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I first encountered this type of system when evaluating an existing structure in Philadelphia that had at one time been used as an enclosed parking garage, but was being used as an office building in the late 1990s. No drawings were available for the structure, but small openings cut in the slab revealed portions of the internal reinforcement and slab thickness to enable an analysis of the load-carrying capacity of the framed floors.

Rather than the typical orthogonal reinforcing bars, however, the exploratory demolition discovered rings of smooth bars. A subsequent investigation of the available literature on flat-plate construction from the approximate time period during which the structure had been built revealed that the slab was very likely designed and constructed using the SMI system.

The concentric rings of the SMI system are located in the top of the slab directly above the columns (referred to as Unit C in the available literature), and in the bottom of the slab at the mid-span of what we would now call a column strip (Unit A), as well as in the bottom of the slab at the mid-span of what is now referred to as a middle strip, or centered in the bay formed by the column grid (Unit B).

There is typically no top reinforcing provided in the middle strip at the intersection with the column strips as is now required by the latest building codes. The concentric rings of bottom reinforcement overlap at the interface zones of Units A and B, while the top reinforcement above the column typically overlaps the Unit A bottom bars below.

The slab is separated into three independent sections as a part of the design of the system. These parts include the column head section (Unit C), the slab between the columns (Unit A) and the central portion of the slab (Unit B). The column head is analyzed as if it were a circular cantilever fixed at the column and loaded uniformly around its circumference by reactions transmitted to it by the adjacent surrounding components. The slab between the columns and the central portion of the slab is analyzed for positive bending moments only.

The design of the SMI system is based on the same flexural theory of reinforced concrete used by all other previous methods of analysis — i.e., bending moments are resisted by internal stress in the concrete, compressive on one side of the neutral axis of the section, and tension on the other. The primary difference with the SMI system is that the tensile stresses in the structure are offset by the concentric rings of reinforcing bars, which resist the tendency of the concrete within the ring to deform or elongate due to the tensile bending forces.

In other words, the rings were subjected to hoop stresses — axial forces acting on the rebar perpendicular to the radial direction of the concrete tension. The rings consist of smooth bars. The ends of the rings are lapped to develop their full strength. The laps of the concentric rings are staggered to avoid adjacent laps from occurring at the same radial location within the designated unit.

Comments by one of the authors of the 4th edition (1925) of Concrete Plain and Reinforced, Volume 1, by Frederick Taylor, Sanford Thompson, and Smulski, indicates that the SMI system required 20 to 24 percent less reinforcing than comparable two-way and four-way flat-slab systems designed during the same historical time period.

Comparisons between weights of reinforcing for different two-way and four-way flat-slab systems provided in the Concrete Reinforcing Steel Institute (CRSI) publication Evaluation of Reinforcing Steel Systems in Old Reinforced Concrete Structures (1981) does not list the pounds of steel required in a typical interior panel of the SMI system; however, other information concerning this system is provided in the same document.

W.K. Hatt, a professor of civil engineering at Purdue University, conducted load tests of the SMI system prior to 1920. The results of these tests appeared in the 1918 ACI Journal, Proceedings. An "extensometer" developed by Claude Berry, a civil engineering professor at the University of Pennsylvania, measured stresses within the reinforcing rings.

The two-bay-by-two-bay test frame, measuring 41 feet by 36.5 feet (12.5 by 11 meters), with cantilevers on three sides and an upturned spandrel beam on the fourth, was loaded using bricks stacked in such a way to prevent arching action of the masonry units. The center-to-center spacing of the columns was 16 feet (4.9 meters). All columns included a capital. The slab thickness was 5.5 inches (14 centimeters). The test frame was loaded from 150 to 950 pounds per square foot (730 to 4,640 kilograms per square meter) until failure occurred.

The following working stress formulas are used to analyze SMI slabs and size the required reinforcement:

Column Head (Unit C) 2Asfs = 6.64(M/jd) Where: M = Bending Moment per 0.5 of the circumference As = Sum of the cross-section of rings Based on the assumption that the directions of the bending moments are radial. The circumference of the unit was typically established as the average of the inflection points for the continuous orthogonal and diagonal moment diagrams between the column spacings.

