERGROUND CONSTRUCTION OF THE SUPERCONDUCTING SUPER COLLIDERTapes are nowhere near an accurate measurement. Even using 300′ metal tapes (much better than other tapes), there is no possible way to measure within 0.10 foot, over the size of something like WTC1.
I’m still very confused as to why this is even a consideration… Why are you wasting your time on this…?
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