«R. SHANKAR NAIR R. Shankar Nair R. Shankar Nair, Ph.D., P.E., S.E. is a principal and senior vice president of Teng & Associates, Inc. in Chicago. In ...»
time plots from a response history analysis of an elastic single degree of freedom structure. The structure has a natural period of vibration of 0.5 seconds, a stiffness of 100 kips/inch and moderate damping. A load of 100 kips is instantaneously applied to the structure. In response to this the structure experiences an instantaneous deflection of 2 inches, then oscillates with slowly decaying amplitude until a steady state deflection of 1 inch is approached. The maximum force in the structure is 200 kips, or twice the statically applied amount and the maximum deflection of the structure is 2 inches, or twice the static value, resulting in the impact coefficient of 2 used in the federal progressive collapse design guidelines.
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Figure 8 – Elastic Strength Demand on Structure with Instantaneous Load Application Under the federal progressive collapse design guidelines, members are permitted to experience “flexural inelasticity” based on permissible values contained in seismic guidelines recognizing that the amplified loading occurs for a very short duration and that long term loading following removal is a static condition. Specifically, compact framing is considered acceptable if the ratio of moment computed from an elastic analysis (MA) to the expected plastic moment capacity of the section (MpE), is less than 3. Noncompact sections are permitted to be designed with a limiting ratio MA/MPE of 2. Figure 9 is a plot of displacement vs. time from a nonlinear response history analysis of the same structure analyzed previously except that it has been assumed that the structure has a limiting plastic strength of 120 kips. Using the procedures in the federal guidelines, the MA/MPE ratio for this structure would be (2 x 100 kips / 120 kips) or 1.66, which would be within the permissible level of inelasticity either for compact or noncompact sections. As can be seen, the ratio of maximum displacement to steady state displacement increases to more than 2.5 for this structure.
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Figure 9 – Inelastic Displacement Response of a Moderately Strong Structure with Instantaneous Load Application Figure 10 is a plot from a similar analysis, in which the strength of the structure has been further decreased to 80 kips. In this case, the ratio of MA/MPE is 2.5, more than permitted for noncompact sections but less than the value of 3, permitted for compact sections. As can be seen, the structure is subject to unlimited increasing displacements, or stated simply, collapses. This identifies a basic flaw in the federal progressive collapse guidelines. While it should clearly be permissible to permit some inelastic deformation of framing used to resist collapse, as measured by the MA/MPE ratio, the structure must, as a minimum, have sufficient plastic strength to support the weight of the structure, in a static condition. The structure illustrated in Figure 10 did not have this strength. The federal progressive collapse guidelines do not actually require this evaluation but should.
Figure 10 – Inelastic Displacement Response of a WeakStructure with Instantaneous Load Application Fortunately, the assumption that load redistribution occurs through flexural behavior alone is very conservative and results in the design of members that are much larger than actually required to resist progressive collapse. Figure 11 illustrates an alternative load resisting mechanism for redistribution of load that relies on catenary behavior of the steel framing and compressive arching of the concrete floor slab. In the top illustration in this figure, the frame is supporting loads prior to column removal. In the middle illustration the central column has been removed beneath the floor and the frame is redistributing loads to the outer columns through flexure, as the floor locally falls downward. If the girders are not sufficiently strong to resist the strength demands resulting from the instantaneous removal of the central support column in an elastic manner, which is what is inherently assumed by the federal guidelines, plastic hinges will from at the two ends of the beams and in the mid-span region, near the removed column. Neglecting loading along the beam span, the two-span beam will have a strength equivalent to 8Mp/L, where Mp is the plastic moment capacity of the beam and L is the distance between the outer columns, to resist the load imposed on the beam by the now discontinuous central column and to slow the downward movement of the floor system.. If this strength is not sufficient to accomplish this, the beam will deflect sufficiently to mobilize catenary tensile action, which if sufficient, will eventually arrest the collapse. This mode of behavior, which is not explicitly considered in the federal guidelines, but is relied upon, is illustrated in the lower figure where the beam has formed plastic hinges at the beam-column joints and is now resisting loads from the interior column through catenary tensile behavior of the beam, balanced at the columns by compressive action in the slab. In fact, if the beam were compact, and laterally supported, the federal guidelines would permit the beam to arrest the collapse of a central column load with a magnitude as high as 12Mp/L. Clearly, in such a case, even though neglected by the federal guidelines, either catenary tensile behavior will be mobilized or the structure will fail to arrest collapse..
Most designs presently neglect, at least explicitly, the ability to develop catenary behavior and implicitly rely solely on the flexural mechanism. As an illustration of the potential efficiency of the catenary mechanism, in a recent study, it was determined that in a structure with 30 foot bay spacing, ASTM A992, W36 horizontal framing could safely support the weight of nearly 20 stories of structure above in the event of column removal (Hamburger, 2003), although deflection would be significant. There are several potential implications of this finding. First, it is not necessary to provide moment resisting framing at each level of a structure, in order to provide progressive collapse resistance. Second, it is not necessary to have substantial flexural capacity in the horizontal framing, either in the beam section itself or in the connection, in order to provide this collapse resistance. Third, it may not be necessary to provide full moment resistance in the horizontal framing and conventional steel framing may be able to provide progressive collapse resistance as long as connections with sufficient tensile capacity to develop catenary behavior are provided.
