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THE OPEN UNIVERSITY OF SRI LANKADEPARTMENT OF CIVIL ENGINEERING

Diploma in Technology (Civil) Level 3Academic Year 2012/13

CEX3233 SURVEYING IModel Answers for Assignment No. 1

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1. (a) Reason for not considering accidental errors to be as serious as gross errors orsystematic errors: A systematic error is of constant and known character. It is eitheralways positive or always negative, and its effect is, therefore, cumulative. If acorrection is not applied, the final effect can be large.Gross errors occur due to inexperience or negligence of the operator. If undetected, theycan produce very serious effects on the measured quantity.On the other hand, accidental or random errors, which occur without the knowledge ofthe operator, are generally small in magnitude. In fact, the probability for a largerandom error to occur is very small. It is found that small errors occur more frequently,and large errors are very rare. Owing to the nature of these errors, they are equallylikely to be positive or negative, and therefore, tend to balance out in the final result.Due to the above reasons, accidental errors are not considered as serious as gross orsystematic errors.

(b) The need to make the triangles formed by chain lines well-conditioned: The chain linesare plotted on the paper in the form of triangles using arcs. When these triangles are notwell-conditioned (i.e., if they contain very small or very large angles), these arcs willintersect at small angles, thereby making it difficult to accurately locate the point ofintersection. If they intersect at an angle not very far from 90o, the intersection point canbe located fairly accurately. Since the sum of the three angles is 180 o, angles close to60o are acceptable (if one is 90o, then at least one of the remaining two will become toosmall).

(c) How a wire chain becomes longer than its nominal length: A wire chain can becomelonger than its nominal length due to opening out of some of the connecting rings (Fig.1.1), or due to wearing out of the contact surfaces of some of the connecting rings (Fig.1.2).

Fig. 1.1

Fig. 1.2

How a wire chain becomes shorter than its nominal length: A wire chain can becomeshorter than its nominal length due to bending of some of the links (Fig. 1.3), or due tothe accumulation of mud on the contact surfaces of some of the connecting rings (Fig.1.4.

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Fig. 1.3 Fig. 1.4

(d) Why the lengths of lines in a compass traverse are measured with a wire chain, whilethey are measured using a steel band in a theodolite traverse: There is a significantdifference in the accuracy that can be achieved in the two types of traverse survey.Compass bearings are measured only to the nearest 15 as compared to the accuracy ofangles measured with a theodolite, ranging from about 1 to 1 depending on theinstrument used. Therefore, there is no useful purpose served by measuring the lengthsin a compass traverse to the same degree of accuracy as in a theodolite traverse, but itonly increases the time and cost of fieldwork. So, a wire chain is used for linearmeasurements in the compass traverse.

2. (a) Standardisation correction not applied as no mention is made of any differencebetween the actual length and nominal length of steel band.Slope correction negative correction to be applied to spans 1 3 only (to the combinedlength, since the slope is the same).Temperature correction positive correction to be applied to the total length of fourspans.Pull correction positive correction to be applied to span 1 only.Sag correction negative correction to be applied separately to each of the four spans.Altitude correction negative correction to be applied to the total length of four spans.

Let us now compute these corrections using a set of hypothetical values. Let us assumethe measured lengths of the four spans as 29.900, 29.850, 29.950 and 21.600 m, theslope of spans 1 3 as 3o, temperature at the time of measurement as 26oC, standardtemperature as 20oC, pull applied for span 1 as 120 N and the standard pull as 100 N.

Let us also assume the following material properties.Mass of steel band = 0.024 kg/mCross sectional area of band = 2.40 mm2

Elastic modulus of steel = 206 kN/mm2

Coefficient of linear expansion of steel = 11.5 x 10-6 per oC

Correction for slope (spans 1 - 3) = (-) (29.90 + 29.85 + 29.95)(1 - cos 3o)= (-) 0.123 m

Correction for temperature = (+)(29.90 + 29.85 + 29.95 + 21.60) x 11.5 X 10 -6 x(26 - 20)

= (+) 0.008 m

Correction for pull (span 1 only) = (+) (120 - 100) x 29.90 / (2.40 x 206000)= (+) 0.001 m

Correction for sag = (-) (0.0242 x 9.812/ 24) {29.903/ 1202 +(29.853 + 29.953 + 21.603)/ 1002}

= (-) 0.019 m

Correction for altitude = (-) 0.0001575 x 1500 x (29.90 + 29.85 + 29.95 +21.60)/1000

= (-) 0.026 m

(b) Chaining a line in which the two ends are not inter-visible due to topographical features:

Here, the obstruction is for ranging the line, but there is no obstruction for chaining. Thefollowing procedure can be adopted for ranging the line.

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A and B are the two ends of the chain line (see fig. 2). Select two intermediate points C 1and D1 such that ranging poles placed at these points are seen from both ends. Theperson who holds the pole at C1 directs the one at D1 to a new position D2 in line with C1and B. Then the person at D2 directs the other person to a new position C2 in line with D2and A. Next the person at C2 directs the other to a new position D3 in line with C2 and B.This process is continued until both persons at intermediate points are satisfied that theother one is in line with the remote pole and his. This happens when both are in line withA and B.

Fig. 2

Once the line is ranged, chaining can proceed as usual. If necessary, additional rangingpoles may be located in between the poles already fixed.

3. (a) When the lower clamp of the theodolite is fixed, the horizontal scale does not move.

When the telescope is rotated with the upper clamp slack, the index moves against thestationary scale and indicates a change in the horizontal circle reading.

When the upper clamp is fixed and the lower clamp is slack, the upper and lower platesrotate as one unit. Since the index (on the upper plate) and the horizontal graduatedcircle (on the lower plate) move together, there will be no change in the reading.

(b) If the trunnion axis of the theodolite is not exactly perpendicular to the vertical axis(trunnion axis error), or the collimation axis is not exactly perpendicular to the trunnionaxis (collimation axis error), an error will occur in the measured horizontal angle (notethat this error will not occur if the angle is measured between two targets which are atthe same elevation). When the face of the instrument is reversed (right to left, or left toright), the error also reverses (i.e., positive to negative, or negative to positive).

Therefore, if we take an equal number of observations on each face and average them,the effects of collimation axis error andtrunnion axis error will be eliminated.

It is not necessary that we always rotate the telescope in the clockwise direction whenthe instrument is on face right, and in the anti-clockwise direction when it is on face left.The only requirement is that the telescope must be rotated in the same direction in aparticular round of observations. This precaution is taken in order to prevent anybacklash errors occurring in the measurements.

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