SUR $280$

Homework $3$ Taping Corrections

Note that your field lab was an exercise of ordinary or normal taping. Tape calibration reports are generally not available. Care is taken to measure with the tape horizontal using a plumb bob on variable terrain. The crew applies estimated tension. Today, the steel tape is generally used to measure or layout short distances on level terrain.

This purpose of this lab homework is to familiarize you with precise taping corrections. Precise taping takes place with a tape that has been calibrated. The calibration report tells you what the tape's length is given a specific temperature, under a specific tension, and support. If work is being done over level ground or ground that has a uniform slope, the tape has probably been calibrated as "supported through$-$out." If the tape is going to be used to measure between points with no support, then the tape is calibrated with no support between the end points. Then a sag correction is necessary only if you use the tape other than how it was calibrated. Important point: All problems dealing tape corrections start with a data from a calibration report.

A and $B$ are two fixed points. The distance between them was measured with a calibrated tape. The calibration data for the tape supported its full length was:

Length: $100\mathrm{.}012$ ft $.$

Temperature: $,68F$

Pull $($tension$)$: $,12lbs$

Cross Sectional Area: $,0\mathrm{.}006$ in ${?}^2$

Weight of Tape: $,0\mathrm{.}015lb\frac{s}{f}t$

Coefficient of thermal expansion $()$ : $,\frac{0\mathrm{.}00000645}{}F$

Modulus of elasticity$($E$)$: $2\mathrm{.}9{10}^{7}lb\frac{s}{i}{n}^2$

The distance $AB$ was measured with the tape supported at the ends only, the temperature was $90F,$ and pull $8$ lbs $.$ Under these conditions the measured distance was $486\mathrm{.}73$ feet $($the distances of $100,100,100,100,$ and $86\mathrm{.}73$ feet were measured on the ground$).$ Compute the corrected length of line AB$.$ Don't worry about the order of the corrections. The impact of one correction on another is too small to be a concern. Note that sag correction is necessary in addition to length, temperature and tension because the tape was not used like it was calibrated.

$2.C$ and $D$ are two fixed points. The distance between them was measured with a calibrated tape. The calibration data for the tape supported its full length was:

Length:

$30\mathrm{.}009$ meters

Temperature: $,20C$

Pull $($tension$)$: $,5\mathrm{.}5kg$

Cross Sectional Area: $,0\mathrm{.}039c{m}^2$

Weight of Tape: $,0\mathrm{.}909kg$

Coefficient of thermal expansion $()$:$1\mathrm{.}15\frac{{10}^{-5}}{}C$

Modulus of elasticity$($E$)$: $2\mathrm{.}1{10}^{6}k\frac{g}{c}{m}^2$

The distance CD has a uniform $4\%$ grade. It was measured with the tape supported throughout with a tension of $12$ kg $.$ The temperature was $2C.$ The slope measurement was recorded as $381\mathrm{.}615$ meters. What is the corrected horizontal measurement?

$3.$ A calibrated tape has the following calibration data:

Length: $,100\mathrm{.}00ft.$

Temperature: $,68F$

Pull $($tension$)$: $,28lbs$

Coefficient of thermal expansion $()$:$,\frac{0\mathrm{.}00000645}{}F$

Modulus of elasticity $(E)$:$2\mathrm{.}9{10}^{7}lb\frac{s}{i}{n}^2$

a$)$ If the tape is used at a temperature of $-10F,$ what is the actual length of the tape if it is supported throughout and tension is applied at $28$ lbs$?$

b$)$ For the conditions deseribed above in a$),$ what is the correction to be applied to a measured distance recorded in your field book as $683\mathrm{.}46$ feet?

c$)$ For the conditions described in part a$,$ what is the correction to a distance that is to be laid out to be $375\mathrm{.}00$ feet.

$($Note watch you significant digits and include proper sign$).$