1. CIVL3310 STRUCTURAL ANALYSIS
Chapter 6:
Influence Lines for Statically Determinate Structures
CIVL3310 STRUCTURAL ANALYSIS
Professor CC Chang

2. Why Influence Lines? Vmax and Mmax under dead & live loads?
Concentrated
Live Load
Concentrated
Live Load
Concentrated
Live Load w P
Distributed Live Load
Distributed Live Load
Distributed Live Load
Dead Load A B C D V M
Analysis
w, P
V, M
Design
Note: loads can vary- LIVE LOADS
Vmax and Mmax under dead & live loads?

3. Can my bridge survive?

4. What is Influence Line ?
Force

5. Influence Lines Measurement

6. KSM Influence Lines Measurement

7. KSM Influence Lines Measurement

8. Influence Lines Shear force and moment diagrams Fixed loads V M x
V and M at different locations of the beam x
Influence Lines
Load moves along the beam V M x x
V and M at a fixed location

9. Influence Lines Influence line:
A graph of a response function (such as reactions or internal forces) of a structure as a function of the position of a downward unit load moving across the structure
Response
Location of downward unit load

10. Constructing Influence Lines
Point-by-point calculation
Influence-line equation
Graphical approach: Müller Breslau Principle

11. Point-by-point calculation
Construct the influence line for Ay

12. Influence-line equation
Linear function of x

13. Influence Lines
All statically determinate structures have influence lines that consist of straight line segments
More examples!

14. Müller Breslau Principle
Influence line for any action (reaction, internal shear/moment) in a structure is equal to the deflection curve when we remove the action and replace it with a corresponding unit displacement or rotation
Influence line = properly disturbed shape

15. Müller Breslau Principle

16. Virtual work principle for a rigid-body system
Virtual deformation
A structure in equilibrium:
imaginary deformation
Resultant force=0
Virtual work:
Virtual work principle for a rigid-body system

17. Müller Breslau Principle
Influence line = properly disturbed shape x 1 Ay By 1 Ay 1 Ay 1
f(x) By
Influence line of Ay
Virtual work

18. Müller Breslau Principle
Influence line = properly disturbed shape x 1 Ay By 1 By 1 By
Influence line of By 1
f(x) Ay
Virtual work

19. Müller Breslau Principle
Influence line = properly disturbed shape
Include ONLY the reaction/force in the virtual work x 1 V Ay By V M
f(x) 1 D2 1 q2 q1 Ay D1 By M V = 1 =

20. Müller Breslau Principle
Influence line = properly disturbed shape
Include ONLY the reaction/force in the virtual work x 1 M Ay By V M
f(x) 1 D 1 q1 q2 Ay By = 1

21. Müller Breslau Principle
Influence line = properly disturbed shape
Deflect the structure such that only the force which influence line that you are looking for and the downward unit force contribute to the virtual work due to the imaginary deflection.
All other forces that act on the virtually deflected structure should not contribute to the virtual work.

22. Influence Lines for Floor Girders
Draw the influence line for the shear in panel CD of the floor girder

23. Influence Lines for Trusses

24. Example 6.15
Draw the influence line for member force GB

25. Example 6.15
Draw the influence line for the member force GB

26. Application of Influence Lines1 1 wl SB MB A B C D a b SB MB y

27. Distributed Loads Concentrated Concentrated Concentrated Live Load
Distributed Live Load
Distributed Live Load
Distributed Live Load
Dead Load A B C D

28. Application of Influence Lines
Concentrated
Live Load P
Given dead load
and live loads
Find maximum forces
Distributed Live Load wl 1 wd A B C D SB MB

29. Application of Influence Lines
Max shear force at C?

30. Application of Influence Lines
Max shear force at C?

31. 6. Influence Lines What is influence line? Müller Breslau Principle
What is the use of influence line?