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 parabolic three-hinged arch has a span of $40\text{ m}$ and a central rise of $8\text{ m}$. A uniformly distributed load (UDL) of $15\text{ kN/m}$ is applied over the left half of the span (from support A to the crown hinge C). Calculate the vertical and horizontal reactions at both 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.

A three-hinged arch with a span of $24\text{ m}$ and a rise of $6\text{ m}$ is subjected to a horizontal wind load of $50\text{ kN}$ applied at the crown hinge C, directed from left to right. Determine the horizontal and vertical reactions at supports A (left) and B (right).

A symmetric three-hinged arch has a span of $20\text{ m}$ and a rise of $4\text{ m}$. It is subjected to a linearly varying (triangular) vertical load on the left half. The load intensity is $0$ at support A and increases to $30\text{ kN/m}$ at the crown C. Determine the horizontal thrust at the supports.

A three-hinged arch with a span of $16\text{ m}$ and a rise of $4\text{ m}$ has a concentrated clockwise moment of $200.\text{ kN}\cdot\text{m}$ applied at the mid-point of the left half (i.e., at $x = 4\text{ m}$ from A). Find the vertical and horizontal reactions at both supports.

A three-hinged semicircular arch has a radius $R = 10\text{ m}$. A concentrated vertical load of $80\text{ kN}$ acts at an angle of $45^\circ$ from the left support A. Determine the horizontal thrust at the supports.

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.

When considering the construction phase of a large-span structure, why is a three-hinged arch often preferred by engineers and contractors over a solid two-hinged or fixed arch?

A flat bridge deck spanning $40\text{ m}$ requires massive steel girders due to large bending moments. If an engineer replaces the simple beam with a three-hinged arch of the same span and a rise of $10\text{ m}$, explain fundamentally how the arch reduces the bending moments compared to the beam.