Barrel Shells
The elements of a barrel shell are: (1) The the cylinder, (2) The frame or ties at the ends, including the columns, and (3) The side elements, which may be a cylindrical element, a folded plate element, columns, or all combined. for the shell shown in the sketch, the end frame is solid and the side element is a vertical beam.

A barrel shell carries load longitudinally as a beam and transversally as an arch. The arch, however, is supported by internal shears, and so may be calculated.

Here is a photograph of a north lignt barrel shell.

Folded Plates

The elements of a folded plate structure are similar to those of a barrel shell except that all elements are planar, and the moments in the slab elements are affected by the differential movement of the joints.

For the structure shown, the end supports and the side supports are both complete walls

To see a picture of a folded plate click HERE

Short Shells

The elements of a short shell are the barrel, which is relatively short compared to radius, the element at the base of the cylinder to pick up the arch loads, and the arches or rigid frame to pick up the entire ensemble. In this case it is a ridgid frame arch. The size of the arch could have been reduced by horizontal ties at the springings. There may be multiple spans.

The short shell carries loads in two ways: (1) As an arch carrying load to the lower elements. and (2) As as a curved beam to the arches. The thickness of the shell can be quite thin due to these properties.

Here is a photograph of a short shell

Hyperbolic Paraboloid

This is only one of thousands of possibile shapes for hypars. The surfaces are made by sliding a line over two other lines that are at varying angles. Consequently this surface can be constructed with straight boards. They have a slight twist depending on their width. It makes for inexpensive forming.

The hypar carries load in two directions. In this case, the diagonal element that sags is in tension, and the other element is an arch and is in compression. These forces must be picked up by the side ribs and delivered to the supports.

Click here to see one of the possible types of hyperbolic paraboloids.


Domes are membrane structures, the internal stresses are tension and compression and are staticaly determinate if the proper edge conditions are fullfilled. In a dome of uniform thickness, under its own weight, the ring stresses are compression until the angle to the vertical is about 57 degrees. If the dome is less than a full hemisphere, a ring is required at the base of the dome to contain the forces.

Click on Dome to see a photo of a dome

Translation Shells

A translation shell is a dome set on four arches. The shape is different from a spherical dome and is generated by a vertical circle moving on another circle. All vertical slices have the same radius. It is easier to form than a spherical dome.

The stresses in a translation shell are much like a dome at the top, but at the level of the arches, tension forces are offset by compression in the arch. However there are high tension forces in the corner.

To see a photograph and a description of a translation shell, click HERE.