10. Moving Load

Midas Civil’s Moving Load analysis feature is used to reflect the conditions of live loads or static vehicle moving loads and is mainly used in the following ways:

• Deriving influence lines and influence surfaces for deflection, internal forces, and reactions caused by moving loads.
• Using the derived influence lines and influence surfaces to calculate and verify the maximum/minimum deflections, internal forces, and point reactions for given vehicle moving load conditions.

Moving load analysis performs analysis of loads induced by live loads or vehicle loads moving over a structure and calculates maximum or minimum values for the entire load path.

Influence lines or influence surfaces are useful for finding the location of the highest internal forces without the need for iterative analysis.

For vehicle loads, the lane or lane surface to be loaded with the vehicle load and the method of applying the vehicle load are defined, and the influence line or influence surface is calculated by loading the unit load on the lane or lane surface.

The influence line is the static analysis of the structural components along the structure by loading unit loads and representing the results of each component on the structure line.
The influence surface represents the results of analyzing the panel elements located within the structure's surface by applying unit loads on the panel's nodes.

The process of using influence lines or influence surfaces for analysis of moving loads can be summarized as follows:

1.Define the moving load, the method of load application, and the lane or lane surface.
2.Create the unit load condition and perform a static analysis for each unit load to calculate the influence lines or influence surfaces for each component.
3.Use the influence lines or influence surfaces according to the method of load application to determine the positions for the moving load, and calculate the analysis results accordingly.

The analysis results obtained through these processes have two interpretations, maximum and minimum, for one moving load condition, and can be combined with other load conditions.
Because the moving load condition has two interpretations, maximum and minimum, the combined result also has two interpretations, maximum and minimum.
The analysis results include joint displacement, point reaction force, truss, beam, and plate element internal force.

The unit load of the influence line or influence surface used in moving load analysis acts in the -Z direction of the global coordinate system, and there is no limit to the number of moving load analysis conditions that can be used.

According to Müller-Breslau's principle, the influence line represents the shape of the deformation of a structure when a unit displacement is introduced at the location where the reactions or sectional forces would be present. The reactions or sectional forces in the structure can be obtained from the shape of the influence line.

Figure 10.1 shows an influence line for a simple beam, and Figure 10.2 shows an influence line for a two-span continuous beam.

Figure 10.1 shows the influence lines for the reactions at points A and B, and the shear and moment at an arbitrary location for a simple beam.
Figure 10.2 shows the influence lines for the reactions at points A, B, and D, as well as the shear and moment at points B and C, for a two-span continuous beam.
It can be seen that the influence line for a statically determinate structure, such as a simple beam, consists of straight lines, while that of a statically indeterminate structure, such as a two-span continuous beam, consists of curves.
The value marked with ∆ at the point where the load is acting on the influence line represents the value of the corresponding reaction or section force when the load is applied at that point.

To explain the method for calculating sectional forces using influence lines, let's calculate the mid-span moment 𝑀. for a two-span continuous beam as shown in Figure 10.2(f).
Since we are dealing with the influence line for moments, we insert a hinge at point B to release the moment and apply a unit rotation at that point to create the deformation shape that represents the influence line.
The value of ∆ at the midpoint of span AB represents the value of 𝑀_𝐵when the moving load is located at that point. Since the structure is symmetrical with respect to point B, we can obtain ∆= 𝑀_𝐵 for one side of the simple beam when a moment 𝑀 is applied.