Dimensioning & Scaling

CIVIL ENGINEERING DRAWING

General Rules for DimensioningDimensioning should be done so completely that further

calculation or assumption of any dimension or direct measurement from drawing is not necessary.

Every dimension must be given but none should be given more than once.

The dimension should be placed on the view where its use is shown more clearly.

Dimensions should be placed outside the views. Mutual crossing of dimension lines and dimensioning

between hidden lines should be avoided.Dimension line should not cross any other drawing of the

line.An outline or a centre line should never be used as a

dimension line. A centre line may be extended to serve as an extension line.

Aligned system of dimensioning is recommended.

Representation of ScalesScale can be expressed in the following two ways.Engineering Scale

Engineering scale is represented by writing the relation between the dimension on the drawing and the corresponding actual dimension of the object itself. It is expressed as 1mm=1mm 1mm=5 m, 1mm=8km 1mm=0.2mm, 1mm=5µm

The engineering scale is usually written on the drawings in numerical forms.

Graphical ScaleGraphical scale is represented by its representative fraction and is captioned on the drawing itself. As the drawing becomes old, the drawing sheet may shrink and the engineering scale would provide inaccurate results.However, the scale made on the drawing sheet along with drawing of object will shrink in the same relative proportion. This will always provide an accurate result. It is a basic advantage gained by graphical representation of a scale.

Representative Fraction (R.F.)Representative fraction is defined as the ratio of the length of an element of the object in the drawing to the corresponding actual length of the corresponding element of the object itself.

Representative Fraction (R.F.)Example 1

If 1 cm length of drawing represents 5m length of the object than in engineering scale it is written as 1cmcm=5m and in graphical scale it is denoted by


If a 5cm long line in the drawing represents 3 km length of a road then in engineering scale it is written as 1cm=600m and in graphical scale it is denoted as


If a gear with a 15cm diameter in the drawing represents an actual gear of 6mm diameter in graphical scale, it is expressed by

Scale 1:1 represents full size scaleScale 1:x represents reducing scaleScale x:1 represents enlarging scale.

Construction of scalesR.F. of the scaleThe maximum length of scale to be drawn on

the drawing sheetThe least count of the scale, i.e. minimum

length which the scale should show and measure

The maximum length of the scale to be drawn on the drawing sheet is determined by the following expression:

Types of ScaleScales are classified asPlain scaleDiagonal ScaleComparative Scale (plain and Diagonal Type)Vernier Scale

Plain ScaleThe plain scale is used to represent two consecutive units i.e., a unit and its sub-division. Example Meter and decimeter Kilometer and hectometer Feet and inches

1. In every scale the zero should be placed at the end of first main division. 2. From zero mark the units should be numbered to the right and its subdivision to the left.3. The names of the units and the subdivision should be stated clearly below or at the

respective ends. 4. The name of the scale or its R.F. should be mentioned below the scale.

Steps1. Determine R.F. of the scale2. Determine length of the scale using the formula mentioned earliar3. Draw the line of the length of scale.4. Mark zero at the end of first division and 1,2,3,4 and onward etc. at the end of each

subsequent division to its right.5. Divide the first division into 10-15 equal subdivisions, each division represents the least

count of the scale. 6. Mark the units

Plain ScaleExerciseProblem 1: Construct a scale of 1:4 to show centimeters

and long enough to measure upto 5 decimeters

Problem 2: Draw scale of 1:60 to show meters and decimeters and long enough to measure 6 meters.

Problem 3: Construct a scale of 1.5 inches = 1 foot to show inches and long enough to measure 4 feet

Problem 4: Construct a scale of R.F. = 1/60 to read yards and feet and long enough to measure upto 5 yards.

Diagonal ScaleA diagonal scale is used when very minute distances such as 0.1 mm etc. are to be accurately measured or when measurements are required in 3 units e.g. decimeter, centimeter and millimeter or yard, foot and inch.

Small divisions of short lines are obtained by the principal of diagonal division

Principle of Diagonal ScaleTo obtain the divisions of given short line A B in multiples of 1/10 its length e.g. 0.1AB, 0.2AB, 0.3AB etc.

1. Draw line AB2. Draw perpendicular from B to C3. Divide BC in 10 equal parts4. Number the division points 9,8,7,…,1 as shown. 5. Join A to C6. Through the points 1,2 etc. draw lines parallel to AB and cutting AC at

1’,2’ etc. 7. Through the rules of similar triangles 1’1 = 0.1AB, 2’2 = 0.2AB, 3’3 =

0.3AB and so on.

Diagonal ScaleProblem: Construct a diagonal scale of R.F. =

1/4000 to show meters and long enough to measure upto 500 meters. 1. Find the length of scale2. Draw line of length of scale and divide into 5

equal parts. Each part will show 100 meters. 3. Divide the first part into 10 equal divisions.

Each division will show 10 meters. 4. Add the left hand end, erect a perpendicular

and on it mark equal 10 divisions of any length.5. Draw the rectangle and complete the scale as

shown.

Comparative ScaleScales having same representative fraction but

graduated to read different units are called comparative scales.

Comparative scales may be plain scales or diagonal scales and may be constructed separately or one above the other.

