Dimensioning & Scaling CIVIL ENGINEERING DRAWING

General Rules for Dimensioning Dimensioning 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 Scales Scale 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 Scale Graphical 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

Representative Fraction (R.F.) Example 2 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

Representative Fraction (R.F.) Example 3 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 scale Scale 1:x represents reducing scale Scale x:1 represents enlarging scale.

Construction of scales R.F. of the scale The maximum length of scale to be drawn on the drawing sheet The 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 Scale Scales are classified as Plain scale Diagonal Scale Comparative Scale (plain and Diagonal Type) Vernier Scale

Plain Scale The 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 In every scale the zero should be placed at the end of first main division. From zero mark the units should be numbered to the right and its subdivision to the left. The names of the units and the subdivision should be stated clearly below or at the respective ends. The name of the scale or its R.F. should be mentioned below the scale. Steps Determine R.F. of the scale Determine length of the scale using the formula mentioned earliar Draw the line of the length of scale. 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. Divide the first division into 10-15 equal subdivisions, each division represents the least count of the scale. Mark the units

Plain Scale Exercise Problem 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 Scale A 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 Scale To 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. Draw line AB Draw perpendicular from B to C Divide BC in 10 equal parts Number the division points 9,8,7,…,1 as shown. Join A to C Through the points 1,2 etc. draw lines parallel to AB and cutting AC at 1’,2’ etc. Through the rules of similar triangles 1’1 = 0.1AB, 2’2 = 0.2AB, 3’3 = 0.3AB and so on.

Diagonal Scale Problem: Construct a diagonal scale of R.F. = 1/4000 to show meters and long enough to measure upto 500 meters. Find the length of scale Draw line of length of scale and divide into 5 equal parts. Each part will show 100 meters. Divide the first part into 10 equal divisions. Each division will show 10 meters. Add the left hand end, erect a perpendicular and on it mark equal 10 divisions of any length. Draw the rectangle and complete the scale as shown.

Comparative Scale Scales 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 Scale Problem: 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 Scale Vernier 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 CONSTRUCTION BISECTING 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 it When the point is near the middle of the line When the point is near the end of the line To draw a perpendicular to a given line from a point outside it 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 CONSTRUCTION TO 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 CONSTRUCTION TO 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 CONSTRUCTION TO 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 CONSTRUCTION TO TRISECT AN ANGLE To trisect given right angle

GEOMETRICAL CONSTRUCTION TO 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

GEOMETRICAL CONSTRUCTION TO FIND THE CENTRE OF AN ARC (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 CONSTRUCTION TO 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 CONSTRUCTION TO FIND THE CENTRE OF AN ARC (contd.) To draw an arc of a given radius touching two given arcs Case 1 b) Case 2 c) Case 3

GEOMETRICAL CONSTRUCTION TO FIND THE CENTRE OF AN ARC (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 CONSTRUCTION Steps: Let A, B, C, D, and E be the given points. Draw lines joining A with B, B with C, C with D etc. Draw perpendicular bisectors of AB and BC intersecting at O. With O as centre and radius equal to OA, draw an arc ABC. Draw a line joining O and C. Draw the perpendicular bisector of CD intersecting OC or OC produced, at P. With P as centre and radius equal to PC, draw an arc CD. 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 CONSTRUCTION TO 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 1 Inscribe Circle Method b) Arc Method

GEOMETRICAL CONSTRUCTION Method 2

GEOMETRICAL CONSTRUCTION SPECIAL METHODS FOR DRAWING REGULAR POLYGONS: To construct a pentagon, length of side given Method 1 Method 2

GEOMETRICAL CONSTRUCTION SPECIAL 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 CONSTRUCTION TO DRAW REGULAR FIGURES USING T-SQUARE AND SET-SQUARES To describe an equilateral triangle about a given circle. To draw a square about a given circle

GEOMETRICAL CONSTRUCTION TO 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 CONSTRUCTION TO DRAW TANGENTS: To draw common tangent to two given circles of equal radii. a) External Tangents b) Internal Tangents

GEOMETRICAL CONSTRUCTION TO DRAW TANGENTS: (contd.) To draw common tangents to two given circles of unequal radii. a) External Tangents b) Internal Tangents

GEOMETRICAL CONSTRUCTION LENGTH OF ARCS: To determine length of given arc