An influence line shows the variation of shear, moment, reaction, or member stress in a structure due to a moving unit load. It is constructed by plotting the value of the specific function as a unit load is moved along the structure. Influence lines for determinate structures are always straight lines. To construct an influence line, the effect of a unit load is observed as it is moved along the span, and the controlling ordinates are calculated and plotted. The Muller-Breslau principle states that the ordinates of an influence line are proportional to the deflected shape of the structure if the capacity for a specific force is removed and an equivalent displacement is introduced.

1. 1

2. 2
Influence Line
It is the diagram showing the variation in the shear,
moment, reaction, stress in a truss member or any other
direct function due to a unit load moving across the
structure. An influence line is constructed by plotting
direct under the point, where the unit load is placed. An
ordinate the height of which represents to some scale the
value of the particular function being studied when the
load is in that position.
For determinate structures influence lines are always
straight lines.

3.  First>>> Decide how the stress is to be
calculated.
 Second>> Move the unit load along the span and
observe the effect on the stress in question.
 Third>>> Calculate the controlling ordinates on
the influence line and complete the diagram.
3
Influence Line

4. 4
 
 
0; ,
1 0
1
B
A
A
M clockwise ve
R L L x
L x x
R
L L
 
   

   

 0; ,
1 0
1 1 0
BA
B
B
V upward ve
R R
x
R
L
x
R
L
 
  
    
 

Influence Line of Beam

5. 5
 0; ,
1 0
, 1
A
B
B
A
M clockwise ve
a R L
a
R
L
a
and R
L
 
   
 
 

 0; ,
0BC
BC
V upward ve
V R
V R
 
 
  

 0; ,
0C A
C A
V upward ve
V R
V R
 
  
 

IL of VC:
When load at left side of point C;
When load at right side of point C;

6. 6
 
 
 
 
0; ,
0
C
B
C
BC
C
M L a
R L a
a
M L a
L
M clockwise ve
R
M
 

  
 

 

 
 1
0; ,
0
C
C
C A
BC
a
a a
M a L a
L L
M clockwise ve
M R
M aR

 
     
 
 
  
 

IL of MC:
When load at left side of point C;
When load at right side of point C;

7. Muller-Breslau Principle :
The ordinates of an influence line for any force are proportional to
the deflected shape of the structure produce by removing the
capacity of the structure to carry the force and then introducing
into the modified structure. A displacement the corresponds to the
restrained removed.
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8. 8

9. 9

10. 10
Calculation

11. 11

12. 12

13. Calculation
13

14. 14

15. 15

16. Calculation
16

17. 17

18. 18

19. Calculation
19

20. 20

21. 21
More in PDF File (Influence line of girder & Truss).

22. 22
Influence Lines of Truss

23. 23

24. 24
Calculation

25. Calculation (Cont’d)
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26. Calculation (Cont’d)
26

27. 27

28. Calculation
28

29. 29
Calculation (Cont’d)

30. 30
Calculation (Cont’d)

31. 31
Calculation (Cont’d)

32. 32

33. Calculation
33

34. 34
Calculation (Cont’d)
More problems in PDF File (Influence line of girder & Truss).