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Seismology Meeting – Structural Analysis

There is a play between discipline and curiosity. On July 22nd, 2022, the SEAONC Seismology Committee held its first meeting of a two-part series on exploring engineering creativity. This first meeting focused on historical structural analysis methods. Professor Edmond Saliklis, from the Department of Architectural Engineering at California Polytechnic State University, San Luis Obispo, presented on the Modern Muller-Breslau Method and Dr. Alessandro Beghini, from Skidmore, Owings & Merrill, presented on various structural analysis methods used in conceptual structural design. The presentations and follow-up discussion aimed to provide a linkage between these structural analysis methods and the design of innovative structures.

Professor Saliklis, as an educator, has contemplated methods to teach students Statics without tedious algebraic calculations. Visually oriented students can lose interest in the subject when taught with traditional methods and this begs for an alternative. The method he discovered, developed by Heinrich Muller, addresses this need and can establish statically equilibrium of a structure through diagrams. Sometimes, also referred to as the influence line method, the Muller-Breslau Method uses geometry to determine reactions and internal forces within a structure. The principle behind this method can be understood through equation 1, which is similar to the virtual work method equation. The Δ in the equation corresponds to a perturbation of the structure at the point of interest. The second term in the equation (Σ Forcei⋅lofti) corresponds to the external work due to this perturbation. The unknown term can be solved for graphically. The original method rigidly fixes the horizontal displacement of the structure at each point and only allows vertical displacement. This has the effect of stretching the elements of the structure and therefore this method cannot be used for lateral loads. Professor Saliklis altered the tradition equation so that the structure rotates at its supports and therefore the structural elements do not stretch. This modified Muller-Breslau Method has the advantage that it can be used for lateral loads as well as vertical loads. These methods, both the traditional and modified versions, can be used to analyze frames (determinate or indeterminate), trusses, and arches. It can also be used to solve more complex and academic problems such as buckling. As the forces, moments and reactions of these structures are acquired by drawing, the engineer can visualize the load flow throughout the structure.


Unknown ⋅ +Σ Forcei⋅lofti=0 (Equation 1)


Dr. Alessandro Beghini followed Professor Saliklis with a presentation on conceptual structural design and the use of different structural analysis methods during this design phase. Over time, SOM has developed and explored a variety of different analysis tools such as graphic statics, Airy stress function, and the force density method. Their knowledge of multiple different analysis tools allows them to verify solutions from one method with another method and therefore gain greater confidence in the result. Dr. Beghini presented a variety of topics to highlight these analysis tools and their use in practice. The first topic he presented on was topology optimization. This method can be used to find an efficient truss or the optimal location for holes in a concrete beam. Dr. Beghini showed an example using this method which found that optimal intersection point of the trusses is ¾ of the truss module height, counter to general engineering intuition. The next method presented on was Maxwell’s theorem. This theorem states that the difference between the tension load path and compression load path is a constant. This has two implications. One implication is that optimizing the tension load path automatically optimizes the compression load path. The implication is that the weight of the structure is correlated to its load path efficiency. SOM made use of this theory when designing trusses for the LA Federal Courthouse. The third topic presented was the Force Density Method. This ancient structural analysis method can be traced back to the work of Frei Otto, who created models with hanging chains to understand the structural form created by gravity. Dr. Beghini illustrated how SOM collaborated with an artist, Janet Echelman, to build large scale rope sculptures and how SOM used the force density method to stretch Janet’s concepts to fit the site. The fourth and final topic presented on was pavilions and the structural analysis methods used to design these structures. Due to the small scale nature of these pavilions, they are ideal for testing research ideas. One example Dr. Beghini presented on was a foldable pavilion developed using the theory of rigid origami. Another example was a timbrel vault built by robots. Timbrel vaults are vaults native to Spain which can be constructed without falsework and the shape of these vaults are determined by the Airy stress function, another history structural analysis method. SOM combine this historical method with super modern construction techniques to design a glass pavilion.

There is an elegance underneath historical structural analysis methods. Before computers, engineers had to use these methods and through these methods, they gained insight on the structure they were designing. Nowadays, computers allow for quick solutions and engineers don’t necessarily need to understand the structure they are designing. For example, the beauty in graphic statics in not that one can design a truss quickly with this method, but that it shows a linkage between form and forces. This intuition can allow engineers to go beyond standard, prescriptive design methods. While Pier Nervi and Robert Maillart did not have access to computers during their career, their understanding of structures lead to the design of novel structures. Long ago, there was no distinction between engineers, scientist, and other professions. Everyone was just considered natural philosophers and this abundant curiosity led to much innovation. It may behoove this generation of engineers to learn from the past, so we design more innovative structures in the future.