Location of the third hinge in a three-hinged arch In a standard three-hinged arch used for bridges and long-span roofs, where is the third (internal) hinge generally placed for analysis and construction convenience?

Introduction / Context:The position of hinges controls force flow and computational simplicity. A crown hinge provides a clear geometric reference and simplifies bending checks at midspan.

Given Data / Assumptions:

• Hinges exist at both springings (supports).
• One internal hinge is placed along the arch rib.
• Symmetric spans and loading are common in practice.

Concept / Approach:Placing the third hinge at the crown (highest point) divides the arch into two determinate segments and ensures zero bending moment at that location. It also enhances tolerance to temperature variations and settlements by allowing relative rotation.

Step-by-Step Solution:Model arch with hinges at supports A and B.Insert the third hinge at the crown → internal moment there is zero.Use sectional equilibrium to solve reactions without compatibility equations.

Verification / Alternative check:Influence lines for a three-hinged arch show a zero-moment line passing through the crown hinge, confirming the benefit of that location.

Why Other Options Are Wrong:Off-crown hinge locations complicate analysis and are atypical in standard three-hinged arch configurations.

Common Pitfalls:Confusing three-hinged with two-hinged arches, where no crown hinge exists and indeterminacy arises.

Final Answer:crown of the arch