ANALYSIS OF A STEEL FRAME SUBJECTED TO BLAST EFFECTS AND SUBSEQUENT PROGRESSIVE COLLAPSE DEMANDS John E. Crawford and Joseph M. Magallanes Karagozian & Case, 2550 North Hollywood Way, Suite 500 Burbank, CA 91505-5026 1.0 INTRODUCTION This paper presents the analytical methods and results of an analysis of a steel-framed structure subjected to blast effects similar to those arising from a terrorist attack. The building studied was built in 1970 and has six stories above grade with two additional stories below grade. The building’s footprint spans 180 feet by 150 feet. Typical bays are 30 feet square. The building was designed for a low seismic risk zone and exhibits moment connections at almost every column/girder intersection. Structural details for the building are not included for the sake of brevity. 2.0 OVERVIEW OF NONLINEAR FINITE ELEMENT ANALYSIS Nonlinear finite element (FE) analysis is often used to analyze structural components and systems subjected to blast effects when neither test data nor validated simplified engineering models are available. Specialists within the defense community have contributed significantly to recent advances in FE analysis, especially in high-fidelity physics-based (HFPB) methodologies. Computer codes exhibiting HFPB capabilities are based on first principle physics rather than on simplified engineering assumptions. Codes like DYNA3D [1], FLEX [2], LS-DYNA [3], and PRONTO [4] implement a Lagrangian FE formulation which is typically used for structural response calculations. Hence, complex constitutive material models become critical inputs to these codes. Other important attributes of these calculations include contact algorithms, large-deformation geometry, and explicit time-integration of the basic physical equations. Computational results from HFPB FE calculations have been shown to compare well against test data and are often used in the defense community to create virtual data as an alternative to executing expensive field tests [5,6,7,8,9 (AFRL)]. Although these methods exhibit attractive benefits to the analyst, very specialized training and expertise is required to generate accurate results. 3.0 HFPB FE ANALYSIS OF THE STEEL FRAME In the absence of test data and validated engineering models, HFPB FE methods provide a good alternative to help understand the effects of blast loads on steel structures. An analysis was performed on the structure in question to provide an estimate of the anticipated structural response to a terrorist attack similar to that which was experienced in the attack on the Oklahoma City Murrah Building [10]. A thorough discussion of the details of the HFPB FE methodologies used in the analysis is not provided. Instead, this summary focuses on the general analytical approach and on the discussion of results and the implications of the computations. 3.1 EXPLOSIVE THREAT Based on the Murrah Bombing, the explosive threat of interest is an off-axis detonation of a 4,000-pound TNT equivalent explosive adjacent to Column G3. The center of the bomb is offset normally by 12’-6” from the face of the column marble cladding and is offset laterally by 7’-0” from the center of this cladding. This is illustrated in Figure 1.
Transcript
ANALYSIS OF A STEEL FRAME SUBJECTED TO BLAST EFFECTS AND SUBSEQUENT PROGRESSIVE COLLAPSE DEMANDS
John E. Crawford and Joseph M. Magallanes Karagozian & Case, 2550 North Hollywood Way, Suite 500
Burbank, CA 91505-5026
1.0 INTRODUCTION
This paper presents the analytical methods and results of an analysis of a steel-framed structure subjected to blast effects similar to those arising from a terrorist attack. The building studied was built in 1970 and has six stories above grade with two additional stories below grade. The building’s footprint spans 180 feet by 150 feet. Typical bays are 30 feet square. The building was designed for a low seismic risk zone and exhibits moment connections at almost every column/girder intersection. Structural details for the building are not included for the sake of brevity.
2.0 OVERVIEW OF NONLINEAR FINITE ELEMENT ANALYSIS Nonlinear finite element (FE) analysis is often used to analyze structural components and systems
subjected to blast effects when neither test data nor validated simplified engineering models are available. Specialists within the defense community have contributed significantly to recent advances in FE analysis, especially in high-fidelity physics-based (HFPB) methodologies.
Computer codes exhibiting HFPB capabilities are based on first principle physics rather than on simplified engineering assumptions. Codes like DYNA3D [1], FLEX [2], LS-DYNA [3], and PRONTO [4] implement a Lagrangian FE formulation which is typically used for structural response calculations. Hence, complex constitutive material models become critical inputs to these codes. Other important attributes of these calculations include contact algorithms, large-deformation geometry, and explicit time-integration of the basic physical equations.
Computational results from HFPB FE calculations have been shown to compare well against test data and are often used in the defense community to create virtual data as an alternative to executing expensive field tests [5,6,7,8,9 (AFRL)]. Although these methods exhibit attractive benefits to the analyst, very specialized training and expertise is required to generate accurate results.
