Will it Fall Over?

Is the arch in the picture below stable, or has it been created in Photoshop, or perhaps with the assistance of some glue or external straps?

Book Arch

Book Arch

A simple analysis suggests that tension will be generated at the bottom of the crown, and at the tops of the columns, suggesting that the books would not be stable in this configuration without some reinforcement.

Analysis 1

Analysis 1

But looking at the problem from a geometric perspective, it is possible to fit a catenary within the shape of the arch, and the structure should therefore be stable:



A slightly more detailed analysis, allowing the arch segments to separate rather than develop tension suggests that the structure would be able to develop a compressive path to carry the gravity loads to the base.

Analysis 2

Analysis 2

The stability of structures is not always obvious. The ray tracings below from, PM 2ring, show two different types of “pseudo arch”, which are both stable, if correctly configured:



This entry was posted in Arch structures, Finite Element Analysis, Newton, Ray Tracing and tagged , . Bookmark the permalink.

2 Responses to Will it Fall Over?

  1. Bill Harvey says:

    proper, no tension, thrust line calc done in Excel produces the results shown at:



  2. Pingback: Book Arch ~ My Heart is Set On It……………………………………………. « Going Beyond Survival in a School Library

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