4. Arch

An arch structure refers to a structure in which members resistant to compression, such as stones or bricks, are stacked in a curved shape to support the load at the top of the opening.
The external force acting vertically in the arch generates a large horizontal reaction force directed from the ends to the center, and this horizontal reaction force reduces the bending moment at each section.

The ratio of the arch height to the span of the arch is called the rise ratio.

If the rise ratio is too small, the axial force to widen the arch increases.
On the other hand, if the rise ratio is large, the arch resists the external force with axial force, which is structurally good, but it becomes uneconomical because the size of the arch increases to form the required span.
It is known that a rise ratio of about 0.3 is good when economic feasibility and structural efficiency are considered at the same time.

The reason why an arch structure can be constructed by stacking and connecting stones, as shown in figure, is because it is designed to only generate compressive stress along the axis of the arch structure.
Figure shows one side of a symmetrical arch structure with point B as the center.
If tensile stress occurs at the bottom of point B, where the keystone is located, the arch will collapse.
However, if tensile stress that can be caused by moment M is offset by lateral force H, no tensile stress will occur.
For this reason, an arch structure can have load-bearing capacity.
The lateral reaction force H at point A of the arch prevents it from spreading sideways.