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Nondestructive testing techniques
Determining whether the dome over Low was safe required the use of a variety of nondestructive testing methods. These allowed the team to "see" within the dome's structure without having to penetrate it with chisels, drills, or probes. Silman Associates hired GB Geotechnics, a Cambridge, England–based firm that specializes in nondestructive testing, to help. The firm used two techniques at Low: impulse radar and electromagnetic testing. Impulse radar uses an instrument to measure the speed at which high-frequency electromagnetic waves applied to a surface bounce back. It is convenient to use in locations that are difficult to reach because it only requires access to one side of the material being tested. Experts viewing the instruments' output can determine if voids or multiple layers of different materials are present in the area being sampled.

Electromagnetic detection was also used. This employs an instrument that passes an alternating electrical current through a coil of metallic wire that, in turn, creates a magnetic field. When the coil is passed over a surface and the instrument indicates that its magnetic field has been disturbed, the presence of a ferrous material like steel or iron is indicated. As impulse radar and electromagnetic detection were applied to the exterior surface of Low's dome, engineers concentrated in areas where it was likely that reinforcing would be found, if it existed. They were able to determine that, in fact, the dome is made entirely of unreinforced brick and is likely the largest of its kind in the U.S. From the nondestructive testing and visual inspections alone, the dome appeared to be solid and stable.

The monumental stone arches visible inside the rotunda only do a small part of the job of supporting Low’s masonry outer dome. Huge brick arches (above right) built on top of the stone ones do the real work. These can only be seen from inside Low’s lower attic. In the upper attic, Low’s brick outer dome can be seen arching over the iron and lath that support the plaster inner dome (above left). The CAD-rendered axonometric detail section (scroll down, bottom left) was created by corroborating information from original working drawings with data gathered using laser surveys, visual inspections, and hand-taped measurements. Photography © Elliott Kaufman. Click here to take a virtual tour inside the dome.

Laser survey simplifies CAD drawings and structural analysis
Silman Associates used version 7.44 of SAP2000 Plus, a program for static and dynamic finite element analysis of structures, to verify where tensile stresses would be high in the outer dome and its supporting structure. This would show the engineers the obvious places where they should look for cracking. In order to use the program, the engineers needed to be able to create a mathematical model of the geometry of the dome and its support and to assign loads to this hypothetical structural system. This required an extensive set of drawings, and estimates from the engineers of the size of the dome's dead load—wind and live loads were considered to be negligible—and how it was distributed.

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But the team couldn't just tape off these measurements. The space is very complicated, and most of it is impossible to access. The apex of the plaster dome is more than 100 feet above the rotunda floor. GB Geotechnics quickly established dimensions by positioning a laser surveying instrument in a number of locations in and around the building: inside the dome's attic, outside on the roof, and in the rotunda proper. The locations of millions of points were recorded by the survey. These were supplemented by handmade measurements, all the points referenced back to a single station, and the data compiled in a way that allowed AutoCAD drawings to be made.

Once the dimensions of the dome, arches, and piers were known, and the volume of material in the dome calculated, loads could be estimated by using the known density of the type of brick the dome was made of. Among the graphical options for SAP2000 Plus are wire-frame axonometrics that use different colors to represent different kinds of stress. These showed a surprising amount of tension in the dome's lower portion, which surely would have failed if not for a pair of monumental 1-inch-by-12-inch iron tension rings that encircle its base. Elsewhere, cracks did appear where the computer model led engineers to expect them: at the tops of the supporting arches. So far, there were no surprises. The last question was whether the cracks were getting worse.

The wire-frame diagrams above were created using SAP2000 Plus. The one on the left is simply a rendering of the dome’s structure. The one on the right uses color to indicate the level of stress distribution. Red and orange tones are tensile stresses. Other colors indicate compression. Red also represents the high-tensile zone that corresponds to the cracked region identified from the visual exam and nondestructive testing surveys. The upper portion of this dome has been made transparent for clarity.