AHSANULLAH UNIVERSITY OF SCIENCE & TECHNOLOGY

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

Presented by-Md. Nasim AnjumID:08.01.03.106Dept. of Civil Engineering Ahsanullah University of Science & Technology

Influence Line of Reaction for Determinate Structure Due to

Moving Load

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.

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.)

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.

Why do we need the influence lines?

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.

Structure Subjected to a variable position loads.

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.

B

  1

A

L

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

δy = 1 A B

Ay By

Variation of Reaction RA & RB

as function of load position.

Moving Concentrated Load

RA occurs only at A; RB occurs only at B

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.

4 m 4 m 4 m

= 48000 N = 48 KN

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