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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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SHOCK (NCEL, 1988) is a computer code for estimating internal shock loads. This code can be used to calculate the blast impulse and pressure on all or part of a cubicle surface bounded by one to four rigid reflecting surfaces. The code calculates the maximum average pressure on the blast surface from the incident and each reflected wave and the total average impulse from the sum of all the waves. The duration of this impulse is also calculated by assuming a linear decay from the peak pressure. This code is based on the procedures in TM 5-1300 (Departments of the Army, Navy, and Air Force 1990). Shock impulse and pressure are calculated for each grid point for the incident wave and for the shock reflecting off each adjacent surface. The program includes a reduced area option which allows determination of average shock impulse over a portion of the blast surface or at a single point on the surface. The code calculates blast parameters for scaled standoff distances (R/W 1/3) between 0.2 (0.079 m/kg 1/3) and 100.0 ft/lb 1/3 (39.7 m/kg 1/3). The program, however, does not account for gas pressure load contributions. W hen an explosion from a high-explosive source occurs within a structure, the blast wave reflects from the inner surfaces of the structure, implodes toward the center, and re-reflects one or more times. The amplitude of the re-reflected waves usually decays with each reflection, and eventually the pressure settles to what is termed the gas pressure loading phase. Considering poorly vented or unvented chambers, the gas load duration can be much longer than the response time of the structure, appearing nearly static over the time to maximum response. Under this condition, the gas load is often referred to as a quasi-static load. For vented chambers, the gas pressure drops more quickly in time as a function of room volume, vent area, mass of vent panels, and energy release of the explosion. Depending on the response time of structural elements under consideration, it may not be considered quasi-static. The gas load starts at time zero and overlaps the shock load phase without adding to the shock load, as illustrated in Figure 5, where the shock phase and the gas phase are idealized as triangular pulses. The quasistatic portion of the pressure pulse can be obtained with the computer code FRANG (W ager and Connett, 1989) to predict of the load history and combining the two curves to form the complete pressure-time history. Noting that the shock and quasi-static pressures are not added where they overlap, but are merely intersected to define the load history, is important.

Figure 5 Typical Combined Shock and Gas Load in a Small Chamber (Departments of the Army, Navy, and Air Force 1990).

The code BLASTX (Britt 1992) treats the combined shock wave (including multiple reflections off walls) and explosive gas pressure produced by the detonation of a conventional high explosive in a closed or vented, rigid or responding walls that are allowed to fail under gas pressure loading in rectangular, cylindrical, or L-shaped rooms. The code allows the propagation of shocks and gas into adjacent rectangular or box-shaped spaces. The code does have the capability to treat multiple non simultaneous explosions in a room, modifications of shock arrival times and peak pressures to account for Mach stem effects, and the option to obtain pressure and impulse wave forms averaged over a number of target points on a wall. As with SHOCK, it does not account for movement of any of the walls or the roof, although recent versions of the code do allow openings to occur based on defined failure criteria and as created by combined shock and gas pressures. Although gas pressures are propagated through failed surfaces, shocks are not vented through failed openings.

Ballistic Attack, Fragmentation, and Ground Shock

Another class of threats is related to ballistic attack and fragmentation effects. Information on various weapon systems that could be used for such applications can be found in several sources (e.g., Department of the Army 1986, Department of the Army, Navy, and Air Force 1990, US Department of Energy 1992, Conrath at al. 1999). However, since these types of threat may not pose a direct hazard to cause massive structural failure, they are not addressed here. Usually, ground shock is also not a significant issue for terrorist incidents, since typical attacks involve above ground explosions.

Nevertheless, one may have to consider ground shock for special cases (e.g., if a threat might include a buried charge).

Therefore, these issues will not be addressed further in this paper, and the interested reader is referred to the sources cited above.

BLAST-RESISTANT STRUCTURAL STEEL CONNECTIONS AND PROGRESSIVE COLLAPSE

One of the important issues in structural behavior is the ability of connections to resist severe dynamic loads. Design guidelines for structural steel connections in the US (AISC, 1994) were developed based on experimental and theoretical investigations. However, the findings from the Northridge earthquake, and in recent reports ( e.g., Bonowitz et al 1995, Engelhardt and Hussain 1993, Engelhardt et al. 1995) on damage to steel structures due to seismic loads suggested a surprisingly poor performance of their connections, as compared to expected behavior (AISC 1992). An extensive research program was undertaken to address the observed deficiencies (Engelhardt et al. 1995, Kaufman et al. 1996a,b, Richard et al. 1995, Tsai and Popov 1995, El-Tawil et al 2000, Stojadinoviƒ et al. 2000, Davis 2001), and important design modification were introduced (AISC 1997, FEM A 2000). Nevertheless, these modified connection details may exhibit similar deficiencies under blast effects. Therefore, it is very important to assess their behavior under blast effects, and to identify any possible behavioral difficulties. Structural behavior under dynamic loads requires attention to the relationship between the dynamic characteristics of the structure and the applied loads. Design specifications should address this relationship to insure that the various structural details are blast resistant. TM 5-1300 (Department of the Army, Navy, and Air Force, 1990)contains guidelines for the safe design of blast resistant steel connections. However, the adequacy of these design procedures is not well defined because of insufficient information about the behavior of the steel connections under blast loads.





