1) An influence line shows the variation of internal forces, reactions, or displacements at a point in a structure as a unit load moves across the structure. 2) Influence lines for determinate structures are always piecewise linear. They are generated by releasing the structure at the point of interest and applying a unit displacement or rotation. 3) Influence lines are used to find the critical load positions that cause maximum shear, reaction, or bending moment values so that the structure can be designed accordingly.

1. COURSE NO:CE-416
COURSE NAME: PRE-STRESSED CONCRETE SESSIONAL.
COURSE TEACHER: GALIB MUKTADIR & SABREENA NASRIN

2. Influence Line of Reaction for Determinate
Structure Due to Moving Load
Presented byMd. Nasim Anjum
ID:08.01.03.106
Dept. of Civil Engineering
Ahsanullah University of Science & Technology

3. DEFINITION
 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
structure.
 Variation of Reaction, shear & Moment at a specific point on a
structure as a concentrated load (one unit) moves over the
structure.
NOTE: Influence lines for statically determinate structures are always
piecewise linear.

4. 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.)

5. 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.

6. Muller-Breslau Principle
 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.
Releases:
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.

7. Structure Subjected to a variable position loads.

8. 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
1
A
B
L
δy = 1
B
A
Ay
By

9. Moving Concentrated Load
Variation of Reaction RA & RB as function of
load position.

10. RA occurs only at A; RB occurs only at B

11. EXAMPLE
 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.
4m
= 48000 N = 48 KN
4m
4m