Influence line of reaction for determinate structure: determining maximum /minimum reaction due to moving load

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

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Influence line of reaction for determinate structure: determining maximum /minimum reaction due to moving load

  1. 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. 2. DEFINITION IMPORTANCE & NOTATION INFLUENCE LINE DRAWING PROCEDURE MATHMATICAL EXAMPLE OF DETERMINING MAXIMUM AND MINIMUM REACTION
  3. 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. 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. 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
  6. 6. Live Loads for Railroad BRIDGES
  7. 7. • Devised by LOAD Theodore Cooper DESIGNITION • Loading on Driving E -72 axle M -72 • Devised by D.B. Steinman • Loading on Driving Axle
  8. 8. Maximum “support reaction”due to wheel load
  9. 9. 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
  10. 10. SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD
  11. 11. SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD
  12. 12. SAMPLE CALCULATION OF DETERMINING MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD
  13. 13. Reaction due to moving concentrated load FIGURE OF MOVING CONCENTRATED LOAD EQUATION FOR REACTION

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