The document describes the Williot-Mohr diagram method for finding unknown displacements in trusses. The Williot diagram assumes member lengths are zero and draws deformations to scale. However, it only works for cantilever and symmetrical trusses. The Mohr diagram corrects this by taking one member as vertical/horizontal after deformation. It rotates the truss 90 degrees from known supports. Displacements are measured as the length between nodes in the truss and diagram. The Williot-Mohr diagram combines these methods to provide a powerful graphical technique for analyzing truss deflections.

1. williot
Williot – Mohr Diagram

2. Williot – Mohr diagram
₰ It is a graphical method of finding the unknown displacement of
the truss.
₰ This method is very powerful method to find deflection in truss
₰ The analytic methods are so tedious, when it comes to finding
deflection or displacement.

3. 10 kN
T
T
C
C
Idea-ology

15. Only thing bad
about, this
method “its is
impossible”
Because
The deformation is so less
compared to length of the
member, the deformed truss
will actually look like the
actual truss…
So Williot have found a new method, Williot Diagram

16. williot
Williot Diagram

17. Williot diagram
→ The problem in the previous method the scale of member and
deformation is same .
→ So Williot assume members length are “Zero - 0”.
→ Deformation is drawn to suitable scale for desired accuracy.

18. TA B
C D E
T TC
C C
1
2 6
3 5
4
a,c 13
2
d
5
4
b
6

19. a,c
13
2
d
5
4
b
6
e
TA B
C D E
T TC
C C
1
2 6
3 5
4

20. williot
Worked Out Example
Williot Diagram

21. T
CC T
C
A B
3 m
D F G
1 2
3
4
5
7
6
T
200 kN 100 kN
C
3 m
4 m

22. T
CC T
C
A B C
D F G
1 2
3
4
5
7
6
T
200 kN 100 kN a,d
1
3
b
5
f
6
c
2
g
4
∆𝑪 𝑽 = 𝟐𝟎. 𝟎𝟎 𝒎𝒎
∆𝑪 𝑯 = 𝟓. 𝟖𝟎 𝒎𝒎

23. Problems with Williot diagram
₰ Only applicable for
cantilever truss
₰ And symmetrical
truss ( in loading, EI
, and support
condition )

24. Mohr
Williot Diagram corrected by
Mohr

25. 100 kN
9 m 9 m
3 m
A
B
C
FD
T
C
T
C CC T

26. 100 kN
9 m 9 m
3 m
A
B
C
FD
T
C
T
C CC T
a b
f
d
c

27. 100 kN
9 m 9 m
3 m
A
B
C
FD
T
C
T
C CC T
a b
f
d
c
AB
C
FD

28. a
b
f
d
c
A B
C
FD

29. Williot – Mohr diagram
₰ The Williot - Mohr diagram follow same procedure as
Williot diagram, but it takes one member as vertical or
horizontal after deformation
₰ After completing Williot diagram the truss is drawn at 90°
inclination in the Williot diagram from the known supports.
₰ The deformation is measured by finding the length
between node in truss and node in the Williot diagram.

30. You can now wake up your friends
near you

31. Basic idea
MEMBER LENGTH
ZERO
DEFORMATION TO
SCALE
Williot diagram
A MEMBER ASSUMED TO VERTICAL
OR HORIZONTAL
TRUSS IS ROTATED AND DRAWN AT
90°
THE NODAL DISPLACEMENT IS
MEASURED BY DIFFERENCE
Williot – Mohr diagram