Chain and Tape Surveying Questions and Answers

Answer: B

The correct statement is Sag correction is always negative.

A tape suspended between two supports hangs in a curve, so the straight distance between the ends is shorter than the length read on the tape. The measured length is always too long, and the sag correction is always subtracted.

The correction for wrong alignment is also always negative, for the same reason (a crooked line is longer than the straight one), so 'always positive' is wrong. The slope correction is always negative too, since the horizontal distance is shorter than the slope distance. The temperature correction can have either sign: positive when the field temperature is above the standard temperature and negative when it is below.

Answer: D

For survey work of greater accuracy, an invar tape is used.

Invar is an alloy of about 36% nickel and 64% steel with a very low coefficient of thermal expansion, roughly a tenth or less of that of steel. An invar tape therefore hardly changes length with temperature, which is why it is used for base line measurement in triangulation and other precise work.

A cloth (linen) tape stretches and shrinks with moisture and pull, and is used only for rough work. A metallic tape is cloth woven with brass wire, more stable but still for ordinary work. A steel tape is accurate but expands noticeably with temperature, so it needs temperature corrections that invar largely avoids.

Answer: B

Perpendicular offsets are set out with a metallic tape and cross staff.

In chain surveying, details on either side of the main survey line are located by offsets, perpendicular distances from the chain line to the object. A cross staff (or an optical square) is used to set out the right angle at the chain line, and a tape, usually a metallic tape, measures the offset length.

A plumb bob transfers points vertically, for instance when chaining on slopes, and an arrow marks the end of each chain length; neither sets out a right angle. The steel tape with plumb bob pairing is used for step chaining, not for perpendicular offsets.

Answer: A

An engineer's chain is 100 ft long.

The engineer's chain has 100 links, each 1 foot long, giving 100 feet. It was used for engineering surveys in feet.

The 66 ft chain is Gunter's chain (surveyor's chain) of 100 links of 0.66 ft, used for land measurement because 10 square Gunter's chains make an acre. 33 ft is the half-length revenue chain used in India. Metric surveys now use 20 m and 30 m chains.

Answer: A

The longest line in chain triangulation is the base line.

In chain surveying the area is divided into triangles. The base line is the longest of the main survey lines, usually running through the middle of the area, and the whole framework is built on it, so it is measured with the most care.

Check lines (proof lines) join points on the sides of triangles to check their accuracy. Tie lines join points on the main lines to locate details. Both are shorter than the base line.

Answer: D

The correct length of AB is 347.4 m.

A tape that is too short reads more than the true distance, because each 'tape length' laid down actually covers only 19.95 m:

\[ \begin{aligned} L &= \frac{L'}{L_n} \times l' = 348.28 \times \frac{19.95}{20} \\ &= 347.41\ \text{m} \end{aligned} \]

So the true length is a little less than the measured one. The other options are far from 348.28 m, while a 0.05 m error per 20 m can change the length by less than 1 m, so none of them can be right.

Answer: B

The pull correction is \(Cp = \frac{(P - P_{o})L}{AE}\).

A tape is standardised under a pull \(P_o\). If it is used under a larger pull \(P\), the extra force stretches it, and by Hooke's law the extension of a length \(L\) of cross-section \(A\) and modulus \(E\) is:

\[ C_p = \frac{(P - P_o)\,L}{A\,E} \]

The correction is positive when \(P > P_o\). The other options misplace terms: an extension must grow with both the excess pull and the length, so neither can sit in the denominator, and \(AE\) is the stiffness that resists stretching, so it cannot be in the numerator.