# Influence Line

## Influence Lines for Beams

A downward concentrated load of magnitude 1 unit moves across the simply supported beam *AB* from *A* to *B*. We wish to determine the following functions:

- reaction at
*A* - reaction at
*B* - shear at
*C*and - moment at
*C*

when the unit load is at a distance *x* from support *A*. Since the value of the above functions will vary according to the location of the unit load, the best way to represent these functions is by influence diagram.

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## Influence Lines

Influence line is the graphical representation of the response function of the structure as the downward unit load moves across the structure. The ordinate of the influence line show the magnitude and character of the function.

The most common response functions of our interest are *support reaction*, *shear at a section*, *bending moment at a section*, and *force in truss member*.

With the aid of influence diagram, we can...

- determine the position of the load to cause maximum response in the function.
- calculate the maximum value of the function.

Value of the function for any type of load

$\displaystyle \text{Function} = \int_{x_1}^{x_2} y_i (y \, dx)$

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