1. What is a shell structure?
To answer this question, we have to investigate some important notions of structural design.

2. Two-dimensional structures: beams and arches
A beam responds to loading by bending
Click on the beam above to see the effect of bending: the top elements of the beam are compressed and the bottom is extended: the development of internal tension and compression is necessary to resist the applied vertical loading.
An arch responds to loading by compressing.
Click on the arch above to see the effect of axial compression (compression along the axis or length of the arch. The elements through the thickness of the arch are being compressed approximately equally. Note that there is some bending also present.

3. An arch shaped incorrectly for the applied loads will bend and compress
This is the same arch subjected to a concentrated load to the right of the crown--its main response is by bending
An arch experiences only compression (no bending) when it is exactly shaped to resist the loads
This parabolic arch is exactly the right shape to resist uniformly distributed loads, and develops compression only when it is loaded

4. A plate responds to transverse loads by bending
Plate Bending
A plate responds to transverse loads by bending
This is a fundamentally inefficient use of material, by analogy to the beam. Moreover, bending introduces tension into the convex side of the bent plate.
(click on the plate to see the effect of plate bending)

5. Membrane Stresses in a Plate
It is much more efficient for a plate to develop tensile or compressive stresses within the plane of the plate--these are known as membrane stresses.
Click on the plate to view the action of membrane stresses.

6. Plate bending vs. membrane stresses
Note: this is an experiment you can try yourself by folding a sheet of paper into a box.
This slide shows a concrete plate of 6” thickness, spanning 100 feet, resisting its own weight by plate bending
If the plate is shaped into a box, then each of the sides of the box resists bending by the development of membrane stresses. The box structure is much stronger and stiffer!

7. End of Section
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A shell is shaped so that it will develop membrane stresses in response to loads
The half-dome shell responds to transverse loads by development of membrane forces. Note that lines on the shell retain approximately their original shape.
Click here to return to discussion of domes (if you came back to this slide from there)