Kahn's first design for the galleries called for angular vaults of folded concrete plates with light slots at the top.
Brown liked the light slots but rejected this particular design because it had the ceilings 30 feet (9 m) high, too high for the museum he envisioned.
 Further research by Marshall Meyers, Kahn's project architect for the Kimbell museum, revealed that using a cycloid curve for the gallery vaults would reduce the ceiling height and provide other benefits as well.
 The relatively flat cycloid curve would produce elegant galleries that were wide in proportion to their height, allowing the ceiling to be lowered to 20 feet (6 m).
 More importantly, that curve could also be used to produce a beautiful distribution of natural light from a slot in the top of the gallery across the entire gallery ceiling.

Kahn was pleased with this development because it allowed him to design the museum with galleries that resembled the ancient Roman vaults he had always admired.
 The thin, curved shells needed for the roof were challenging to build, however, so Kahn called in a leading authority on concrete construction, August Komendant, with whom he had worked before (and who, like Kahn, was born in Estonia).
 Kahn generally referred to the museum's roof form as a vault, but Komendant explained that it was actually a shell playing the role of a beam.
 More precisely, as professor Steven Fleming points out, the shells that form the gallery roofs are "post-tensioned curved concrete beams, spanning an incredible 100 feet" (30.5 m), which "happened to have been the maximum distance that concrete walls or vaults could be produced without requiring expansion control joints."
Both terms, vault and shell, are used in professional literature describing the museum.

True vaults, such as the Roman vaults that Kahn admired, will collapse if not supported along the entire lengths of each side.
 Not fully understanding the capabilities of modern concrete shells, Kahn initially planned to include many more support columns than were necessary for the gallery roofs.
 Komendant was able to use post-tensioned concrete that was only five inches thick to create gallery "vaults" that need support columns only at their four corners.

The Geren firm, which had been asked to look for ways to keep costs low, objected that the cycloid vaults would be too expensive and urged a flat roof instead.
 Kahn, however, insisted on a vaulted roof, which would enable him to create galleries with a comforting, room-like atmosphere yet with minimal need for columns or other internal structures that would reduce the museum's flexibility.
Eventually a deal was struck whereby Geren would be responsible for the foundation and basement while Komendant would be responsible for the upper floors and cycloid shells.
 Kahn placed one of these shells at the front of each of the three wings as a porch or portico to illustrate how the building was constructed.
 The effect was, in his words, "like a piece of sculpture outside the building."

Thos.
S. Byrne, Ltd. was the contractor for the project, with A. T. Seymour as project manager.
 Virgil Earp and L. G. Shaw, Byrne's project superintendents, designed forms with a cycloid shape that were made from hinged plywood and lined with an oily coating so they could be reused to pour concrete for multiple sections of the vaults, helping to ensure consistency.
 The long, straight channels at the bottoms of the shells were cast first so they could be used as platforms to support the workmen pouring concrete for the cycloid curves.
 After all the concrete had been poured and strengthened with internal post-tensioning cables, however, the curved parts of the shells carried the weight of their lower straight edges instead of the other way around.

To prevent the shells from collapsing at the long light slots at their apexes, concrete struts were inserted at 10-foot (3 m) intervals.
 A relatively thick concrete arch was added to each end of the shells to stiffen them further.
 To make it clear that the curved shells are supported only at their f
Kahn's first design for the galleries called for angular vaults of folded concrete plates with light slots at the top. Brown liked the light slots but rejected this particular design because it had the ceilings 30 feet (9 m) high, too high for the museum he envisioned.  Further research by Marshall Meyers, Kahn's project architect for the Kimbell museum, revealed that using a cycloid curve for the gallery vaults would reduce the ceiling height and provide other benefits as well.  The relatively flat cycloid curve would produce elegant galleries that were wide in proportion to their height, allowing the ceiling to be lowered to 20 feet (6 m).  More importantly, that curve could also be used to produce a beautiful distribution of natural light from a slot in the top of the gallery across the entire gallery ceiling.
Kahn was pleased with this development because it allowed him to design the museum with galleries that resembled the ancient Roman vaults he had always admired.  The thin, curved shells needed for the roof were challenging to build, however, so Kahn called in a leading authority on concrete construction, August Komendant, with whom he had worked before (and who, like Kahn, was born in Estonia).  Kahn generally referred to the museum's roof form as a vault, but Komendant explained that it was actually a shell playing the role of a beam.  More precisely, as professor Steven Fleming points out, the shells that form the gallery roofs are "post-tensioned curved concrete beams, spanning an incredible 100 feet" (30.5 m), which "happened to have been the maximum distance that concrete walls or vaults could be produced without requiring expansion control joints." Both terms, vault and shell, are used in professional literature describing the museum.
True vaults, such as the Roman vaults that Kahn admired, will collapse if not supported along the entire lengths of each side.  Not fully understanding the capabilities of modern concrete shells, Kahn initially planned to include many more support columns than were necessary for the gallery roofs.  Komendant was able to use post-tensioned concrete that was only five inches thick to create gallery "vaults" that need support columns only at their four corners.
The Geren firm, which had been asked to look for ways to keep costs low, objected that the cycloid vaults would be too expensive and urged a flat roof instead.  Kahn, however, insisted on a vaulted roof, which would enable him to create galleries with a comforting, room-like atmosphere yet with minimal need for columns or other internal structures that would reduce the museum's flexibility. Eventually a deal was struck whereby Geren would be responsible for the foundation and basement while Komendant would be responsible for the upper floors and cycloid shells.  Kahn placed one of these shells at the front of each of the three wings as a porch or portico to illustrate how the building was constructed.  The effect was, in his words, "like a piece of sculpture outside the building."
Thos. S. Byrne, Ltd. was the contractor for the project, with A. T. Seymour as project manager.  Virgil Earp and L. G. Shaw, Byrne's project superintendents, designed forms with a cycloid shape that were made from hinged plywood and lined with an oily coating so they could be reused to pour concrete for multiple sections of the vaults, helping to ensure consistency.  The long, straight channels at the bottoms of the shells were cast first so they could be used as platforms to support the workmen pouring concrete for the cycloid curves.  After all the concrete had been poured and strengthened with internal post-tensioning cables, however, the curved parts of the shells carried the weight of their lower straight edges instead of the other way around.
To prevent the shells from collapsing at the long light slots at their apexes, concrete struts were inserted at 10-foot (3 m) intervals.  A relatively thick concrete arch was added to each end of the shells to stiffen them further.  To make it clear that the curved shells are supported only at their f
Kimbell Art Museum