Example A$.1$

A $30-m$ steel tape standardized at $20C$ and supported throughout under a tension

of $5\mathrm{.}45$ kg was found to be $30\mathrm{.}012$ m long. The tape had a cross$-$sectional area of

$0\mathrm{.}050c{m}^2$ and a weight of $0\mathrm{.}03967k\frac{g}{m}.$ This tape was held horizontal, supported at

the ends only, with a constant tension of $9\mathrm{.}09$ kg $,$ to measure a line from $A$ to $B$ in three

segments. The data listed in the following table were recorded. Apply corrections for

tape length, temperature, pull, and sag to determine the correct length of the line.

$($a$)$ The tape length correction by Equation $(6\mathrm{.}3)$ is

$C_L=(\frac{30\mathrm{.}012-30\mathrm{.}000}{30\mathrm{.}000})81\mathrm{.}151=+0\mathrm{.}0324m$

$($b$)$ Temperature corrections by Equation $(6\mathrm{.}4)$ are $($Note: separate corrections

are required for distances observed at different temperatures.$)$:

ure A$.1$

ling between

d points, tape

long.

$C_{T_1}=0\mathrm{.}000011(14-20)30\mathrm{.}000=-0\mathrm{.}0021m$

$C_{T_2}=0\mathrm{.}0000116(15-20)30\mathrm{.}000=-0\mathrm{.}0017m$

$C_{T_3}=0\mathrm{.}0000116(16-20)21\mathrm{.}151=-0\mathrm{.}0010m$

${\displaystyle \underset{?}{\overset{?}{}}}{C}_T=-0\mathrm{.}0048m$

$($c$)$ The pull correction by Equation $(6\mathrm{.}5)$ is