3.0 HFPB FE ANALYSIS OF THE STEEL FRAME In the absence of test data and validated engineering models, HFPB FE methods provide a good alternative
to help understand the effects of blast loads on steel structures. An analysis was performed on the structure in question to provide an estimate of the anticipated structural response to a terrorist attack similar to that which was experienced in the attack on the Oklahoma City Murrah Building [10].
A thorough discussion of the details of the HFPB FE methodologies used in the analysis is not provided. Instead, this summary focuses on the general analytical approach and on the discussion of results and the implications of the computations.
3.1 EXPLOSIVE THREAT Based on the Murrah Bombing, the explosive threat of interest is an off-axis detonation of a 4,000-pound
TNT equivalent explosive adjacent to Column G3. The center of the bomb is offset normally by 12’-6” from the face of the column marble cladding and is offset laterally by 7’-0” from the center of this cladding. This is illustrated in Figure 1.
3.2 SUBSTRUCTURE MODEL OF COLUMN G3 Figure 2a is a rendering of the building’s steel framing between gridlines F and G. To compute the
response of the building to the explosive threat of interest, a substructure model of Column G3 was created. The FE mesh for this model is shown in Figure 2b. The model features a full-height model for Column G3 including all main girders framing into this column in both the normal and lateral directions. The column and main girder sizes used in the FE model of the substructure are given in Figure 3.
Two major constraint features are included to complete the substructure model. First, a portion of the 10-inch thick basement wall and pilaster was modeled to provide a realistic boundary condition at the base the column. This basement wall was then restrained from all translations along the side and bottom edges of the model. Second, 24-inch long joist stubs, spaced at 10-feet on center along the length of the girder, are included in the model for account for the support conditions that steel framing would provide to similar girders when subjected to horizontal blast loads. The rear ends of these joist stubs are restrained against all horizontal translations, but are allowed to move vertically with the girder.
All major structural steel components, including columns, girders, steel joists and connection tabs were modeled with Midlin shell elements with 5 Gauss integration points through the thickness of the shell. Figure 4 shows the details of the FE mesh at the first story connection. All upper story connections are modeled in a similar manner. Although bolts and welds can be effectively modeled, they are not explicitly accounted for in this calculation to reduce the models complexity and the execution runtime. However, the connection tabs themselves are explicitly modeled and merged into the FE mesh of the connecting column and girder meshes, thereby providing adequate rotational and translational flexibility to the model in the connection areas. This simplification has proved to be adequate for modeling the overall structure behavior, but is very poor in predicting localized connection failures.
The FE mesh at the base of Column G3 is shown in Figure 5. As before, all steel is modeled with shell elements. The basement wall, however, is modeled with low-order continuum elements using an elastic concrete material. The column and base plate meshes are merged into the wall continuum elements, resulting in a very stiff and likely over-constrained support condition. Although modeling this basement wall with a nonlinear concrete material would yield a better representation of the base boundary condition, this requires additional effort and also requires explicit modeling of reinforcing bars [11, 12]. For the sake of simplicity and runtime efficiency, this increase in fidelity was sacrificed.
Figure 6 shows the support condition model at the girder ends away from Column G3. Ideally, the substructure model would provide a boundary constraint which transfers the flexibility of the connecting structural elements to the girder model via six principal degrees of freedom for Cartesian coordinates (i.e., three translations and three rotations). Furthermore, an ideal substructure model would account for the degradation of this flexibility from the same blast effects affecting the primary model. The approach used in this study simplifies this rather complex idealization by implementing rigid girder caps connected to single degree of freedom linear translational springs to model the horizontal in-plane flexibility of the adjacent bays (along the axis of the principal girders). All other five degrees of freedom are restrained from motion in this methodology. Although rotational flexibility was observed during post-Northridge test programs on moment connections [13], especially in connections exhibiting non-stiffened column webs, the purpose of the model is to compute global behavior which makes this simplification acceptable.
Loads were computed using ConWep [14], a fast-running engineering airblast code, and applied to two orthogonal grids of shell elements modeling 2-inch thick marble cladding debris as illustrated in Figure 7. The use of ConWep was employed primarily to remain consistent with simplified analyses in lieu of more fidelic airblast computational methods. In this approach, airblast histories were computed at the center of each individual cladding segment and applied as a uniform pressure-history over each element. This marble cladding debris, 3-inch square in planar dimension, is assumed to have no cohesive strength once struck by the airblast loading, allowing each individual piece of debris to behave independently and impact Column G3 with different initial velocities. Figure 8 show the cladding debris at 2 ms after detonation. Note that at this time, the debris at the lower half of the column has impacted the column, thereby imparting a series of discrete impulsive loads. Although not clearly show in this
figure, the weak axis of the column is receiving similar impulsive loadings from debris on the opposite face of the column.
