Spherical shells are defined as those shells that are formed by a portion of a spherical surface.

This type of shell can withstand load variations, as long as they are gradual, otherwise moments would occur. In the case where there were large discontinuities in the distributed loads, the moments would be reduced to the area of ​​the discontinuity and would not expand through the structure.

This is why this type of structures can be considered antifunicular for different load cases, although its shape is not actually funicular.

If we analyze the internal forces developed, we see that two types are produced: meridional forces and forces perpendicular to them. The meridional forces developed under a distributed vertical load are always compressive. Perpendicular forces, on the other hand, can be traction or compression, depending on the position in which they are (in the upper compression zone and in the lower traction zone).

In addition, shear stresses are produced that contribute to supporting these loads.

Finally, we will analyze the support conditions. You have to be especially careful with these, since you have to create a ring at the base that prevents the shell from "opening." This implies the appearance of deformations imposed on the base by preventing this movement, which cause moments in nearby areas. Generally, this is usually solved by increasing the thickness in these areas.

These shapes work like shells when they form vaults, where they are similar to a multitude of arches joined together. If its surface is rigid enough, the shell also behaves like a plate, which can be useful for supporting non-uniform loads.

It must be taken into account that if instead of being supported longitudinally, it is placed supported on the ends, like a beam, its behavior will be more similar to this as the covered span increases.

It is a shell formed by a ruled surface. If their edges are sufficiently rigid, an arc-like action will develop in regions of convex curvature, while in those of concave curvature, a cable-like action will develop; varying the compressions and tractions depending on this.

If this type of shell becomes too flat, with very reduced curvatures, there is a risk that it will begin to work like a plate, so this is an aspect to take into account.

Many types of hyperbolic paraboloid shells can be created by joining them together. As a clear reference in this model, we must mention the Spanish architect Candela, who created numerous shells of this type.

Structure in architecture, The Building of Buildings, Mario Salvadori with Robert Heller

Concrete Shell Buckling, Egor P. Popov and Stefan J. Medwadowski

Structures, Daniel L. Schodek & Martin Bechthold.

• - Mark Ketchum's Concrete Shell page.

• - Historic Preservation of Thin-Shell Concrete Structures - Includes case studies of the Seattle Kingdome and MIT's Kresge Auditorium, both concrete domes.

• - Monolithic Dome Institute - Promotes the construction technologies of modern monolithic domes according to the patents of David South and Barry South of Dome Technology.

• - C-Shells Concrete Thin Shell Architecture - Advancing the architectural design and development of air-formed concrete thin shells utilizing technologies pioneered by Dome Technology.

• - Heinz Isler on the Structurae website.

• - Heinz Isler on German Wikipedia.

• - Heinz Isler at Princeton University Art Museum.

Spherical shells are defined as those shells that are formed by a portion of a spherical surface.

This type of shell can withstand load variations, as long as they are gradual, otherwise moments would occur. In the case where there were large discontinuities in the distributed loads, the moments would be reduced to the area of ​​the discontinuity and would not expand through the structure.

This is why this type of structures can be considered antifunicular for different load cases, although its shape is not actually funicular.

If we analyze the internal forces developed, we see that two types are produced: meridional forces and forces perpendicular to them. The meridional forces developed under a distributed vertical load are always compressive. Perpendicular forces, on the other hand, can be traction or compression, depending on the position in which they are (in the upper compression zone and in the lower traction zone).

In addition, shear stresses are produced that contribute to supporting these loads.

Finally, we will analyze the support conditions. You have to be especially careful with these, since you have to create a ring at the base that prevents the shell from "opening." This implies the appearance of deformations imposed on the base by preventing this movement, which cause moments in nearby areas. Generally, this is usually solved by increasing the thickness in these areas.

These shapes work like shells when they form vaults, where they are similar to a multitude of arches joined together. If its surface is rigid enough, the shell also behaves like a plate, which can be useful for supporting non-uniform loads.

It must be taken into account that if instead of being supported longitudinally, it is placed supported on the ends, like a beam, its behavior will be more similar to this as the covered span increases.

It is a shell formed by a ruled surface. If their edges are sufficiently rigid, an arc-like action will develop in regions of convex curvature, while in those of concave curvature, a cable-like action will develop; varying the compressions and tractions depending on this.

If this type of shell becomes too flat, with very reduced curvatures, there is a risk that it will begin to work like a plate, so this is an aspect to take into account.

Many types of hyperbolic paraboloid shells can be created by joining them together. As a clear reference in this model, we must mention the Spanish architect Candela, who created numerous shells of this type.

Structure in architecture, The Building of Buildings, Mario Salvadori with Robert Heller

Concrete Shell Buckling, Egor P. Popov and Stefan J. Medwadowski

Structures, Daniel L. Schodek & Martin Bechthold.

• - Mark Ketchum's Concrete Shell page.

• - Historic Preservation of Thin-Shell Concrete Structures - Includes case studies of the Seattle Kingdome and MIT's Kresge Auditorium, both concrete domes.

• - Monolithic Dome Institute - Promotes the construction technologies of modern monolithic domes according to the patents of David South and Barry South of Dome Technology.

• - C-Shells Concrete Thin Shell Architecture - Advancing the architectural design and development of air-formed concrete thin shells utilizing technologies pioneered by Dome Technology.

• - Heinz Isler on the Structurae website.

• - Heinz Isler on German Wikipedia.

• - Heinz Isler at Princeton University Art Museum.