Three-hinged arch basics in structural engineering A three-hinged arch is typically provided with hinges at both supports. Where is the third hinge commonly located for analysis and construction convenience?

Introduction / Context:A three-hinged arch is a classical statically determinate structure used in roofs, bridges, and temporary works. Understanding where the third hinge is placed is fundamental for computing reactions, internal forces, and ensuring thermal and settlement compatibility.

Given Data / Assumptions:

• Supports are hinged at both springings (arch ends).
• The arch is designed as a three-hinged system.
• No special geometric irregularities are assumed.

Concept / Approach:Adding a third hinge at the crown creates a statically determinate system. The crown hinge divides the arch into two determinate segments, simplifying analysis for horizontal thrust and bending moments. It also relieves the structure of secondary stresses from temperature and support settlements by providing an internal release at the highest point.

Step-by-Step Solution:Identify support conditions: two end hinges are present.Add a third hinge: the most effective position is at the crown.Outcome: the structure becomes determinate; analysis uses simple statics on each half.

Verification / Alternative check:Standard structural analysis texts model three-hinged arches with the third hinge at the crown specifically to exploit symmetry and facilitate closed-form solutions for thrust and moments.

Why Other Options Are Wrong:One-quarter span: uncommon and offers no special analytical advantage.Anywhere along the rib: theoretically possible but not standard and complicates analysis.Only two hinges: that would be a two-hinged (indeterminate) arch, not three-hinged.

Common Pitfalls:

• Confusing two-hinged and three-hinged arches and their determinacy.
• Assuming the crown hinge is optional; it is essential to the three-hinged definition.

Final Answer:at the crown