The document summarizes the moment distribution method for structural analysis. It includes the following key points: - The moment distribution method is an iterative approach that distributes joint moments in continuous beams and rigid frames through successive approximations. - It calculates member stiffness factors based on the member's properties and boundary conditions. Distribution factors are then determined as the member stiffness over the total stiffness. - An initial set of joint moments is assumed and distributed to each member based on the distribution factors. New joint moments are calculated and the process is repeated until the values converge. - The method is demonstrated on a sample frame, showing the iterative calculations, distribution of moments to members, and convergence to the final fixed end moments.

1. Structural Analysis
UNIT 4
MOMENT DISTRIBUTION METHOD
Dr. Mohammad Ahmed Hussain, 2nd Year 2nd Sem

2. Introduction
(Method developed by Prof. Hardy Cross in 1932)
The method solves for the joint moments in continuous beams and
rigid frames by successive approximation.
Moment distribution method is basically a displacement method of
analysis.
This method side steps the calculation of the displacement and instead
makes it possible to apply a series of converging corrections that allow
direct calculation of the end moments.
MOMENT DISTRIBUTION METHOD -
INTRODUCTION AND BASIC PRINCIPLES

3. Basic Principles and definitions
Member stiffness factor
A clockwise moment MA is applied at A to
produce a +ve bending in beam AB.
B
A
MA
MB
A
A
RA RB
L
A
MA
A B
RA RB
L
AA
L
EI
M 
4
 AA
L
EI
M 
3

Case 1: Far End Fixed Case 2: Far End Hinged
Stiffness factor L
EI
K
4
 Stiffness factor L
EI
K
3


4. 2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A B C D
I 2I I
3 m
2.5 m
Fixed end moments

5. Fixed end moments
8
)5)(8(
8
8
)5)(8(
8
)6(
)3)(2)(5(
)6(
)2)(3)(5(
12
)6)(2(
12
12
)6)(2(
12
2
2
2
2
2
2
2
2
22
22






wl
M
wl
M
l
wba
M
l
wab
M
wl
M
wl
M
FDC
FCD
FCB
FBC
FBA
FAB
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A B C D
I 2I I
3 m
2.5 m

6. Fixed end moments
kNm
wl
M
kNm
wl
M
kNm
l
wba
M
kNm
l
wab
M
kNm
wl
M
kNm
wl
M
FDC
FCD
FCB
FBC
FBA
FAB
5
8
)5)(8(
8
5
8
)5)(8(
8
6.3
)6(
)3)(2)(5(
4.2
)6(
)2)(3)(5(
6
12
)6)(2(
12
6
12
)6)(2(
12
2
2
2
2
2
2
2
2
22
22






2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A B C D
I 2I I
3 m
2.5 m

7. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/6
BC 4E2I/5
C
CB 4E2I/5
CD 4EI/5
Distribution Factors
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A B C D
I 2I I
3 m
2.5 m

8. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/6 5/17
BC 4E2I/5 12/17
C
CB 4E2I/5 2/3
CD 4EI/5 1/3
Distribution Factors
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A B C D
I 2I I
3 m
2.5 m

9. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 +5.0

10. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 +5.0
-1.06 -2.54 +0.93 +0.47

11. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 +5.0
-1.06 -2.54 +0.93 +0.47

12. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 +5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23

13. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42

14. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42

15. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21

16. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05

17. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05

18. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05
+0.05 -0.15-0.06 +0.025

19. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05
+0.05 -0.15-0.06 +0.025
-0.02 -0.03 0.1 0.05

20. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C.O to
fixed end
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05
+0.05 -0.15-0.06 +0.025
-0.02 -0.03 0.1 0.05

21. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C.O to
fixed end
Final
Moments
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05
+0.05 -0.15-0.06 +0.025
-0.02 -0.03 0.1 0.05
-0.01 +0.025

22. F E M
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C.O to
fixed end
Final
Moments
A CB D
5/17 12/17 2/3 1/3
-6.0 6.0 -2.4 3.6 -5.0 5.0
-1.06 -2.54 +0.93 +0.47
+0.46 -1.27-0.53 +0.23
-0.14 -0.32 0.85 0.42
+0.42 -0.16-0.07 +0.21
-0.12 -0.30 0.11 0.05
+0.05 -0.15-0.06 +0.025
-0.02 -0.03 0.1 0.05
-0.01 +0.025
-6.67 +4.66 -4.66 +4.01 -4.01 5.49

