Chapter-2:�Linear Measurements

Dept. of Civil Engineering

Indus Institute of Tech. & Engg.

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Subject: Elements of Civil & Environment Engineering

Subject Code:FY410021

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Topics to be covered(Teaching hours: 05)

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• Methods of linear measurement
• Approximate methods
• Instruments used in Chain surveying
• Principles of Chain Surveying
• Terms related with chain surveying
• Selection of survey stations
• Operations in Chain Surveying
• Chaining
• Ranging
• Offsetting
• Errors in Chaining
• Corrections
• Conventional symbols

Introduction

• The determination of the distance between two points on the surface of the earth is one of the basic operation of surveying.
• Measurement of horizontal distances or measuring linear measurement is required in chain surveying, traverse surveying and other types of surveying.

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Methods

• There are 3 methods of making linear measurements.
• 1- Direct Method.
• 2- Optical Method.
• 3- E.D.M Method.

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Direct Method

• In the direct method, the distance is actually measured during field work using a chain or a tape. This is the most commonly used method for linear measurements.

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Optical Method

• In the optical methods, principles of optics are used. The distance is not actually measured in field but it is computed indirectly. The instrument used for making observations is called tacheometer.

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E.D.M Method

• Electronic Distance Measuring (E.D.M) instruments have been developed quite recently.
• These are practically replacing the measurement of distances using chains or tapes. There is a large variety of such instruments and depending upon the precision required the instruments should be used.

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Approximate Methods

• Pacing.
• Passometer.
• Pedometer.
• Odometer.
• Speedometer.
• Measuring Wheel.

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Pacing

• The distance between two points can be approximately be determined by counting the number of paces and multiplying it with average length of the pace.

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Passometer

• It is a small instrument which counts the number of paces

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Pedometer

• This instrument directly gives the distance by multiplying the number of paces with the average pace length of the person carrying the instrument.

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Odometer

• An odometer is a simple device which can be attached to the wheel of a bicycle or any such vehicle.
• The odometer registers the number of revolution made by the wheel. The distance covered is equal to the product of the number of revolutions and the perimeter of the wheel

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Speedometer

• This is used in automobiles for measuring distances.

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Measuring Wheel

• It is a wheel fitted with a fork and handle. The wheel is graduated and shows a distance per revolution. There is a dial which records the number of revolution. Thus the distance can be computed.

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Instruments used in Chain Surveying

1) Chains

2) Tapes

3) Arrows

4) Ranging Rods and Offset Rod

5) Pegs

6) Plumb- bob

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Chains

• Various types of chains used in surveying are
• Metric chain
• Gunter’s chain or Surveyor’s chain
• Engineer’s chain
• Revenue chain
• Steel band or Band chain

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Metric Chain

• Chain consists of galvanized mild steel wire of 4 mm diameter known as link.
• The ends of the links are bent into loop and connected together by means of three oval rings which provide the flexibility to the chain and make it less liable to kinking.

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Gunter’s Chain

• A 66 feet long chain consists of 100 links each of 0.66 ft it is known as Gunter’s Chain
• Here, 10 sq chain are equal to 1 acre,
• 10 chains= 1 furlong and 8 furlongs = 1 mile
• This chain is suitable for taking length in miles and areas in acres.

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Engineer’s Chain

• A 100 ft chain of 100 links each of 1 foot is known as Engineer’s chain.
• Brass tags are fastened at every 10 links.
• This chain is used to measure length in feet and area in square yards.

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Revenue Chain

• Revenue chain is 33 ft long chain consisting of 16 links. This chain is used for distance measurements in feet & inches for small areas.

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Steel Band or Band Chain

• Steel bands are preferred than chains because they are more accurate, but the disadvantages is that they get broken easily and are difficult to repair in the field.
• They are numbered at every metre and divided by brass studs at every 20 cm.

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Tapes

• Tapes are used for more accurate measurement. The tapes are classified based on the materials of which they are made of such as:
• Cloth or linen tape.
• Fibre tape.
• Metallic tape.
• Steel tape.
• Invar tape.

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Cloth or linen tape

• Linen tapes are closely woven linen and varnished to resist moisture.
• They are generally 10 m, 20 m, 25 m and 30 m long in length and 12 to 15 mm wide. They are generally used for offset measurements. These tapes are light and flexible.

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Fibre tape

• These tapes are similar to linen and plastic coated tapes but these are made of glass fibre.
• The tapes are quite flexible, strong and non-conductive.
• These tapes do not stretch or shrink due to changes in temperature or moisture.

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Metallic tape

• A linen tape reinforced with brass or copper wires to prevent stretching or twisting of fibres is called a metallic tape.
• As the wires are interwoven and tape is varnished these wires are visible to naked eyes. This is supplied in a lather case with a winding device.

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Steel tape

• The steel tape is made of steel ribbon of width varying from 6 to 16 mm.
• The commonly available length are 10 m, 15 m, 20 m, 30 m and 50 m.
• Steel tapes are used for accurate measurement of distances.

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Invar tape

• Invar tape are made of alloy of nickel 36 % and steel 64 % having very low co-efficient of thermal expansion.
• It is not affected by change of temperature therefore, it is used when high degree of precesion is required.

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Arrows

• Arrows are made of tempered steel wire of diameter 4mm.
• One end of the arrow is bent into a ring of diameter 50mm and the other end is pointed.
• Its overall length is 400mm.
• An arrow is inserted into the ground after every chain measured on the ground.

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Ranging Rods and Offset Rod

• Ranging rods are 2 to 3 m in length.
• Used for ranging some intermediate points on the survey line.
• Painted with alternate bands of black and white or red and white colours.
• With length of each equalising 20 cm.

