Mathematical model of a moment-less arch

Area of Science:

• Structural Engineering
• Applied Mathematics
• Civil Engineering

Background:

• Traditional arch design often relies on simplified load assumptions.
• Existing models for moment-less arches may not account for self-weight or general loading conditions.

Purpose of the Study:

• To develop a comprehensive mathematical model for predicting moment-less arch geometries.
• To analyze the structural behavior of moment-less arches under combined uniform and self-weight loads.
• To compare the stress development in optimized moment-less arches versus traditional parabolic arches.

Main Methods:

• Formulation of a novel mathematical model for rigid, two-pin, moment-less arches.
• Inclusion of arch self-weight (q) and uniformly distributed load per unit span (w) in the model.
• Derivation of classical parabolic and catenary arch forms as special cases.
• Analysis of arch behavior under combined permanent loading (w+q) for various span/rise and w/q ratios.

Main Results:

• The model accurately predicts moment-less arch shapes for any span/rise ratio and load combination (w/q).
• Optimized moment-less arches demonstrate substantially lower stress levels compared to parabolic arches under identical loading conditions.
• Even with minor geometric differences, stress variations between moment-less and parabolic arches can be significant.

Conclusions:

• The developed model offers a more realistic approach to designing moment-less arches.
• Accounting for self-weight and general loads leads to superior structural performance in moment-less arch designs.
• This research provides valuable insights for optimizing arch structures in engineering applications.