In structural analysis, a three-hinged arch (with hinges at both supports and at the crown) is classified as which type of structure?

Introduction / Context:
Arches can be two-hinged, three-hinged, or fixed. The number and placement of hinges determine the degree of static determinacy and the complexity of analysis.

Given Data / Assumptions:

• Three hinges: two at the supports, one at the crown.
• Planar structure under coplanar loading.

Concept / Approach:
A three-hinged arch provides enough internal releases so that support reactions and internal forces can be found using only equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0), making it statically determinate and insensitive to temperature and settlement effects in terms of determinacy.

Step-by-Step Solution:
Count unknown reactions (typically three for pin-roller supports) and use global equilibrium equations.Use the crown hinge as a moment-release location to form additional static equations by taking moments of one arch segment about the crown hinge.All internal forces are solvable without compatibility equations → determinate.

Verification / Alternative check:
Contrast with two-hinged arches which are statically indeterminate to degree one and require deformation compatibility.

Why Other Options Are Wrong:

• Statically indeterminate: applies to two-hinged and fixed arches, not three-hinged.
• A bent beam: not the standard classification; arches carry thrust with curved axis.
• None of these: incorrect because 'statically determinate' is correct.

Common Pitfalls:

• Assuming all arches are indeterminate; the third hinge removes indeterminacy.

Final Answer:
statically determinate structure