ECIV 320 Structural Analysis I
Influence Lines
HOMEWORK
DUE 3/16/2009
6-15, 6-16, 6-26, 6-28
6-59, 6-68
So Far…
Analysis of Forces due to DEAD LOADS
DETERMINATE STRUCTURES
• Axial Force Elements - Trusses
• Compute element Forces
• Flexural Elements - Beams and Frames
• Shear and Moment Diagrams
LIVE LOADS
Common Structures
Bridges
Industrial Crane
Rails
Conveyors
Floor Girders
any other structure where
loads move across its span
ANALYSIS OF FORCES DUE TO
LIVE LOADS
LIVE or MOVING LOADS
•
•
Variable point of Application
Temporary Loads
P
V1
P
Shear Diagrams
V1  V2
V2
Definition of Influence Lines
QUESTION
Where should a structural engineer place the live load on
the structure so that it creates the greates influence at a
specified point?
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection
at a SPECIFIC POINT
due to a concentrated force moving on member
Procedure - METHOD I
Tabulate Values
• Place UNIT LOAD at a number of fixed locations
Perform a series of static analyses to determine the value of
reaction/shear/moment/deflection at the specific point. Tabulate Values
Sign Convention
Reaction is positive when it acts upwards on the beam
Shear and Moment as Before
HINT
Influence lines of statically determinate beams consist of straight line segments
Place unit load at points representing the end points of these segments
Example
Procedure - METHOD II
Influence Line Equations
•Place UNIT LOAD at a variable location x
Perform a static analysis to determine the function of
reaction/shear/moment/deflection at the specific point as a
function of x.
Example
Qualitative Influence Lines
Muller-Breslau Principle
Influence Line for a function is to the same scale as the
deflected shape of the beam when the beam is acted upon
by the function
Qualitative Influence Lines
Qualitative Influence Lines