CE 332  Introduction
to
Influence
Lines (Ch, 6 in Hibbeler)
What is an influence line?
A diagram used when you have movable (i.e. live) loads that shows the
effect of
the location
of that movable load on a specified:
Reaction
Moment
at a given point
Shear
at a given point
Axial force
at a given point
Deformation
at a given point
An influence line is simply a graph. For each point on the graph
(X"Yl),
the x
value is the location on the beam of a concentrated, unit force. The corresponding
Yvalue
(Yl)
is the value of the function for which the influence line is made when
the unit force is located at
XL·
Influence lines help us determine where live loads should be placed on a structure
to create the maximum reaction, shear, moment or axial force at a specific
location that a structure will experience.
Example:
Calculate the Influence Line for the vertical
reaction
(R.J at A due to the
point live1oad, P. For convenience, set P =
t.
C
A
B
LI ~/tl
, I I
L
e
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View Full DocumentApply a unit load at various locations on the structure and calculate RAfor each:
Load at A: R
A
=
I
x
R
Load halfway between A and B: RA
=
0.5
o
U2
L
L+e
I
0.5
o
elL
Load at B: RA=
0
Load at C:
EMB: I(e)
+
RA(L) = 0
+
RA=
elL
Connect the points to get the Influence Line.
I
CA======:n:r:r=:::::::=:I
C
f; ]
elL
B
NOTE:
Influence
lines are not moment
diagrams,
shear diagrams,
axial diagrams,
or deflected
shapes.
Influence
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 Fall '10
 Hosteng
 Force, Shear Stress, Line segment, Hibbeler, influence line

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