23. Fixed end moments
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A
B C D
I 2I I
3 m
2.5 m

24. Fixed end moments
kNm
wl
M
kNm
wl
M
kNm
l
wba
M
kNm
l
wab
M
kNm
wl
M
kNm
wl
M
FDC
FCD
FCB
FBC
FBA
FAB
5
8
)5)(8(
8
5
8
)5)(8(
8
6.3
)6(
)3)(2)(5(
4.2
)6(
)2)(3)(5(
6
12
)6)(2(
12
6
12
)6)(2(
12
2
2
2
2
2
2
2
2
22
22






2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A
B C D
I 2I I
3 m
2.5 m

25. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 3EI/6
BC 4E2I/5
C
CB 4E2I/5
CD 3EI/5
Distribution Factors
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A
B C D
I 2I I
3 m
2.5 m

26. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 3EI/6 5/21
BC 4E2I/5 16/21
C
CB 4E2I/5 8/11
CD 3EI/5 3/11
Distribution Factors
2 kN/m 8 kN5 kN
6 m 5m 2.5 m
A
B C D
I 2I I
3 m
2.5 m

27. F E M
Release
Jt . A and D
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0

28. F E M
Release
Jt . A and D
C. O
Initial Moment
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5

29. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5

30. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06

31. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06

32. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52

33. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69

34. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69

35. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54

36. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14

37. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35

38. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1

39. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1

40. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07

41. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07
-0.03 -0.09 0.05 0.02

42. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07
-0.03 -0.09 0.05 0.02
+0.02 -0.05

43. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07
-0.03 -0.09 0.05 0.02
+0.02 -0.05
-0.01 -0.01 0.03 0.02

44. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
Final Moments
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07
-0.03 -0.09 0.05 0.02
+0.02 -0.05
-0.01 -0.01 0.03 0.02

45. F E M
Release
Jt . A and D
C. O
Initial Moment
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
C. O
Balance
Final Moments
A CB D
5/21 16/21 8/11 3/11
-6.0 6.0 -2.4 3.6 -5.0 +5.0
6.0 -5.0
3.0 -2.5
9.0 -2.4 3.6 -7.5
-1.56 -5.04 2.84 1.06
+1.42 -2.52
-0.34 -1.08 1.83 0.69
+0.92 -0.54
-0.22 -0.70 0.40 0.14
+0.20 -0.35
-0.05 -0.15 0.25 0.1
+0.12 -0.07
-0.03 -0.09 0.05 0.02
+0.02 -0.05
-0.01 -0.01 0.03 0.02
6.79 -6.79 5.46 -5.460 0

46. 3 m 2m 2 m
A B C D
I I I
Support B sinks by 30 mm
I = 3 X 106 mm4
E =2 X 105 N/mm2
0
6
6
2
2



FDCFCD
FCBFBC
FBAFAB
MM
l
EI
MM
l
EI
MM


F E M
Since no external loads coming on to the
Structure the FEM comprise only due to the
Moment induced due to sinking of supports

47. 3 m 2m 2 m
A B C D
I I I
Support B sinks by 30 mm
I = 3 X 106 mm4
E =2 X 105 N/mm2
0
27
6
12
6
2
2



FDCFCD
FCBFBC
FBAFAB
MM
kNm
l
EI
MM
kNm
l
EI
MM



48. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/3
BC 4EI/2
C
CB 4EI/2
CD 4EI/2
Distribution Factors
3 m 2m 2 m
A B C D
I I I

49. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/3 0.4
BC 4EI/2 0.6
C
CB 4EI/2 0.5
CD 4EI/2 0.5
Distribution Factors
3 m 2m 2 m
A B C D
I I I

50. F E M
Balance
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27

51. F E M
Balance
C. O
Balance
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

52. F E M
Balance
C. O
Balance
-3.0 -6.75 -4.5 -6.75
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

53. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

54. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

55. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35 1.13 2.03 1.13
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

56. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

57. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22 -0.5 -0.34 -0.51
C. O
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

58. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

59. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1 0.08 0.15 0.08
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

60. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1
-0.03
0.08 0.15
-0.05 -0.08
0.08
-0.07
C. O
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

61. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1
-0.03
0.08 0.15
-0.05 -0.08
0.08
-0.07
C. O
Balance
-0.02 -0.04 -0.03 -0.03
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

62. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1
-0.03
0.08 0.15
-0.05 -0.08
0.08
-0.07
C. O
Balance
-0.02
0.02
-0.04 -0.03
0.02 0.01
-0.03
0.02
C. O to A and D 0.01 0.01
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

63. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1
-0.03
0.08 0.15
-0.05 -0.08
0.08
-0.07
C. O
Balance
-0.02
0.02
-0.04 -0.03
0.02 0.01
-0.03
0.02
C. O to A and D 0.01 0.01
Final Moments
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

64. F E M
Balance
C. O
Balance
-3.0
2.7
-6.75 -4.5
4.05 +2.25
-6.75
+2.25
C. O
Balance
+1.35
-0.45
1.13 2.03
-0.68 -1.01
1.13
-1.02
C. O
Balance
-0.22
0.2
-0.5 -0.34
0.3 0.17
-0.51
0.17
C. O
Balance
0.1
-0.03
0.08 0.15
-0.05 -0.08
0.08
-0.07
C. O
Balance
-0.02
0.02
-0.04 -0.03
0.02 0.01
-0.03
0.02
C. O to A and D 0.01 0.01
Final Moments -13.78 -15.56 +15.56 +12.15 -12.15 -6.07
A CB D
0.4 0.6 0.5 0.5
-12.0 -12.0 27 27
-6.0 -9.0 -13.5 -13.5

65. 12
12
6
6
6
12
6
12
2
2
22
2
22
2
2
2
2
2
wl
M
wl
M
l
EI
l
wba
M
l
EI
l
wab
M
l
EIwl
M
l
EIwl
M
FDC
FCD
FCB
FBC
FBA
FAB









Support B sinks by 10 mm
I = 1.2 X 10-4 m4
E =2 X 105 N/mm2

66. kNm26.67
kNm26.67-
kNm93.6
kNm33.6
kNm20
kNm100-






12
12
6
6
6
12
6
12
2
2
22
2
22
2
2
2
2
2
wl
M
wl
M
l
EI
l
wba
M
l
EI
l
wab
M
l
EIwl
M
l
EIwl
M
FDC
FCD
FCB
FBC
FBA
FAB




Support B sinks by 10 mm
I = 1.2 X 10-4 m4
E =2 X 105 N/mm2

67. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/6
BC 4EI/5
C
CB 4EI/5
CD 3EI/4
Distribution factor

68. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 4EI/6 0.46
BC 4EI/5 0.54
C
CB 4EI/5 0.51
CD 3EI/4 0.49
Distribution factor

78. 2
812
812
12
12
2
2
2
2
2
2
2
2
wlFDE
FDC
FCD
FCB
FBC
FBA
FAB
M
l
wba
M
l
wab
M
wlwl
M
wlwl
M
wl
M
wl
M






Fixed End Moments

79. 10
2
2
2
2
2
2
2
2
2
3
9
41
812
41
812
4
12
4
12







wlFDE
FDC
FCD
FCB
FBC
FBA
FAB
M
kNm
l
wba
M
kNm
l
wab
M
kNm
wlwl
M
kNm
wlwl
M
kNm
wl
M
kNm
wl
MFixed End Moments

80. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 3E3I/4
BC 4E10I/8
C
CB 4E10I/8
CD 3E2I/4
Note: Since support ‘A’ is simply supported end the absolute stiffness was calculated by
(3EI/L) and also since ‘D’ can be considered as simply supported with a definite
moment , therefore the absolute stiffness of CD has also been calculated using the
formula (3EI/L)
.

81. Joint Member Absolute
Stiffness
Distribution
Factor
( k / ∑k )
B
BA 3E3I/4 0.31
BC 4E10I/8 0.69
C
CB 4E10I/8 0.77
CD 3E2I/4 0.23

92. 2 kN/m 10 kN
1.5 m 3m 1 m
A
B C D
I 2I I
2 m1.5 m
12kN
Assignment -1
Find The Final Moments from slope deflection method and
Moment Distribution method and Draw Bending Moment diagram
2 kN/m 9 kN
1.5 m
3m
1 m
A
B C D
I I 2I
2 m1.5 m
8 kN
8 kN
1.5 m

93. 4 kN/m 5 kN
1.5 m 3m 1 m
A
B C D
I I I
2 m1.5 m
6 kN
Support C sinks by 20 mm
I = 2.4 X 106 mm4
E =2 X 105 N/mm2
2 kN/m 9 kN
1.5 m 3m 1 m
A
B C D
I I I
2 m1.5 m
8 kN
Support A sinks by 10 mm
Support B sinks by 30 mm
Support C sinks by 20 mm
I = 2.4 X 106 mm4
E =2 X 105 N/mm2