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1.
ENGINEERING APPLICATIONS
OF
THE PRINCIPLES
OF
PROJECTIONS OF SOLIDS.
SECTIONS OF SOLIDS.
2.
Some times the objects are so complicated that, it becomes very
difficult to visualize the object with the help of its front view and top
view
Some objects are hollow. Their internal details are not visible with
the help of simple front view and top view.
In such cases the object is cut by some imaginary cutting plane to
understand internal details of that object
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
SECTION PLANE.
First let us know the types of cutting planes.
3.
PLANES
1
PRINCIPAL PLANES
HP AND VP
AUXILIARY PLANES
Auxiliary Vertical Plane
(A.V.P.)
Øº
A.V.P.
⊥ to Hp & ∠ to Vp
Auxiliary Inclined Plane
(A.I.P.)
A.I
.P.
⊥t
o V
p
∠ &
to
Hp
θº
Profile Plane
( P.P.)
4.
An A.V.P. appears as a straight line in its top view.
The straight line is its H.T.
So an A.V.P. always cuts T.V. of a
solid
Its position is described in the problem
Properties of section lines:
1. They are light.
2. Inclined at 45º with the
reference line.
3. 1 to 2 mm apart.
X
Y
As per B.I.S. the cutting
plane is shown as centre
line inside the object and
as solid line out side the
object
H
Remember:1. After launching a section
plane either in FV or TV, the
part towards observer is
assumed to be removed.
2. As far as possible the
smaller part is assumed to
be removed.
T
observer
5.
An A.I.P. appears as a straight line in its front view.
The straight line is its V.T.
So an A.I.P. always cuts F.V. of a
solid
Its position is described in the problem
observer
Properties of section lines:
They are light.
Inclined at 45º with the
reference line.
3. 1 to 2 mm apart.
1.
2.
As per B.I.S. the cutting
plane is shown as centre
line inside the object and
as solid line out side the
object
V
T
X
Remember:1. After launching a section
plane either in FV or TV, the
part towards observer is
assumed to be removed.
2. As far as possible the
smaller part is assumed to
be removed.
Y
6.
SECTIONING A SOLID.
An object ( here a solid ) is cut by
some imaginary cutting plane
to understand internal details of that
object.
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
SECTION PLANE.
wo cutting actions means section planes are recommended.
OBSERVER
Section Plane perpendicular to Vp and inclined to Hp.
( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)
NOTE:- This section plane appears
as a straight line in FV.
Section Plane perpendicular to Hp and inclined to Vp.
( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)
NOTE:- This section plane appears
as a straight line in TV.
emember:After launching a section plane
either in FV or TV, the part towards observer
is assumed to be removed.
As far as possible the smaller part is
assumed to be removed.
ASSUME
UPPER PART
REMOVED
E
AN
PL
ON FV.
CT IN
SE
(A)
(B)
ASSUME
LOWER PART
REMOVED
OBSERVER
SE
CT
ON
IN PLA
TV
NE
.
7.
ILLUSTRATION SHOWING
IMPORTANT TERMS
IN SECTIONING.
For TV
Fo
rT
ru
e
Sh
ap
e
SECTION
PLANE
TRUE SHAPE
Of SECTION
x
y
Apparent Shape
of section
SECTION LINES
(450 to XY)
SECTIONAL T.V.
8.
Section Plane
Ellipse
Section PlaneTriangle Through Generators
Through Apex
Pa
rab
ola
Typical Section Planes
&
Typical Shapes
Of
Sections.
Section Plane Parallel
to end generator.
Ellipse
Cylinder through
generators.
Section Plane Hyperbola
Parallel to Axis.
Trapezium
Sq. Pyramid through
all slant edges
9.
Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with
two edges of the base perpendicular to the VP. It is cut by a section plane, perpendicular to the
VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side
view and true shape of the section.
True
shape of
the
section
3
o”
o’
2
Sectiona
l side
View
4
2”
2’ 3’
Properties of section lines:
1.
They are light.
2.
Inclined at 45º with
the reference line.
3.
1 to 2 mm apart.
