The reason why forces are transmitted in arches is similar to the joint structure in the other question. Additionally there are the internal bending moments that also change the undeformed shape of the element (be it beam or arch).
arches build with stone
Although not in your original post, I will focus on the forces in stone arches. In order to understand it, from another perspective have a look at this image, from the "The Geometrical Design of Masonry Arches".
Figure: Left, line of thrust in a semi-arch. (source The Geometrical Design of Masonry Arches
In the image above the arch is designed as part of individually cut stones which each is cut in a specific way, and are placed in a specific order. The general shape of all the stones is similar to a keystone
Figure 2: keystone basic shape
The forces acting on the voussoir are like in the image below:
Figure 3: Forces acting on a voussoir
- $T_1$ is upward, because the stone on the left develops friction which stops the stone to move downwards (due to gravity).
- $T_2$ is the downward force applied from the stone on the right (which due to gravity is downwards).
It is noteworthy, that due to the angled shape of the stone and the added weight of the stone:
- $N_1$ is greater than $N_2$
- the friction forces which develop are also greater (because the normal forces are greater).
the above differences in forces results in a bending moment, which in turn results in an (sort of) triangular distribution of the normal Forces ($N_1, N_2$).
It is interesting to note that the stones become larger. There is a very good reason for that. The reason is that the added weight acts to stabilise the column (the resulting force vector is more vertical). See the following figure:
Figure: use of gargoyles to increase stability of columns from lateral weight (source: how-gargoyles-and-pinnacles-saved-gothic-architecture)