Date of Award

Spring 12-4-2014

Document Type


Degree Name

Master of Science (MS)

First Advisor

Victor Saouma

Second Advisor

George Hearn

Third Advisor

Abbie Liel


Prior 20th century, the study of masonry arches and domes consumed years of work with some of the greatest minds in history. However, with the advancements of materials, such as steel and concrete, and the use of computer analysis programs, the art of masonry arch and shell design has become stagnant. With various design methods seen throughout literature, an appreciation for the development of these methods, through basic hand calculations, must be understood to first, ensure correct design principles are applied and second, aid in the further development of these methods.

This thesis starts with an extensive literature review of historical analysis and design methodology, starting in the 16th century and continuing on through the mid-20th century and today's current practices. The review focuses first on masonry arch design, including principles of geometric design, wedge theory, line of thrust and the ultimate load theorem. The second part views the design and analysis of domes and vaults, concluding with a case study of St. Peter's Dome in Rome.

The thesis continues by reviewing the derivations of a beam and plate subjected to flexure, prior to the thin shell derivation. In all three cases, equilibrium, compatibility and stress-strain relationships are considered to develop the differential equation relating transverse displacement to the load. This methodology is chosen in order to introduce the shell gradually by building upon the initial derivations of the beam and plate.

Tying the historical design methods and derivation of the shell equation, the design and analysis of a circular cylindrical shell will be conducted. The derived shell equation will first be simplified to membrane theory, followed by the derivations of the governing equations for shells through the theory of shallow shells. The analysis of the cylindrical shell will hold similarity to the analysis of statically indeterminate beams.

Finally, the methodology of shallow shells will be incorporated into the development of a reinforced concrete design and analysis program. The development of this program will simplify future analyses of circular cylindrical shells and improve design efficiency. The resulting design methodology will be recorded to aid in the future design of shells and the inspection of current structures. The thesis concludes by offering future studies to further develop the field of masonry arch and dome design.