Date of Award

Spring 12-4-2014

Document Type


Degree Name

Master of Science (MS)

First Advisor

Victor Saouma

Second Advisor

Abie Liel

Third Advisor

George Hearn


The purpose of this thesis is to develop a preliminary guide for the analysis and design of symmetrical circular arches.

In the context of the graduate curriculum that typically limits itself to rectilinear structures, this thesis makes an effort to apply basic principles (virtual work and the flexibility method) towards deriving analytic solutions for different types of elastic arches (reactions and internal forces). To the best of our knowledge, this is the most comprehensive repository of such closed formed solutions. To illustrate their application, the preliminary design of a concrete arch is reported. Furthermore, analytical results are assessed to assist engineers gain a "feel" for arch behavior.

The study broadly covers semicircular arches. The analysis includes different loading as well as support conditions that lead to statically determinate or indeterminate structural design cases. Effects of unsymmetrical loading conditions on these structures are also briefly covered in their analysis. The analytical solutions are derived with Mathematica, compared with reported analytical solutions (when available),validated with SAP 2000 models and used through Matlab for the design example.

Further,this design guide helps relate structural behavior of semicircular arches with their geometry. Influence of aspects like span - to - rise ratio on horizontal thrust, support reactions, and forces across the span provides intuitive understanding of these structures. The study concludes with simplified analytical solutions and preliminary design recommendations.

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Engineering Commons