INFLUENCE LINE OF REACTION FOR DETERMINATE STRUCTURE

Determining Maximum/Minimum Reaction Due To Moving load SUBMITTED BY

MD RIFAT HASSAN09.01.03.008DEPT. OF CE

4TH YEAR, 2ND SEMESTERAHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

INFLUENCE LINES FOR STATICALLY DETERMINATE STRUCTURES Determining Maximum /Minimum Reaction Due to Moving Load - AN OVERVIEWDEFINITION

IMPORTANCE & NOTATION

INFLUENCE LINE DRAWING PROCEDURE

MATHMATICAL EXAMPLE OF DETERMINING MAXIMUM AND MINIMUM REACTION

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 STRUCTUREStatical 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 LOADIn 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.

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 directionsShear Forces - +ve shear forces cause clockwise rotation & - ve shear force causes anti-clockwise rotationBending Moments: +ve bending moments cause “cup holding water” deformed shape

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

Live Loads for Railroad BRIDGES

LOAD DESIGNITION E -72

•Devised by Theodore Cooper•Loading on Driving axle

M -72 •Devised by D.B. Steinman•Loading on Driving Axle

Maximum “support reaction”due to wheel load

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 P; i.e., Σan 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

SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD

SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD

SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD

Reaction due to moving concentrated loadFIGURE OF MOVING CONCENTRATED LOAD

EQUATION FOR REACTION

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