Influence lines

Influence lines and mobile loads are used in the design of e.g. bridge structures where the effect of loads moving along the structure predominates. Once the calculation of influence lines has been performed, the linearity of the system allows for the evaluation of utilisation of influence lines with respect to the motion of an arbitrary load-system defined according to a particular technical standard or according to the judgment of the user.

The influence line represents the change of resultant or effect – of e.g. bending moment, shear force, etc. – in the particular point of a structure as a result of the move of unit load along the structure (following the given track).

It is important to say that the effect is evaluated in a fixed point. X-coordinate of individual influence lines represents the position of the unit load moving along the structure and the Y-coordinate of the same point corresponds to the effect caused by the unit load in the fixed point. The final aim is to find the position of the load-system which results in the maximal effect on the structure in the point.

The linearity of the system makes it possible to evaluate the motion of unit load along the structure and then calculate the utilisation of the mobile load-system consisting of several concentrated forces and distributed loads (e.g. a train on the rails) using the superposition of influence lines multiplied by the size of the load.

The influence lines and their utilisation are calculated for a fixed section. One can obtain an envelope of maximal effects and save other corresponding values. This envelope can be combined with a standard load (e.g. self-weight) and thus the overview of the overall behaviour of the structure can be obtained.