As an example of the efficiency of moment-resisting steel frame structures in the resistance of progressive collapse a study was conducted of the cost premium associated with providing progressive collapse resistance in a typical structure. In this study, a structure with a regular 30-foot grid pattern was reviewed. The floor system was comprised of 3-inch, 20-gauge metal deck, supporting a 5-1/2 inch (total thickness) lightweight concrete slab, with non-composite floor beams. Initially framing was designed without moment-resistance. The resulting framing, as illustrated in Figure 12 used W18x40, A992 beams and W24x62 A992 girders. Next, the beams and girders along column lines were assumed to be provided with moment-resistance and an evaluation of the structure for ability to resist instantaneous removal of a single interior column was performed using the federal progressive collapse guidelines. It was determined that the maximum value of MA/MPE in the framing was 1.5, or half the permissible value for compact sections. Thus, it was determined that progressive collapse resistance can be achieved in steel moment frame structures without increase in the weight of the framing.
Although collapse resistance can be provided without weight increase, there is, of course, a significant cost premium associated with the provision of moment connections between every beam, girder and column. therefore, an additional study was performed to determine if the number of moment-resisting connections in the building could be reduced. As a first step in this process, it was determined that if the moment-resistance was not provided for the W18x40 beams on the column lines but was provided for the W24x62 girders, the maximum value of MA/MPE is increased only to 1.9, which is still well within the limits permitted by the guidelines. Next, it an investigation was preformed to determine if it would be possible to provide the desired resistance to collapse by providing moment resistance on only a few of the floors in a multi-story buildings. It was determined that by using W36x300 sections as the beams and girders at one floor level, it would be possible to provide progressive collapse protection for as many as 15 supported stories. This results in very few moment connections and a total increase in framing weight of about 1.5 pounds per square foot, demonstrating that very economical solutions for providing collapse resistance in steel structures is possible.
While the use of catenary behavior to provide progressive collapse resistance holds great promise for steel structure design, it is not immediately apparent what types of connections of beams to columns will possess sufficient robustness to permit the necessary development of plastic rotations at beam ends together with large tensile forces.
Figures 13 and 14 are pictures of bolted web–welded flange moment resisting connections that fractured in the 1994 Northridge earthquake. These fractures occurred at beam column joints at an estimated drift demand of approximately 0.01 radian.
Mobilization of catenary action in framing may require plastic rotations on the order of 0.07 radians or more. It is true that there are substantial differences in the loading demand that occurs on beam-column joints in an earthquake as compared to those that occur in a frame resisting progressive collapse. Earthquake demands are cyclic and induce low-cycle fatigue failure of connections. However, demands applied on members and connections when resisting direct air-blast loadings might produce somewhat high strain rates, may be of larger magnitude and will occur simultaneously with large axial tension demands. Under conditions of high strain rate, steel framing becomes both stronger but more brittle. There is evidence that standard beam-column connection framing is quite vulnerable to such loading. Figure 15 is a photograph of a failed beam-column connection in the Deutsche Bank building. The beam which connected to the column using a bolted flange plate type connection was sheared directly off the column due to the impact of debris falling onto the structure from the adjacent collapsing South Tower of the World Trade Center. Also visible at the bottom of this picture is failure of the bolted column splice. Figure 16 is a picture of a failed bolted shear connection in the World Trade Center 5 building that resulted from development of large tensile forces in the beam due to fire effects. Clearly, these failures indicate that standard connection types commonly used in steel framing today may not be capable of allowing the structure to develop the large inelastic rotations and tensile strains necessary to resist progressive collapse through large deformation behavior. Despite these poor behaviors, it is also known that when properly configured and constructed, using materials with appropriate toughness, steel connections can provide outstanding ductility and toughness. Figure 17 illustrates the deformation capacity of beam-column connections designed with appropriate configurations and materials.
Following the damage experienced in steel buildings in the 1994 Northridge earthquake an extensive program of investigation was undertaken to develop beam-column connections capable of providing reliable behavior under the severe inelastic demands produced by earthquake loading. A number of connection configurations capable of acceptable behavior were developed (SAC 2000a). In parallel with these connection configurations, a series of materials, fabrication and construction quality specifications were also produced (SAC 2000b). While these technologies have been demonstrated capable of providing acceptable seismic performance, it is unclear whether these technologies are appropriate to providing protection against progressive collapse. Indeed, some of the connection configurations presented in the SAC documents rely on relief of high stress and strain conditions in the beam-column connection through intentional reduction in cross section that could lead to other failures under high impact load conditions. However, it is also possible that less robust connections than those demonstrated as necessary for seismic resistance could be adequate to arrest collapse in some structures. The moment-resisting connections in the World Trade Center 6 building, for example, which were not particularly robust by seismic standards, were able to successfully arrest collapse of that structure.
Figure 15 - Failed beam-column connection in Deutsche Bank Building Figure 16 - Failed bolted high strength shear connection in World Trade Center 5 Figure 17 -. Extreme plastic deformation of beam-column connection designed for enhanced inelastic behavior Designers urgently need a program of research and development similar to that conducted after the 1994 earthquake to determine the types of connection technologies that can be effective in resisting progressive collapse so that less conservative but more reliable approaches to blast resistant design can be adopted by the community.
A portion of the work reported herein was performed under support provided by the Department of Defense, United States Army and Applied Technology Institute under the Vanadium Technologies Program. The authors also wish to acknowledge the support of the Federal Emergency Management Agency and the Applied Technology Council.
Federal Emergency Management Agency (FEMA). Recommended Design Criteria for New Steel Moment Frame Construction, Report No. FEMA 350, prepared by the SAC Joint Venture for FEMA, Washington, D.C., 2000c.