Influence Line of Reaction for Determinate
Structure Due to Moving Load
Presented byMd. Nasim Anjum
Dept. of Civil Engineering
Ahsanullah University of Science & Technology
An influence line is a diagram whose ordinates, which are
plotted as a function of distance along the span, give the value
of an internal force, a reaction, or a displacement at a
particular point in a structure as a unit load move across the
Variation of Reaction, shear & Moment at a specific point on a
structure as a concentrated load (one unit) moves over the
NOTE: Influence lines for statically determinate structures are always
Qualitative Influence Lines
“If any deforming function – stress, shear, moment or
reaction is allowed to act through a very small unit
displacement the resulting shape of the deflected
structure will be an influence line for that function” (T. C.
Shedd and J. Vawter.)
Why do we need the influence lines?
Influence lines are used to determine where to determine
for maximum result & to compute the resulting magnitude
of the reaction or other actions once the loads are placed in
their critical position.
For instance, when loads pass over a structure, say a
bridge, one needs to know when the maximum values of
shear/reaction/bending-moment will occur at a point so
that the section may be designed.
The influence line for a response function is given by the
deflected shape of the released structure due to a unit
displacement (or rotation) at the location and in the direction
of the response function.
A released structure is obtained by removing the
displacement constraint corresponding to the response
function of interest from the original structure.
CAUTION: Principle is only valid for force response functions.
Support reaction - remove translational support restraint.
Internal shear - introduce an internal glide support to allow differential displacement movement.
Bending moment - introduce an internal hinge to allow differential rotation movement.
Structure Subjected to a variable position loads.
Influence lines for Reaction
As an example, an influence line for
the left reaction of a beam can be
generated by placing a unit vertical
displacement at the reaction point, in
the direction of that reaction.
By the same method, an influence line for
the reaction at B can be found by simply
distorting the reaction at B upwards a unit
distortion & form its own Influence Line
δy = 1
Moving Concentrated Load
Variation of Reaction RA & RB as function of
Determine the maximum reaction at support B on the beam shown due to a single concentrate
live load of 8000 N, a uniform live load of 3000 N/m, a beam weight (dead load) of 1000 N/m.
= 48000 N = 48 KN