Structural Analysis - Applications of Influence Line Diagram

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Applications of Influence Line Diagram

From the influence line we can determine the response (reaction, shear, moment etc. ) of a structure due to multiple point loads as well as due to uniform load. Influence line also helps in finding the maximum value of a response function.

Response due to Point Load

Response due to single point load = magnitude of load x ordinate of ILD at the position of point load.
Response due to multiple point loads = equal to the algebraic sum of the product of load and the corresponding ordinate of ILD.

Illustrative Example: Consider A simply supported beam (figure 1) having a span of 7 m.
Influence line diagram application

The reaction at support B due to 10 kN load will be equal to (10) x (value of ordinate at 2m from the ILD for R_B) = 10 x (2/7) = 20/7 kN.

Similarly the reaction at B due to 5 kN load would be equal to (5) x (value of ordinate at 5 m from the ILD for R_B) = 5 x (5/7) = 25/7 kN
Reaction at support B due to both the loads = 10 x (2/7) + 5 x (5/7)
= 20/7 + 25/7 = 45/7 kN = 6.43 kN

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