3”
1
1”
1’ 4’
X
a’ d’
a
b’ c’
b
1
2
Sectiona
l Top
View
o
3
d
4
c
a” b”
4”
d” c”
Y
10.
Q 14.11: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all
the edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the
VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side
view and true shape of the section.
True
shape of
the
section
21
Sectiona
l side
View
X1
31
o’
o”
41
3”
3’
11
2”
4”
2’ 4’
1’
X
1”
b’ d’
a’
45º
c’
d”
d
4
a
1
o
3
c
2
b
Y1
a” c”
b”
Y
11.
Problems on Section of Solids
To be discussed in the class
14.5,14.11,14.14,14.24,14.25
To draw on the sheet
14.6,14.15,14.26,14.35,14.39,14.17
12.
Q 14.14: A pentagonal pyramid , base 30mm side and axis 60 mm long is lying on one of its triangular faces
on the HP with the axis parallel to the VP. A vertical section plane, whose HT bisects the top view of the axis
and makes an angle of 30º with the reference line, cuts the pyramid removing its top part. Draw the top view,
sectional front view and true shape of the section and development of the surface of the remaining portion of
the pyramid.
o’
a’
60
6’
b’e’
1’
5’
b’e’
b
c’d’
c’d’
4’
b1
o’
3’
c1
c
2
o
a
d
e
a1
30
X
a’
2’
6
d1
1
4
5
o1
3
31’
21’
41’
e1
11’
51’
61’
Y
13.
Q14.13: A hexagonal pyramid, base 30 mm side and axis 65 mm long is resting on its base on
the HP, with two edges of the base parallel to the VP. It is cut by a section plane perpendicular
to VP and inclined at 45º to the HP, intersecting the axis at a point 25 mm above the base.
Draw the front view, sectional top view, sectional side view and true shape of the section.
51
41
61
X2
Y1
31
11
o’
o”
4’
3’5’
71
4”
21
65
3”
X1
2’6’
b’f’
a’
b
2”
25
1’7’
c’e’
d’
b”
c”
c
2
1
3
a
4
o
7
d
5
f
6
5”
e
Y2
6”
1” a”
d”
7”
f”
e”
14.
Problem 14.5: A square prism base 40 mm side, axis 80 mm long, has its base on the H.P. and its
faces equally inclined to the V.P. It is cut by a plane, perpendicular to the V.P., inclined at 60º to
the H.P. and passing through a point on the axis, 55 mm above the H.P. Draw its front view,
sectional top view and another top view on an A.I.P. parallel to the section plane.
b’
p’ d’
a’
x1
c’
t’
q’ s’
a1
t1
q1
c1
b1
30º
p1 d 1
s1
X
11
21
41
2’
4’
1’
y1 p
d,4
q
31
40
r’
3’
45º
c,3
a,1
r1
55
r
t
s
b,2
Y
15.
Q 14.6: A Hexagonal prism has a face on the H.P. and the axis parallel to the V.P. It is cut by a vertical
section plane the H.T. of which makes an angle of 45 with XY and which cuts the axis at a point 20 mm from
one of its ends. Draw its sectional front view and the true shape of the section. Side of base 25 mm long
height 65mm.
a’
f’
b’
e’
c’
d’
6’
7’
a’ f’
65
a’ f’
1’
b’ e’
5’
b’ e’
2’
X
a’
f’
b’
e’
b
a
c’
d’
4’
3’
b1
b1
1 2
37
a1 c1
a1 c1
Y1
25
c
Y
c’d’
c’d’
d
f
e
4 6
f1 d1
e1
f1 d1
20
31’
21’
e1
11 ’
5
41 ’
71 ’
X1
51’
61’
16.
Problem 14.17: A cylinder of 40 mm diameter, 60 mm height and having its axis vertical, is cut
by a section plane perpendicular to the V.P., inclined at 45º to the H.P. and intersecting the axis
32 mm above the base. Draw its front view, sectional top view, sectional side view and true
shape of the section.
p5
p6
p4
p7
p3
y2
p8
11’ 12’
p
10’ 9’2 8’
1’
7’
2’
6’
x1
3’
5’ 4’
12” 11”
1” 2” 3”
p9
p10
p”3
p1
p11
10”
4”
p”4
9”
5’
p”5
p”2
p12
8”
6” 7”
p”6
p”1
p”7
60
x2
p”12
32
p”8
p”11
45º
X
p”10
p”9
Y
12
1
2
11
3
10
4
5
9
8
7
Ø 40
6
y1
17.