Between the Columns (Unit A) 2Asfs = 2(M1/jd) Where: M1 = Bending Moment on portion covered by the rings As = Area of one section of rings Based on the assumption that the principal bending moments act primarily in one direction. Span of unit was typically established as orthogonal distance between the inflection points of the opposing columns.

Center Portion of Slab (Unit B) Asfs = 0.5(M2/jd) Where: M2 = Bending Moment acting in the distance equal to the diameter of a ring As1 = Area of one section of the rings Based on the assumption that the bending moments act diagonally. Span of unit was typically based on diagonal clear span between the inflection points of the opposing columns.

F.E. Turneaure and E.R. Maurer were researching the principles of circumferential and radial bending moment analysis at the University of Wisconsin in the early 1900s, as well. A discussion of their methods of analysis can be found in Principles of Reinforced Concrete Construction, 3rd edition (1919).

The available literature that deals directly with the SMI system indicates that the method of construction was patented by Edward Smulski. However, a cursory search through the U.S. Patent Office indicates that there were only two patents granted to Smulski, one for a cast-in-place counterfort system for retaining walls, and reservoir and dam walls, and one for a two-way, orthogonal reinforced slab system that included encased steel beams.

It is not clear how predominant the use of the SMI system was during the early 1900s and later in the century. The number of such structures that were constructed and the number currently remaining are unknown. In my opinion, it is not likely that this system was used to a large degree or was very popular because of the assumed difficulty associated with properly fabricating and placing perfectly round and concentrically positioned bars in overlapping top and bottom layers.

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D. Matthew Stuart, P.E., S.E., F.ASCE, SECB, is a licensed structural engineer in 20 states. He currently works as a senior project manager at the main office of CMX, located in New Jersey, and also serves as an adjunct professor for the master's of structural engineering program at Lehigh University in Bethlehem, Pennsylvania.

This article is reprinted from the September 2007 issue of STRUCTURE magazine, with permission of the publisher, the National Council of Structural Engineers Associations (NCSEA).

References

Evaluation of Reinforcing Steel Systems in Old Reinforced Concrete Structures, 1st ed. Concrete Reinforcing Steel Institute (CRSI), 1981.

Singleton, Jack. Manual of Structural Design, 3rd ed. H.M. Ives & Sons, 1947.

Smulski, Edward. "A Test of the S-M-I System of Flat-Slab Construction" ACI Journal, Proceedings, 1918. American Concrete Institute.

Taylor, Frederick; Sanford Thompson; and Edward Smulski. Concrete Plain and Reinforced, Volume 1, 4th ed. John Wiley & Sons, Inc., 1925.

Turneaure, F.E., and E.R. Maurer. Principles of Reinforced Concrete Construction, 3rd ed. John Wiley & Sons, Inc., 1919.

SUBSCRIPTION SAMPLE Detail of the column head. Photo: Bob Droke/ HABS Extra Large Image Section and reinforcing plan drawings at an SMI (or circumferential) system column head. Image: Courtesy ACI Journal, Proceedings Extra Large Image Simple plan and section drawings diagram the parts of the flat slab. Image: Courtesy ACI Journal, Proceedings Extra Large Image Hoop stress diagram. Image: Courtesy ACI Journal, Proceedings Extra Large Image SMI bottom-reinforcing scheme. Image: Courtesy ACI Journal, Proceedings Extra Large Image Four-way flat-slab reinforcing plan. Image: Courtesy Structure/ CRSI Extra Large Image California State Printing Office second-floor plan drawing. Image: HABS Extra Large Image Though somewhat different in construction, the lily-pad ("dendriform") concrete columns of Frank Lloyd Wright's Johnson Wax Building can be seen as an evolved and highly stylized structural relative of the SMI system. Photo: Johnson Architectural Images/ Artifice Images Extra Large Image   Click on thumbnail images to view full-size pictures.