Three-Hinged Arch
A three-hinged arch is a type of structural element commonly used in civil engineering. It consists of a curved beam supported at two ends and a third hinge at the crown. This hinge allows the arch to rotate, accommodating both vertical and horizontal movements.

Statically Determinate Structure
A statically determinate structure is one in which all the reactions and internal forces can be determined using the equations of static equilibrium. In other words, the structure is stable and its behavior can be fully analyzed and understood.

Explanation
A three-hinged arch is considered a statically determinate structure. This is because its support conditions and geometry allow for a unique solution to the internal forces and reactions. The three hinges provide additional degrees of freedom, making it easier to analyze the structure.

When analyzing a three-hinged arch, we can use the equations of static equilibrium to determine the reactions at the supports. The vertical and horizontal reactions can be calculated by considering the equilibrium of forces in both directions.

The internal forces, such as moments, shears, and axial forces, can also be determined using equilibrium equations. By considering the equilibrium of moments at different sections along the arch, we can calculate the internal forces at those locations.

Advantages of Statically Determinate Structures
Statically determinate structures have several advantages:

1. Simplicity: The analysis of statically determinate structures is relatively straightforward compared to statically indeterminate structures. The equations of static equilibrium provide a clear and concise method for determining the reactions and internal forces.

2. Efficiency: Statically determinate structures are often more efficient in terms of material usage. Since the internal forces are known, the design can be optimized to minimize material requirements while still satisfying the required strength and stability criteria.

3. Predictability: Statically determinate structures have predictable behavior under different loading conditions. The internal forces and reactions can be accurately calculated, allowing engineers to ensure the structure can safely support the intended loads.

In conclusion, a three-hinged arch is a statically determinate structure. Its unique support conditions and geometry allow for a clear determination of the reactions and internal forces. This makes the analysis and design of three-hinged arches relatively simple and efficient.