Q 14.24: A Cone base 75 mm diameter and axis 80 mm long is resting on its base on H.P. It is cut by a section
plane perpendicular to the V.P., inclined at 45º to the H.P. and cutting the axis at a point 35 mm from the
apex. Draw the front view, sectional top view, sectional side view and true shape of the section.
1
f1
j1
g
1
i
h
1
X1
o”
b
1
a
1
c
1
d’
j’
35
d
1
l1
e
1
k
1
o’
g’
f’
e’ h’
i’
f”
d”
b’
l’
4
c
d
b
6’
8’
5’
9’
7’
4” 5”
3”
5
6
e
f
g
o
7
h
12
i
l
k
11
l”
a”
a
1
k”
b”
3
2
j”
c”
2’ 3’ 4’
1’ 12’ 11’ 10’
X
h”
i”
e”
c’
k’
a’
g”
8
j
10
9
Y1
6”
2”
7”
1”
8” 9”10”
12” 11”
Y
18.
Problem 14.25: A cone, base 75 mm diameter and axis 80 mm long is resting on its base on the
HP. It is cut by a section plane perpendicular to the VP, and parallel to and 12 mm away from
one of its generators. Draw the front view, sectional top view and true shape of the section.
Draw the front view, sectional top view and sectional side view.
X2
Y1 O’
O”
80
12
x
X1 10’ 11’ 12’
9’
8’
12
9’7’
1
3’
5’
2’
6’
1” 12” 11”
2” 3”
2
11
Ø75
4’
3
O
10
4
5
9
8
7
6
Y2
10”
4”
9”
5”
8” 7”
6”
y
19.
Q 14.19: A cylinder 55 mm diameter and 65 mm long, has its axis parallel to both the HP and the VP. It is cut
by a vertical section plane inclined at 30º to the VP so that axis is cut at a point 25 mm from one of its ends
and boyh the bases of cylinder are partly cut. Draw its sectional front view and true shape of the section.
2’ 3’ 4’
1’ 12’ 11’ 10’
5’
9’
6’
8’ 7’
p1’
p2’
p12’
1’
2’ 12’
3’ 11’
4’ 10’
5’ 9’
6’ 8’
X
p6’
3
4
p7’
6
1
2,6
7
12
8
11
10
9
7’
4
3,5
5
2
p8’
1,7
25
8,12
9,11
10
Y
20.
Problem 14.35: A square prism axis 110 mm long is resting on its base in the H.P. the edges of
the base are equally inclined to the V.P. The prism is cut by an A.I.P. passing through the mid
point of the axis in such a way that the true shape of the section is a rhombus having diagonals of
100 mm and 50 mm. Draw the projections and determine the inclination of A.I.P. with the H.P.
Here we are not given side of base of square prism. But the shorter diagonal of the rhombus will be equal to base diagonal of
the prism. So to begin with, draw a square in the top view with base diagonal 50 mm.
The inclination of the cutting plane decides the length of longer diagonal. From the mid point of the axis cut two arcs of 50
mm radius, one on long edge ‘b’ and the other on the long edge ‘d’
11
X1
21
1’
110
41
31
2’ 4’
Y1
3’
X
Y
4d
50
1a
c3
b2
21.
Problem 14.39: A cone, diameter of the base 60 mm and axis 70 mm long is resting on its base
on the H.P. It is cut by an A.I.P. so that the true shape of the section is an isosceles triangle
having 50 mm base. Draw the plan, the elevation and the true shape of the section.
o1
o’
70
b1
X
o
25
60
25
a’ b’
a
b
a1
Y
0
5
22.
Problem 14.26: A cone, base 45 mm diameter and axis 55 mm long is resting on the H.P. on its
base. It is cut by a section plane, perpendicular to both the H.P. and the V.P. and 6 mm away
from the axis. Draw its front view, top view and sectional side view.
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