Constant stress arches and their design space.

Area of Science:

• Structural Engineering
• Applied Mechanics
• Form-Finding Analysis

Background:

• Traditional arch design prioritizes funicular (moment-less) form and minimal weight.
• Minimal weight can compromise structural durability and limit design flexibility.
• Natural structures exhibit constant axial stress for resilience.

Purpose of the Study:

• To propose constant axial stress as a novel design criterion for moment-less arches.
• To ensure structural integrity and durability under permanent and variable loads.
• To analyze asymmetric and symmetric arches, including least-weight solutions.

Main Methods:

• Building on Lewis's analytical form-finding approach.
• Deriving equations for arch centerline profile, reactions, and cross-sectional area for asymmetric arches.
• Analyzing symmetric arches and deriving a volume-minimizing span/rise ratio for least-weight structures.

Main Results:

• A new design space for constant axial stress arches is defined by two non-dimensional parameters.
• For stand-alone arches, a constraint relationship exists between constant stress and span/rise ratio.
• The proposed method ensures no part of the arch is over-stressed relative to others under variable loads.

Conclusions:

• Constant axial stress offers a robust design criterion for moment-less arches, enhancing durability.
• The study provides a theoretical framework and practical limits for designing such arches.
• This approach offers a new perspective on optimizing arch structures beyond traditional weight minimization.