Momentenlinien

Momentenlinien, also known as influence lines, are graphical representations used in structural engineering to visualize the variation of a structural element's internal force or reaction at a specific point as a unit load moves across the structure. They are particularly useful for determining the maximum possible values of shear forces, bending moments, and reactions that a structure might experience under a moving load.

The construction of a momentenlinie involves imagining a unit load of magnitude 1 moving across the structure, typically from one end to the other. For each position of the unit load, the corresponding value of the internal force or reaction at the point of interest is calculated. Plotting these calculated values against the position of the unit load creates the momentenlinie. The vertical ordinate at any point on the line represents the magnitude of the force or reaction when the unit load is at that specific horizontal position.

For bending momentenlinien, the area under the curve multiplied by the magnitude of the moving load gives the actual bending moment at the section. Similarly, for shear force momentenlinien, the ordinate directly represents the shear force at the section when the unit load is at that position. Reactions are also plotted in a similar fashion.

Momentenlinien are indispensable for designing structures that will be subjected to moving loads, such as bridges, cranes, and railway tracks. By examining the momentenlinie, engineers can easily identify the load positions that will produce the critical or maximum values of internal forces and reactions, thereby ensuring the safety and efficiency of the design. They simplify complex calculations by providing a visual and intuitive understanding of load effects.