High loading rates can influence the mechanical properties of structural materials (Department of the Army, Navy, and Air Force, 1990, and Soroushian and Choi 1987), and the use of dynamic increase factors (DIFs) for describing strain rate enhancement is well known. A DIF is the ratio of the strain rate enhanced strength to the static strength (e.g., the ratio of the dynamic and static yield stresses for a material). This effect of higher strain rates on the mechanical properties of steel is important for blast-resistant design. DIFs are used for both design and approximate analyses (e.g., single-degree-of-freedom calculations). Nevertheless, DIFs have to be used with care in advanced numerical simulations. It is well known that the steel yield stress is enhanced by strain rates while the ultimate stress is affected much less. The effects of high rate dynamic loadings on the structural responses were investigated in (Krauthammer et al. 2001, and 2002) by employing the recommended DIF values in TM 5-1300 for both the design and the numerical simulations. In those studies, typical modified structural steel connections for seismic conditions were assessed under explosive loads by employing the design procedure in TM 5-1300, and additional and empirical analysis tools. The maximum safe amount of the contained explosive charge and the blast resistant capacities of the connections were estimated. A reliable finite element code developed for simulating short-duration dynamic events, DYNA3D (W hirley and Engelmann, 1993), was validated and used to investigate the behavior of the structural steel connections under the expected blast loads. A hypothetical one-story frame structure with seismic resistant knee connections, assumed to be part of a multi-story building, was selected, as shown in Figure 6.

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TM 5-1300 provides methods of design for explosive safety. Also, the manual provides procedure for deriving the blast load parameters and for calculating the dynamic responses of structural members. The adopted details of the structural model were based on a typical seismic resistant steel knee connection at a corner of a frame. W -14x730 (A572 GR50) and W -36x260 (A36) were employed for the column and beam members, respectively. The weld was made with E70TGK2 fluxed core electrodes that have a 70 ksi yield stress. The post-Northridge connection was reinforced with 36-mmthick continuity plates between the column flanges and 25-mm-thick cover-plates on the beam flanges, to enhance the required moment resistance. The design procedures outlined in Section 5 of TM 5-1300 were used to evaluate the maximum blast load that can be applied to the beam and column members for the structure. The computer codes Shock and Frang were employed also for deriving by trial-and-error the weight of an equivalent TNT charge. One wall was assumed as a frangible panel (i.e., it was assumed to blow out and permit quick venting of the internal pressures).

Finally, the expected structural deformations were computed based on the given load and the procedure outlined in TM 5-1300.

The internal blast loads were derived from the detonation of a TNT charge at the geometric center of the floor in the structures. According to TM 5-1300, a load pulse from an internal explosion can be represented by a short and intense shock pressure and a longer duration lower intensity gas pressure. The maximum rotational deformations at the connections are typically used to assess structural damage. These rotations were investigated to define the structural capacities of the connections under opening explosive loads (i.e., an internal explosion will cause the connections to open). Stresses and strains at critical points of welds and panel zones were checked to identify more detailed deformation mechanisms. Two types of steel connections were employed in this study, as shown in Figure 7.

The first type of connection was used extensively before the Northridge earthquake, and the second was recommended for seismic applications after the studies of the Northridge earthquake. As a first step, the blast resistant capacity of the corner knee connection was analyzed according to TM 5-1300. The preliminary assessment provided an estimated maximum safe explosive charge weight (W equal to 24.7 lbs or 11.23 kg TNT) that the structure could be expected to resist without exceeding recommended damage levels. The rotational deformations were estimated at the connection, based on the computed structural response. Additionally, that analysis was used also to define the corresponding pressure-time histories that would be applied to the structure in the advanced numerical simulation. Finally, numerical simulations were conducted with DYNA3D for comparison with the findings based on TM 5-1300, and to obtain useful information about the possible responses of the steel connections under internal explosions. Since TM 5-1300 requires one to design a structure for 1.2 times the expected explosive weight, the simulation with DYNA3D were performed for blast loads from the detonation of a charge weight of W/1.2, leading to 20.6 lbs or 9.35 kg TNT. The analysis and design loads are described in Figure 8.

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The maximum rotational deformations at the connections were investigated to define the structural capacities of the connections under opening explosive loads. Stresses and strains at the critical points of welds and panel zones were checked to identify the more detailed deformation mechanism. These connections between W -shape cross-sections were studied in both two-dimensional (2D) and three-dimensional (3D) frame structures. They were developed to obtain preliminary general information of the responses of the steel connections under the blast loads, and for initial comparisons with the results of the approximate analyses. The 3D frame models had 7,652 3-D elements. They were developed to analyze the three-dimensional behavior of the system, and the pressure loads on wall and roof panels were transmitted to the frame members. To investigate the strain rate effect on the steel properties and structural responses, the numerical simulations were done with and without consideration of Dynamic Increasing Factors (DIF). Additionally, since this structural model could be part of a multi story building, the effects of gravity dead loads were considered.

These equivalent gravity loads were represented by a 206.9 MPa axial dead load on the columns and 58.4 kN/m vertical dead load on the beams. Each case was studied with and without DIFs, and with and without dead loads. All the numerical simulations were based on combining DIF values and validation against precision test data, and only the results for the 3D connections are summarized in Tables 1 and 2, and Figures 9 and 10.

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