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# The output results are the same even though the local coordinates are different.

## Question

The output results are the same even though the local coordinates are different.

Axial force and moment have different signs depending on the local axis.

In CIVIL, all member forces are calculated based on the local axis. However, the axial forces (Fx, Fy, Fz) and bending moments (Mx, My, Mz) are also influenced by the local axis but calculated in a slightly different way.

Let's take an example.

Firstly, let's talk about axial forces (Fx, Fy, Fz). These forces follow the position and direction of the local x, y, and z-axes.

In Case I in the figure below, you can see that only two elements in the middle have the opposite direction of the x and y axes.

In this case, if we check the axial forces, we can see that the sign of the axial forces is also opposite at the locations where the direction of axis is opposite. The sign of the axial force changes depending on the direction (sign) of the axis.

In Case II, we can also see that two elements have different Local Axis. However, unlike in Case I, the direction of the y and z axes is different.

In this case, when checking the reaction forces, we can see that we cannot check them together because the positions of the local axes are different for each element. Instead, we need to check the forces separately for Fz and Fy.

Secondly, let's talk about the bending moment. Bending moment is only affected by the position of the Local Axis x, y, z axes and has its own sign convention. The determination of the sign of the + and - of the moment is determined as shown in the figure below.

Let's look at the example below. In Case I, there are two elements in the middle which have the opposite direction in the y and z axes.

Regardless of the direction of the axis, continuous beam moments can be seen as shown in the figure below. This is because beam moments are not affected by the direction (+/- sign) of the axis.

In Case II, we can also see that two elements have different Local Axis. However, unlike in Case I, the direction of the y and z axes is different.

It is similar to axial force in the way that it is influenced by the position of axes. The results can be checked by My and Mz, respectively.

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