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Information about Influence line of reaction for determinate structure: determining...

SUBMITTED TO : GALIB SIR

SUBMITTED BY : MD. RIFAT HASSAN

09.01.03.008

AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

SUBMITTED BY : MD. RIFAT HASSAN

09.01.03.008

AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

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DEFINITION 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 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.

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

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

• Devised by LOAD Theodore Cooper DESIGNITION • Loading on Driving E -72 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 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

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 load FIGURE OF MOVING CONCENTRATED LOAD EQUATION FOR REACTION

... structure: determining maximum /minimum ... INFLUENCE LINE,DETERMINATE STRUCTURE, MOVING LOAD ... MAXIMUM MINIMUM REACTION DUE TO MOVING LOAD.

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... along the line. The scaled maximum and minimum are the ... line.” Instead of moving a unit load ... reaction’s influence line ...

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For a statically determinate structure the influence line ... C Load case for maximum negative reaction ... Influence lines Influence line ...

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... on Influence line of shear for determinate structure : Determinate max/min shear due to moving load. this ... determining maximum /minimum reaction due ...

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Calculation of Maximum and Minimum Shear Force ... the influence line and the uniform load is ... the influence line III Net area IV Force due ...

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... along the line. The scaled maximum and minimum are the ... line.” Instead of moving a unit load ... reaction’s influence line ...

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What is the use of influence line diagram ... Influence lines are useful in determining the load ... of a moving unit load as it crosses the structure from ...

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Learn and talk about Influence line , and check out ... line. The scaled maximum and minimum ... structure and determining ...

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