TA lecture at Indian institute of technology kanpur of bachelor of technology or bachelor of science in first year.

1. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra

2. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
TA 101: Engineering Graphics
2023 - 24 Sem – I
Lecture 21 – Oct 18, 2023
Intersections - II
Sudhir Misra
Department of Civil Engineering
IIT Kanpur, Kanpur 208 016
2
Room No.: WLE 303 C;
Phone – 7346
E-mail: sud@iitk.ac.in

3. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Announcements
1. Can we have the end-semester examination on
the 16th November (instead of November 22nd,
announced by DOAA)
2. If you need additional help – through Academic
Mentors (or tutors), pl send mail to me with a
copy to Tejas Gupta

4. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
AH
BH
XH
YH
AF
BF
XF
YF
A line pierces a Cylinder:
Locate points of intersections
in Top and Front views
If the edge being pierced is in
edge view, then the piercing point
is clearly identified in that view
H
F

5. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Intersection of a line and
curved surface of cylinder
The top view determines the
two piercing points as it is the
edge view of the curved surface

6. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
H
F
Cutting plane method
A line pierces a
Pyramid:
Locate points of
intersections in Top
and Front views
1H
2H
3H
OH
4H
5H
4F
5F
1F 2F 3F
OF
XH
YH
ZH
XF
YF
ZF

7. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
SF RF
BF
AF
BH
AH
VH
XF
YF
N
M
2F 1F
2
H
1H
VF
YH
SH
RH
XH
F
H
N
M
Intersection of a Line and a Cone
1. Take any points X and Y on given line, get
their projections in HP and VP
2. Pass a cutting plane passing through the
points V, X, and Y;
3. Extend it to base and locate points S and R in
VP
4. Project S, R in HP view; S, R cuts cone at 1-2
at the base in HP;
5. Project 1-2 in VP
6. M is the point of intersection of V-2 with AB;
and N is the point of intersection of V-1 with
AB; project M and N in FV.
7. Points M and N are the desired points of
intersection where the given line pierces the
given cone
7

8. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
H
F
5H, 10H 6H, 11H
9H, 14H
7H, 12H
8H, 13H
2H
RH
1H
SH
YH
4H
3H
XH
5F
2F
XF
3F
4F
YF
9F 8F 6F 7F
1F
SF
RF
Two lines pierce a Prism:
Locate points of
intersections in Top and
Front views
10F 14F 13F 11F 12F

9. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
H
F
5H10H 6H11H
9H14H
7H12H
8H13H
2H
RH
1H SH
YH
4H
3H
XH
5F
2F
XF 3F
4F
YF
9F 8F 6F 7F
12F
11F
13F
14F
10F
1F
SF
RF
Expected number of intersection points = 6
When an EV exists and a line hits it, intersection
point is immediately available
Plane and Prism Intersection
See the top view and immediately
locate 4 intersection points
For the other two points:lo
Draw line R-S through point 9-14 in
top view – line R-S is on plane 1-2-
3-4 .
Look for point of intersection
between line R-S and line 9-14
Draw a line X-Y through point 7-12
in top view – line XY is on plane 1-
2-3-4
Look for point of intersection
between line X-Y and line 7-12
Join the intersection points in
front and top views to get the
lines of intersection.

10. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Intersection of a Plane and a Cone
• Method 1: Selected Line Method - When an edge view (EV) of the plane is available!
1
2
3
4
5
6
7
8
9
10
11
12
v
v
1
2 3 4 5 6
7
8
9
10
11
12
a
b
c
l
k
d
j
e
i
f h
g
1) In FP, the cone is seen as a triangle and the
plane as Edge View.
2) Draw lines V-1, V-2 , etc. called ‘elements’
or ‘generators’ in top and front views.
3) The points of intersection of ‘generators’
and EV give the ‘line of intersection’ of
plane and cone in FP.
4) Locate the points of intersection
(e and i) in the HP.
5) Similarly, locate all other points of
intersection in top view and draw the
‘curve of intersection.’
6) What will be the shape of the ‘curve of
intersection’ in top view?
Plane in EV
i
e
a
b
c d
f
g
h
j
k
l
HP
FP

11. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
BH
AH
CH
AF
CF
BF
Take several vertical cutting planes (parallel to the axis of the
cylinder)
Two intersection points obtained in front view per cutting plane
Take more cutting planes for more points
H
F
Intersection of Cylinder with a Plane
Cutting Plane Method

12. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Intersection of a Plane and a Pyramid
Ch
Bh
Ah
Oh
Cv
Bv
Av
Ov
Sv
Qh
Ph
Rh
Sh
Rv
Qv
Pv
1v
2v
3v
4v
5v
5h
4h
2h
1h
Cutting Plane Method
Check visibility for:
1) Path of intersection
2) Plane and solid
3h
VP
HP
Check intersection of:
1) PQ with AOB
2) RS with BOC
3) BO with PQRS
4) PQ with AOC
5) RS with AOC

13. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Edge View Method
BH
AH
CH
AF
CF
BF
H
F
H
A
TL
BA
AA
CA

14. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
14
:: THANK YOU ::