SUBMITTED TO : GALIB SIR SUBMITTED BY : MD. RIFAT HASSAN 09.01.03.008 AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

1. Determining Maximum/Minimum Reaction Due To Moving load
SUBMITTED BY
MD RIFAT HASSAN
09.01.03.008
DEPT. OF CE
4TH YEAR, 2ND SEMESTER
AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

2. DEFINITION
IMPORTANCE & NOTATION
INFLUENCE LINE DRAWING PROCEDURE
MATHMATICAL EXAMPLE OF DETERMINING MAXIMUM AND MINIMUM REACTION

3. DEFINITION OF INFLUENCE
LINE,DETERMINATE
STRUCTURE, MOVING LOAD
INFLUENCE LINE
Influence lines describe the variation of an analysis variable (reaction, shear
force, bending moment, twisting moment, deflection, etc.) at a point
DETERMINATE STRUCTURE
Statical determinacy is a term used in structural mechanics to describe a
structure where force and moment equilibrium conditions alone can be utilized
to calculate internal member actions.
MOVING LOAD
In structural dynamics this is the load that changes in time the place to which is
applied. Examples: vehicles that pass bridges, trains on the
track, guideways, etc.

4. Why do we need the influence lines?
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
Notations:
Normal Forces - +ve forces cause +ve displacements in +ve directions
Shear Forces - +ve shear forces cause clockwise rotation & - ve shear
force causes anti-clockwise rotation
Bending Moments: +ve bending moments cause “cup holding water”
deformed shape

5. Influence lines for moving loads
Procedure:
(1) Allow a unit load (either 1b, 1N, 1kip, or 1 tonne) to move
over beam from left to right
(2) Find the values of shear force or bending moment, at the
point under consideration, as the unit load moves over the
beam from left to right
(3) Plot the values of the shear force or bending moment, over
the length of the beam, computed for the point under
consideration

8. Live Loads for Railroad BRIDGES

9. • Devised by
LOAD
Theodore Cooper
DESIGNITION
• Loading on Driving
E -72
axle
M -72
• Devised by D.B.
Steinman
• Loading on Driving
Axle

10. Maximum “support reaction”due
to wheel load

11. Equation of reaction
∆R = {(ΣP) d1 +
P' e}/L − P1
Considering the difference of support
reaction at A (∆R) between cases with
wheel W1 at A [(ii) in Fig. 1] and wheel
W2 at A [(iii) in Fig. 1], the increase in
support reaction is due to the shift d1 of
load ΣP; i.e., an increase of ordinate by
an amount d1/L. Moreover, there is an
additional increase due to the new load
P' moving a distance e within the
influence line (ordinate increases e/L).
However, since the load P1 has moved
out of the influence line; i.e., its ordinate
decreases by 1, there is a further
decrease of P1 in the support reaction.
Therefore, the overall change of reaction
between (ii) and (iii) is given by

12. SAMPLE CALCULATION OF DETERMINING MAXIMUM
MINIMUM REACTION DUE TO MOVING LOAD

13. SAMPLE CALCULATION OF DETERMINING MAXIMUM
MINIMUM REACTION DUE TO MOVING LOAD

14. SAMPLE CALCULATION OF DETERMINING MAXIMUM
MINIMUM REACTION DUE TO MOVING LOAD

15. Reaction due to moving
concentrated load
FIGURE OF MOVING
CONCENTRATED LOAD
EQUATION FOR REACTION