Shear in a three-hinged arch For a three-hinged arch carrying general loads, where along the span is the shear force commonly at its maximum value?

Introduction / Context:
Shear distribution in arches resembles that in beams: near supports, reactions and geometry combine to produce larger shear values. Recognizing this helps in sizing section depth and detailing near springings.

Given Data / Assumptions:

• Three-hinged arch with hinges at both springings and at the crown.
• Arbitrary static loading (dead plus live).
• Linear elastic response and standard sign conventions.

Concept / Approach:
Support reactions contribute directly to shear near the springings. For typical symmetric or unsymmetric loads, the shear envelopes peak close to supports. The crown hinge enforces zero moment at midspan but does not create maximum shear there.

Step-by-Step Solution:
Compute reactions from statics.Construct shear diagram; highest magnitudes usually occur adjacent to supports.Confirm that the crown region shows lower shear compared to springings under standard loading.

Verification / Alternative check:
Influence lines for shear in an arch show peak ordinates near supports for moving loads.

Why Other Options Are Wrong:
Maximum at crown is uncommon; quarter points may see peaks for special load cases but not generally; varies only with slope is incorrect—shear is load and reaction driven.

Common Pitfalls:
Assuming crown hinge influences shear maxima; it primarily affects moment distribution.

Final Answer:
maximum at springings (supports)