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«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 ...»

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An effective combination of theories was established to analyze progressive collapse of a multi-story steel frame structure. For illustration, the procedure was applied to a two-dimensional steel frame model. Stress/strain failure criteria of linear, elastic-perfectly plastic, and elastic-plastic with kinematic hardening models were considered separately. A buckling failure criterion was also considered to supplement a strain failure criterion in the elasticperfectly plastic model. That approach is currently being developed further to study the physical phenomena associated with progressive collapse, and to develop fast running computational algorithms for the expedient assessment of various

multi-story building systems.

The 1994 Northridge earthquake highlighted troublesome weaknesses in design and construction technologies of welded connections in moment-resisting structural steel frames. As a result, the US steel construction community embarked on an extensive R&D effort to remedy the observed deficiencies. During about the same period, domestic and international terrorist attacks have become critical issues that must be addressed by structural engineers. Here, too, it has been shown that structural detailing played a very significant role during a building’s response to blast. In blast resistant design, however, most of the attention during the last half century has been devoted to structural concrete. Since many buildings that could be targeted by terrorists are moment-resisting steel frames, their behavior under blast is of great interest, with special attention to structural details. Typical structural steel welded connection details, currently recommended for earthquake conditions, underwent preliminary assessments for their performance under blast effects. The assessments also addressed current blast design procedures to determine their applicability for both the design and analysis of such details. The finding highlighted important concerns about the blast resistance of structural steel details, and about the assumed safety in using current blast design procedures for structural steel details.

Obviously, one must address not only the localized effects of blast loads, and the idealized behavior of typical structural elements (e.g., columns, girders, etc.), but also the behavior of structural connections and adjacent elements that define the support conditions of a structural element under consideration. The nature of blast loads, the behavior of structural connections under such conditions, and progressive collapse are addressed in the following sections to provide the background for current and proposed research activities.

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Typical Blast Effects Blast effects are associated with either nuclear or conventional explosive devices. Although small nuclear devices (e.g., tactical size) could be used by terrorists, the associated technical problems include many serious issues that could be far more complicated to address than blast effects on buildings. Therefore, nuclear weapon effects are not addressed in this paper. The interested reader can find useful information on this topic in other sources (e.g., ASCE 1985). Similarly, the effects of some industrial explosions are described elsewhere (ASCE, 1997). Scaling laws are used to predict the properties of blast waves from large explosive devices based on test data with much smaller charges (Johansson and Persson 1970, Baker 1973, Baker et al. 1983). The most common form of blast scaling is the Hopkinson-Cranz, or cube-root scaling (Hopkinson 1915, Cranz 1926). It states that self-similar blast waves are produced at identical scaled distances when two explosive charges of similar geometry and of the same explosive, but of different sizes, are detonated

in the same atmospheric conditions. It is customary to use as a scaled distance a dimensional parameter, Z, as follows:

Z = R/E 1/3, or Z = R/W 1/3 (1)

where R is the distance from the center of the explosive source, E is the total explosive energy released by the detonation (represented by the heat of detonation of the explosive, H), and W is the total weight of a standard explosive, such as TNT, that can represent the explosive energy. Blast data at a distance R from the center of an explosive source of characteristic dimension d will be subjected to a blast wave with amplitude of P, duration td, and a characteristic time history. The integral of the pressure-time history is defined as the impulse I. The Hopkinson-Cranz scaling law then states that such data at a distance ZR from the center of a similar explosive source of characteristic dimension Zd detonated in the same atmosphere will define a blast wave of similar form with amplitude P, duration Ztd and impulse ZI. All characteristic times are scaled by the same factor as the length scale factor Z. In Hopkinson-Cranz scaling, pressures, temperatures, densities, and velocities are unchanged at homologous times. The Hopkinson-Cranz scaling law has been thoroughly verified by many experiments conducted over a large range of explosive charge energies.

Limited reflected impulse measurements (Huffington and Ewing 1985) showed that Hopkinson-Cranz scaling may become inapplicable for close-in detonations, e.g., Z 0.4 ft/lb 1/3 (0.16 m/kg 1/3).

The character of the blast waves from condensed high explosives is remarkably similar to those of TNT, and these curves can be used for other explosives by calculating an equivalent charge weight of the explosive required to produce the same effect as a spherical TNT explosive. Generally, the equivalent weight factors found by comparing airblast data from different high explosives vary little with scaled distance, and also vary little dependent on whether peak overpressure or side-on impulse is used for the comparisons. W hen actual comparative blast data exist, its average value can be used to determine a single number for TNT equivalence. W hen no such data exist, comparative values of heats of detonation, H, for TNT and the explosive in question can be used to predict TNT equivalence (Department of the Army, Navy, and Air Force 1990, U.S. Department of Energy 1992, Conrath et al. 1999).

The theoretical heats of detonation for many of the more commonly used explosives are listed in various sources (e.g., Baker et al. 1983, Appendix A of U.S. Department of Energy 1992), along with TNT equivalency factors (Department of the Army 1986, and Department of the Army, Navy, and Air Force 1990). This method of computing TNT equivalency is related primarily to the shock wave effects of open-air detonations, either free-air or ground bursts.

