ENGINEERING APPLICATIONS
OF
THE PRINCIPLES
OF
PROJECTIONS OF SOLIDES.
1. SECTIONS OF SOLIDS.
2. DEVELOPMENT.
3. INTERSECTIONS.
STUDY CAREFULLY
THE ILLUSTRATIONS GIVEN ON
NEXT SIX PAGES !
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.
Two cutting actions means section planes are recommended.
OBSERVER
A) 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.
B) 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.
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.
ASSUME
UPPER PART
REMOVED
(A)
(B)
ASSUME
LOWER PART
REMOVED
OBSERVER
ILLUSTRATION SHOWING
IMPORTANT TERMS
IN SECTIONING.
For TV
SECTION
PLANE
TRUE SHAPE
Of SECTION
x
y
Apparent Shape
of section
SECTION LINES
(450 to XY)
SECTIONAL T.V.
Typical Section Planes
&
Typical Shapes
Of
Sections.
Section Plane
Ellipse
Section PlaneTriangle Through Generators
Through Apex
Section Plane Parallel
to end generator.
Ellipse
Cylinder through
generators.
Section Plane Hyperbola
Parallel to Axis.
Trapezium
Sq. Pyramid through
all slant edges
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.
21
X1
31
o”
o’
3”
41
3’
11
2”
4”
2’ 4’
1’
X
1”
b’ d’
a’
c’
45º
d”
d
4
a
1
o
3
c
2
b
Y1
a” c”
Y
b”
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’
a’
X
b’e’
b
2’
c’d’
c’d’
4’
b1
o’
3’
c1
c
2
30
o
a
a1
6
d1
d
e
1
4
5
o1
3
31’
21’
41’
e1
11’
51’
61’
Y
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’
c’d’
c’d’
4’
b1
b1
1 2
37
a1 c1
a1 c 1
25
c
Y
3’
d
f
e
Y1
4 6
f1 d1
f1d1
20
31’
21’
e1
e1
11’
5
41’
71’
X1
51’
61’
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.
X1
o”
d’
j’
35
o’
g’
f’
e’ h’
i’
f”
b’
l’
4
10
c
6
8
5
9
4
4” 5”
3”
7
5
6
d
b
e
f
g
o
a
1
7
h
12
j”
c”
k”
l”
a”
3
2
d”
b”
2 3
1 12 11
X
h”
i”
e”
c’
k’
a’
g”
i
l
k
8
j
11
9
10
Y1
6”
2”
7”
1”
8” 9”10”
12” 11”
Y
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
71
11
o’
o”
4’
3’5’
4”
21
65
3”
5”
X1
2’6’
1’7’
b’f’
a’
b
2”
25
c’e’
d’
b”
c”
c
2
1
3
a
4
o
7
d
5
f
6
6”
e
Y2
1” a”
d”
7”
f”
e”