A symmetric three-hinged arch has a span of $L = 20\text{ m}$ and a central rise of $h = 5\text{ m}$. The supports A and B are at the same elevation. A central hinge C is located at the crown. A concentrated vertical load of $100\text{ kN}$ is applied at the crown C. Determine the horizontal and vertical reactions at support A.

A three-hinged arch has a span of $30\text{ m}$ and a rise of $6\text{ m}$ to the crown hinge C. A point load of $120\text{ kN}$ acts vertically at a distance of $10\text{ m}$ from the left support A. Determine the horizontal thrust $H$ at the supports.

A three-hinged arch has a left support A at elevation $0\text{ m}$, a right support B at elevation $4\text{ m}$, and a crown hinge C at elevation $10\text{ m}$. The horizontal distance from A to C is $12\text{ m}$, and from C to B is $8\text{ m}$ (total span $20\text{ m}$). A uniform downward load of $10\text{ kN/m}$ acts over the entire $20\text{ m}$ span. Find the horizontal reaction at B.

Many massive, historic steel arches, such as the Galerie des Machines built for the 1889 Paris Exposition, were designed as three-hinged arches. From a structural statics perspective, why was a hinge intentionally placed at the very top (crown) of the arch, rather than making it a continuous, rigid semi-circle?

Assume a minor earthquake causes the right foundation of an arch bridge to settle (sink) by two inches. Compare the theoretical internal consequences of this settlement on a two-hinged (continuous) arch versus a three-hinged arch.