Limitations of this approach have been discussed in various publications (e.g., Conrath et al. 1999). Typical sources of compiled data for airblast waves from high explosives are for spherical TNT explosive charges detonated at standard sea level. The data are scaled according to the Hopkinson-Cranz (or cube-root) scaling law.

Unconfined Explosions

A typical representation of a blast-induced pressure-time history curve is shown in Figure 3. One can note that the pressure rises sharply above atmospheric levels upon the arrival of the shock wave, then it decays exponentially. During this decay, the pressure will decrease below atmospheric levels, but then recover to it. The phase during which the pressure is above the atmospheric level is termed “positive phase”, while it is known as the “negative phase” for the duration it is below the atmospheric level.

Figure 3 Typical Blast-Induced Pressure-Time history (TM 5-1300, 1990)

An acceptable set of standard airblast curves for the positive-phase blast parameters is shown in various references (e.g., Kingery and Bulmash 1984, Department of the Army 1986, Departments of the Army, Navy, and Air Force 1990). The procedures in (Department of the Army, 1986) have been implemented in the computer code ConW ep (Hyde 1993) that can be used for calculating a wide range of weapon and explosive effects. These sources present the scaled form of various blast wave parameters, e.g., the peak side-on overpressure, P s (psi), side-on specific impulse, is (psi-ms), shock arrival time, ta (ms), positive phase duration, td (ms), peak normally reflected overpressure, P r (psi), normally reflected specific impulse, ir (psi-ms), shock front velocity, U (ft/ms), wave length of positive phase, L W (ft). The normally reflected pressure and impulse are greater than the corresponding side-on values because of the pressure enhancement caused by arresting flow behind the reflected shock wave. Various sources (e.g., U.S. Department of Energy 1992) present methodologies for calculating such parameters. For an explosive charge detonated on the ground surface, one can use the free-air blast curves to determine blast wave parameters by adjusting the charge weight in the ground burst to account for the enhancement from the ground reflection. For a perfect reflecting surface, the explosive weight is simply doubled. W hen significant cratering takes place, a reflection factor of 1.8 is more realistic. This simple approach is recommended for an explosion at or very near the ground surface. This approach is still valid. However, test data are available and have been compiled from tests using hemispherical TNT charges on the ground surface. From these data, blast curves for the positive-phase blast parameters were developed and are widely used as the standard for ground bursts. It is assumed that structures subjected to the explosive output of a surface burst will usually be located in the pressure range where the plane wave concept can be applied. Therefore, for a surface burst, the blast loads acting on structure surface are calculated as described for an air burst except that the incident pressures and other positive-phase parameters of the free-field shock environment are obtained from the appropriate charts. For the normally reflected parameters, the structural element would be perpendicular to the direction of the shock wave. Otherwise, the wave will strike the structure at an oblique angle.

The simplest case of blast wave reflection is that of normal reflection of a plane shock wave from a plane, rigid surface.

In this case, the incident wave moves at velocity U through still air at ambient conditions. The conditions immediately behind the shock front are those for the free-air shock wave. W hen the incident shock wave strikes the plane, rigid surface, it is reflected and moves away from the surface with a velocity U r into the flow field and compressed region associated with the incident wave. In the reflection process, the incident particle velocity u s is arrested (u s = 0 at the reflecting surface), and the pressure, density, and temperature of the reflected wave are all increased above the values in the incident wave. W hen a plane wave strikes a structure at an angle of incidence, the oblique reflected pressures will be a function of the shock strength. Also, as a blast wave from a source some distance from the ground reflects from the ground, the angle of incidence must change from normal to oblique. Normally reflected blast wave properties usually provide upper limits to blast loads on structures. Nevertheless, one may have to consider cases of blast waves that also strike at oblique angles. The effects of the angle of incidence versus the peak reflected pressure P r" are shown in the references cited previously. Accordingly, one can show the incident and reflected pressure pulses on the same time scale, as presented in Figure 4.

–  –  –

Confined Explosions Confined and contained explosions within structures result in complicated pressure-time histories on the inside surfaces.

Such loading cannot be predicted exactly, but approximations and model relationships exist to define blast loads with a good confidence. These include procedures for blast load determination due to initial and reflected shocks, quasi-static pressure, directional and uniform venting effects, and vent closure effects. The loading from a high-explosive detonation within a confined (vented) or contained (unvented) structure consists of two almost distinct phases. The first is the shock phase, where incident and reflected shocks inside structures consist of the initial high-pressure, short-duration reflected wave, and several later reflected shocks reverberations of the initial shock within the structure. The second is called the gas loading phase that attenuated in amplitude because of an irreversible thermodynamic process. These are complicated wave forms because of the involved reflection processes within the vented or unvented structure. The overpressure at the wall surface is termed the normally reflected overpressure, and is designated P r. Following the initial internal blast loading, the shock waves reflected inward will usually strengthen, as they implode toward the center of the structure, and then attenuate, as they move through the air and re-reflect to load the structure again. The secondary shocks will usually be weaker than the initial pulse. The shock phase of the loading will end after several such reflection cycles.

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