Kinematic Method and Müller-Breslau Principle

The kinematic method for influence lines is based on the Müller-Breslau principle. It determines the influence-line shape without moving a unit force through many positions and is particularly useful for qualitative analysis of more complex structures.

Müller-Breslau principle

To obtain the influence line for a reaction or internal force effect, release the restraint associated with that response and impose a small positive generalized displacement in its positive direction. The resulting compatible displacement shape of the released system is proportional to the influence line.

Support reaction

For a vertical support reaction, remove the corresponding vertical restraint and impose a unit vertical displacement in the positive reaction direction. The kinematically admissible displaced shape indicates the sign and geometry of the influence line.

Bending moment and shear

For bending moment at a section, introduce a hinge at that section, thereby releasing moment transfer, and impose a positive relative rotation of the two parts. For shear, introduce the corresponding relative transverse displacement across the cut.

Statically determinate structures

Releasing one restraint in a determinate structure creates a mechanism composed of rigid parts, so its displacement shape is often piecewise linear. The method gives shape and sign; the scale follows from the imposed unit generalized displacement.