Comparative ScaleProblem: on a railway map, an actual distance of

36miles between two stations is represented by a 10cm long line. Draw a plain scale to show a mile, and which is long enough to read up to 60 miles. Also draw comparative scale attached to it to show a kilometer and read up to 90 km. take 1mile=1609meters

Steps:

Calculate R.F.

Calculate length of scale for miles and kilometers

Draw plain scale for both km and miles and attach each other.

Vernier ScaleVernier scale like diagonal scale are used to read to a very small unit with great accuracy. A vernier scale consist of two parts i) primary scale and ii) Vernier Scale.

Primary scale is a plain scale fully divided into minor divisions.

The graduations on the vernier are derived from those on the primary scale.

GEOMETRICAL CONSTRUCTION

CED

GEOMETRICAL CONSTRUCTIONBISECTING A LINE To bisect a given straight line To bisect a given arc

TO DRAW PERPENDICULARS To draw a perpendicular to a given line from a point within ita) When the point is near the middle of the lineb) When the point is near the end of the line To draw a perpendicular to a given line from a point outside ita) When the point is nearer the centre than the end of the line

b) When the point is nearer the end than the centre of the line.

GEOMETRICAL CONSTRUCTIONTO DRAW PARALLEL LINES To draw a line through a given point

parallel to a given straight line

To draw a line parallel to and at a given distance from a given straight line

GEOMETRICAL CONSTRUCTIONTO DIVIDE A LINE: To divide a given straight line to any

number of equal parts

To divide straight line into unequal parts ( let AB be the given line to be divided into unequal parts say 1/6, 1/5, ¼, 1/3 and ½.)

GEOMETRICAL CONSTRUCTIONTO BISECT AN ANGLE

To bisect a given angle

To draw a line inclined to a given line at an angle equal to a given angle

GEOMETRICAL CONSTRUCTIONTO TRISECT AN ANGLE

To trisect given right angle

GEOMETRICAL CONSTRUCTIONTO FIND THE CENTRE OF AN ARC

To find the centre of given arc

To draw an arc of a given radius, touching a given straight line and passing through a given point


(contd.) To draw an arc of a given radius

touching two given straight lines at right angles to each other

To draw an arc of a given radius touching two given straight lines which make any angle between them.

GEOMETRICAL CONSTRUCTIONTO FIND THE CENTRE OF AN ARC (contd.) To draw an arc of a given radius touching a given arc and a given straight line.

a) Case 1

b) Case 2

GEOMETRICAL CONSTRUCTIONTO FIND THE CENTRE OF AN ARC (contd.)

To draw an arc of a given radius touching two given arcs

a) Case 1 b) Case 2 c) Case 3


(contd.)

To draw an arc passing through three given points not in a straight line

To draw continuous curve of circular arcs passing through any number of given points not in a straight line

GEOMETRICAL CONSTRUCTIONSteps:1. Let A, B, C, D, and E be the given points.2. Draw lines joining A with B, B with C, C with D etc.3. Draw perpendicular bisectors of AB and BC intersecting at O.4. With O as centre and radius equal to OA, draw an arc ABC.5. Draw a line joining O and C.6. Draw the perpendicular bisector of CD intersecting OC or OC

produced, at P.7. With P as centre and radius equal to PC, draw an arc CD.8. Repeat the same construction. Note that the centre of the arc is at

the intersection of the perpendicular bisector and the line, or the line-produced, joining the previous centre with the last point of the previous arc.

GEOMETRICAL CONSTRUCTIONTO CONSTRUCT REGULAR POLYGON To construct a regular polygon, given the length of

its side, let the number of sides of the polygon be seven.

Method 1a) Inscribe Circle Method

b) Arc Method

GEOMETRICAL CONSTRUCTIONMethod 2

GEOMETRICAL CONSTRUCTIONSPECIAL METHODS FOR DRAWING REGULAR POLYGONS:

To construct a pentagon, length of side given

Method 1 Method 2

GEOMETRICAL CONSTRUCTIONSPECIAL METHODS FOR DRAWING REGULAR

POLYGONS. (contd.)

To construct a hexagon, length of a side given

To inscribe a regular octagon in a given square.

GEOMETRICAL CONSTRUCTIONTO DRAW REGULAR FIGURES USING T-

SQUARE AND SET-SQUARESTo describe an equilateral triangle about a

given circle.To draw a square about a given circle

GEOMETRICAL CONSTRUCTIONTO DRAW REGULAR FIGURES USING

T-SQUARE AND SET-SQUARES (contd.)

To describe a regular hexagon about a given circle

To describe a regular octagon about a given circle.

GEOMETRICAL CONSTRUCTIONTO DRAW TANGENTS: To draw common tangent to two given circles of

equal radii. a) External Tangents

b) Internal Tangents

GEOMETRICAL CONSTRUCTIONTO DRAW TANGENTS: (contd.)

To draw common tangents to two given circles of unequal radii.

a) External Tangents

b) Internal Tangents

GEOMETRICAL CONSTRUCTIONLENGTH OF ARCS:

To determine length of given arc

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Dimensioning & Scaling