Transcript lecture 3 (CED)

CIVIL ENGINEERING DRAWING
General Rules for Dimensioning
 Dimensioning should be done so completely that further
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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
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.
Steps
1.
2.
3.
4.
5.
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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.
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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.
1.
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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
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To bisect a given straight line
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To bisect a given arc
TO DRAW PERPENDICULARS
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To draw a perpendicular to a given line from a point within it
a)
When the point is near the middle of the line
b)
When the point is near the end of the line
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To draw a perpendicular to a given line from a point outside it
a)
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
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To draw a line through a given point parallel to a
given straight line
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To draw a line parallel to and at a given distance
from a given straight line
GEOMETRICAL CONSTRUCTION
TO DIVIDE A LINE:
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To divide a given straight line to any number of
equal parts
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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
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To bisect a given angle
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To draw a line inclined to a given line at an angle
equal to a given angle
GEOMETRICAL CONSTRUCTION
TO TRISECT AN ANGLE
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To trisect given right angle
GEOMETRICAL CONSTRUCTION
TO FIND THE CENTRE OF AN ARC
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To find the centre of given arc
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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
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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.)
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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
a)
Case 1
b) Case 2
c) Case 3
GEOMETRICAL CONSTRUCTION
TO FIND THE CENTRE OF AN ARC (contd.)
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To draw an arc passing through three given
points not in a straight line
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To draw continuous curve of circular arcs
passing through any number of given
points not in a straight line
GEOMETRICAL CONSTRUCTION
Steps:
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 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
a) 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 TSQUARE 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