Influence line

The interface reactions ( also internal forces or internal forces ) in statics show the interaction of forces and torques within a component. These are the forces and moments that must have placed in the external influences over the component to ( to break or to burst, for example ) not to fail. Therefore, the term " inner strength sizes " clearer. Interface reactions or internal forces are the forces that are visible when a so-called "cut".

Cutting principle

You can (for example, to simplify a calculation ) mentally "cut" each component with all loads at any location that is you have to disconnect it at this point and no longer pay attention to the rest of the component. However, since the cut-away rest of the component physically can not just disappear, its effect on the remaining pieces by the cutting forces is represented.

One must also not arbitrarily cut, but each section must be a so-called " round cut ". Round cut means that the cutting line on the one cuts along, in itself must be closed (round). At each edge formed by the intersection of the three cutting forces arise. One may cut any component anywhere as long as there is a round cut and all the forces ( internal forces and external loads ) are plotted.

The cutting forces in the plane

Interface reactions are subdivided in two-dimensional case in three components. The location of the reference coordinate system is sketched on the static system by the broken fiber. It specifies the location of the x -axis. The z -axis is then always dotted side.

• Shear force (V, formerly Q) - A force perpendicular to the dashed fiber of the component.
• Normal force (N ) - A force parallel to the dashed fiber of the component.
• Moment (M ) - The acting at the interface torque.

All cutting forces are vector quantities. That each force has a direction and every moment rotates either in clockwise or counterclockwise. Therefore, there is a positive definition of the directions.

When cutting through joints, the following applies:

State lines

If you move along the imaginary interface of the component, we obtain a function of the average responses over the entire displacement. With the help of calculus can then be the job of the strongest internal exposure of a component by a fixed external load calculated. As they describe the internal state of the component under the strain, called these functions also state lines. This calculation is normal and shear forces, bending and torsional accessible.

Influence lines

Interface reactions are also needed for the event that changed the loading of the component. This is especially necessary in bridge construction, as these structures are stressed by moving loads. The determination of the interface reactions occur exactly as described above from, the resulting functions are called because of the influence of the moving loads and influence lines. The evaluation of the influence line means that the actual load of the examined location is determined in the multiplying the ordinate of the influence line of the attack point of the force associated with the amount of force itself.

Calculate the average reaction

To calculate average reactions, there are a variety of ways. Depending on which system you have available. A general distinction:

Equilibrium principle

The method provides only for statically determinate systems unambiguous results. In statically indeterminate systems, there are too many unknowns to apply the principle of equilibrium. In this case, force or displacement method lead to a solution. The interface reactions ( in statically determinate systems ) normally are expected from using the balance principle. The equilibrium principle states that:

With these boundary conditions, equations are created ( one unknown ), which enable the missing forces or torques individually to calculate sequential. To this end one makes to the system to be examined several sections, in which only the one to search for force size is unknown as only one.