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Ranging rods

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Pegs

• Made of timber or steel.
• Used to mark the position of stations.
• Pegs are in length of 15 cm.

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Plumb-Bob

• Used to transfer points on ground.
• Used for fixing instrument exactly over the stations.

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Principle of Chain Surveying

• The principle of chain surveying is to divide the area into a number of triangles of suitable sides.
• In this area is divided into a number of triangles with the suitable sides.
• The plan of the area can be easily drawn.
• As a triangle is the only simple plane geometrical figure.

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Terms related with Chain Surveying

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Survey Stations

• Main Stations
• Subsidary Stations
• Tie Stations

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Main Stations

• Main Station Stations along the boundary of an area as controlling points are known as ‘Main Stations’.
• The lines joining the main station are called ‘ Main Survey Lines’.
• The main survey lines should cover the whole area to be surveyed. The main stations are denoted by Δ.

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Subsidiary Stations

• Stations which are on the main survey lines or any other survey lines are known as ‘ Subsidiary Stations’
• These stations are taken to run subsidiary lines for dividing the area into triangles, for checking the accuracy of triangles and for locating interior details.
• These are denoted by

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Tie Stations

• These stations are also subsidiary stations taken on the main survey lines.
• Lines joining the stations are known as ‘ Tie lines’ Tie lines are taken to locate interior details.
• These are also denoted by

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Main Survey Line

• The line joining the main stations are called main survey lines or chain lines.

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Base line

• The line on which the framework of the survey is built is known as ‘ Base line’.
• The longest of the main survey lines is considered as the base line.
• This lines should be taken through fairly level ground, and should be measured very carefully and accurately.

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Check Line

• The line joining the apex point of a triangle to some fixed points on its base is known as ‘ Check line’. It is taken to check the accuracy of the triangle. Sometimes this line helps to locate interior details

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Tie Line

• A line joining tie stations is termed as a tie line. It is run to take the interior details which are far away from the main lines and also to avoids long offsets. It can also serve as check line

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Selection of Survey Stations

• Survey lines should be minimum as far as possible and should be taken on fairly level ground.
• Should be intervisible.
• Should form well conditioned triangles.
• Should be located that tie lines, check lines, baseline etc. an be formed.
• Should be selected within the boundary of the area to be surveyed.

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Operations in Chain Surveying

• Chaining
• Ranging
• Offsetting

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Chaining

• Chaining can further subdivided into two methods:
• Chaining on level ground.
• Chaining on sloping ground.

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Chaining on Level Ground

• Chaining on level ground

It involves following operations

1. Fixing the stations.
2. Unfolding the chain.
3. Ranging.
4. Measuring the distance.
5. Folding the chain.

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Chaining on Sloping Ground

There are 2 methods:

• Direct Method:
• Also called as stepping.
• In this method, the distance is measured in small horizontal stretches say a₁, a₂ …a_n with suitable length of chain or tape.
• Finally the total horizontal distances are added to get the required distances .
• Indirect Method:
• It involves calculation from directly measured lengths.
• There are three methods designed for indirect calculations.

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Chain surveying (“stepping”)

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w

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y

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b

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Chaining on sloping ground

Ranging

• When the length of line exeeds the length of chain , to proceed in straght line intermediate points are required to be established between two stations.
• The process of establishing intermediate points on a straight line between two end points is known as ranging.
• There are 2 methods:
• Direct ranging
• Indirect ranging or reciprocal ranging.

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Direct Ranging

• When intermediate ranging rods are fixed on a straight line by direct observation from end stations, the process is known as direct ranging.
• Direct ranging also can be done with a line ranger it consist of 2 right isosceles triangular prisms. Placed one above other.

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Indirect or Reciprocal Ranging

• When the end stations are not intervisible due to there being high ground between them, intermediate ranging rods are fixed on the line in an indirect way.
• The method is known as indirect ranging or reciprocal ranging.

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Offsetting

• The method of taking perpendicular distances from chain line to the objects which are to be plotted is known as offsetting.
• Lateral measurements to chain lines for locating ground features are known as offsets.

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• There are 2 types of offsets:
• Perpendicular offsets: The offsets which are taken perpendicular to the chain are termed as above.
• Oblique offsets: Oblique distance is always greater than perpendicular distance. All the offsets which are not taken at right angle to chain line are known as above

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Instruments for laying Offsets

• Optical square.
• Indian optical square.
• Open cross staff.
• Prism square.

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Optical Square

Indian Optical Square

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Open Cross Staff

Prism Square

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Errors in Chaining

• There are 2 types
• Cumulative errors : The errors, which occur in the same direction and tend to accumulate are called cumulative errors.
• Compensating errors :The errors, which occur in either direction and tend to compensate are caleed compensating errors.

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Sources of Errors in Chaining

• Instrumental Errors
• Natural errors
• Personal errors

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Errors due to Incorrect Chain

• If chain is too long ,Measured distance will be less. Correction: positive

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• If chain is too small Measured distance will be more. Correction: negative

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Examples on Errors in Chaning

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• A 20 m chain was found to be 8 cm long at the end of day’s work after measuring 4000 m . If the chain was correct before commencement of work, find correct length of line.

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• A 20 m chain was found to be 10 cm too long after chaining a distance of 1500 m . It was found to be 18 cm too long at the end of one day’s work after chaining the total distance of 3900 m . Find the true distance if chain was correct before commencement of work.

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Tape corrections

• Corrections for absolute length
• Corrections for temperature
• Corrections for pull
• Corrections for sag
• Corrections for slope

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Conventional Symbols

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