Stiffness through Curvature (Egg Crushing)

Abstract

This is an in-class activity that tests the strength of an egg shell to demonstrate how curvature in shell structures can generate stiffness, and to help students understand the important role of shape and form in the stiffness of a structure.

Learning Objectives

After this activity, students should be able to:

  • Demonstrate that curvature can increase the stiffness of a structure without adding thickness
  • Relate the forms of certain thin-shell structures to their stiffness

Background

Thin-shell concrete structures are very thin compared to their size, and are typically unsupported by additional structural elements such as columns or buttresses. They can be constructed in the form of flat surfaces, domes, cylindrical sections, may incorporate parts of other curved surfaces such as hyperboloids and hyperbolic paraboloids, or may be inspired by naturalistic forms such as hanging fabric. The form of these concrete shells can combine the inherent strength of curved surfaces with an elegant expression of their thinness. Structural artists who pioneered and built large-scale concrete shells include Eduardo Torroja, Félix Candela, and Heinz Isler.

In this activity, a volunteer student is asked to attempt to squeeze an egg in front of the class. The student is advised to squeeze with even pressures on all surfaces in contact with the student’s hand and to not poke the egg with a finger to prevent stress concentrations. It is seen that it is quite difficult (if not impossible) to crush the egg. Should the egg break, the safety measure of placing the student’s hand and the egg in a gallon zip-lock bag for this outcome. This demonstrates the strength of a thin-shell structure due to its curvature.

egg in bag

Materials List

  • One egg (and maybe one spare)
  • One large Ziploc bag

Procedure

Ask for a student volunteer to place their hand in the Ziploc bag and grasp the egg in their palm. Ask the student to squeeze the egg as evenly as possible (no poking or stress concentrations) to simulate an evenly distributed load on a shell. The goal is for the student to make a lot of effort and realize the strength of the egg curvature, as the egg should be extremely difficult to break despite its thinness.

From the Lecture: Félix Candela and the Hyperbolic Paraboloid

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