The rest of the steel frame in the upper stories was also loaded with airblast pressure-histories computed with ConWep. However, the loads were applied directly to the exposed steel. Hence the girders were loaded in their webs and Column G3 loaded on its front flange. Since the actual structure exhibits concrete cladding, which may shield the steel from blast effects, this was primarily done for simplicity and to remain consistent with simplified loading methods.
3.3 SUBSTRUCTURE MODEL RESULTS Figure 9 shows the displacement of the column at various times in the calculation. At 2 ms, the front
flanges have folded over due to the debris loading. At 4 ms, a shear deformation in the column is clearly visible. A classical flexural deformation mode is not evident until nearly 8 ms into the column response. The column continues to displace in this manner until it peaks near 18 ms. Figure 10 shows the horizontal displacement-histories for various points along the height of the column. The peak deformation in the column is calculated as approximately 12-inches along its strong axis, with a residual displacement of about 11 inches. This maximum deflection occurs near the quarter-height of the column. The peak deformation in the column in the weak axis direction is calculated to be 4.5 inches with a residual deflection of 4 inches.
Figure 11 illustrates the accumulated damage in the column by plotting fringes of von-Mises effective plastic strain (EPS). The peak plastic (true) strain in the front flange is 0.35 in/in. Although the majority of the plastic strains are localized at the base of the column, it is evident that local deformations occur in the interior girder on the first floor. This is also shown in Figure 12.
Figure 12 also shows that the first story exterior girders are severely deformed by the blast impinging on the girder webs. Figure 13 plots the horizontal displacement-histories for the girders closest to the charge center. The first story exterior girders undergo more than 15 inches of deflection in the X-direction. The girder deformation demands decrease along the height of the building. Since the calculation is not able to model brittle connection failures, it is unclear if these large deformations would actually be precluded from brittle failures.
The overall stability of the frame is illustrated in Figure 14 which plots the vertical displacement-history of each story. Recall that the column deformation peaks near 20 ms. During this first 20 ms in the calculation, the P-∆ effects from the column gravity loads are accelerating the frame downward. At 20 ms the downward deflection of the frame a peaks at 2 inches in the upper stories. The permanent downward displacement of the frame is computed to be near 1.25 inches. Collapse of the frame is not expected.
Figure 15 shows a frontal and a side elevation view of the entire substructure model plotted with fringes of horizontal displacement at 150 ms, corresponding to the time when both the blast effects and the P-∆ effects have stabilized. It is clear that the majority of the deformation is localized the first story. The girder displacement, however, is significant up to the third story of the structure. Figure 16 shows the final displaced shape of the ground story, where the majority of the damage was computed.
4.0 SUMMARY The analysis of the steel framed structure presented in Section 3.0 indicates that the frame is not likely to
collapse as a result of the blast effects. Although the primary column was significantly damaged, the structural system was robust enough to resist a progressive collapse. It should be reiterated, that this model did not account for brittle fractures or failures in the connections which may preclude the ductile response computed here.
5.0 REFERENCES 1. Whirley, R. G. and B. E. Engelmann, “DYNA3D: A Nonlinear Explicit Three-Dimensional Finite Element
Code for Solid and Structural Mechanics,” User Manual, Report UCRL-MA-107254, Rev. 1, Lawrence Livermore National Laboratory, Livermore, CA, November 1993.
2. Vaughan, D. K., 1983, “Flex User’s Guide,” Report UG 8298, Weidlinger-Associates, Los Altos, CA, May 1983, plus updates through 2002.
3. “LS-DYNA User’s Manual - Version 960,” Livermore Software Technology Corporation, March 2001. 4. Attaway, S. W., et al, “PRONTO 3D User’s Instructions: A Transient Dynamic Code for Nonlinear Structural
Analysis,” SAND98-0000, Sandia National Laboratories, Albuquerque, NM, March 1998. 5. Magallanes, J. M., K. B. Morrill, and J. W. Koenig, "Results from Discrete Leto Tests 1 to 3 of the
DTRA/GSA Steel Test Program," Karagozian & Case, Burbank, CA, IR-05-4.1, in publication. 6. Magallanes, J. M., K. B. Morrill, and J. W. Koenig, "Discrete Leto 4: Analytic and Test Results," Karagozian
& Case, Burbank, CA, IR-05-13.1, September 2005. 7. Magallanes, J. M., K. B. Morrill, and J. W. Koenig, "Discrete Leto 5: Analytic and Test Results," Karagozian
& Case, Burbank, CA, TR-05-15.1, September 2005. 8. Magallanes, J. M., K. B. Morrill, and J. W. Koenig, "Discrete Leto 6: Analytic and Test Results," Karagozian
& Case, Burbank, CA, IR-05-16.1, September 2005. 9. Bogosian, D. D., W. Wathugala, and B. Gerber, “Fast-Running Models for Predicting Response of CMU
Walls and Reinforced Concrete Columns and Beams,” Karagozian & Case, Burbank, CA, TR-04-7.2, May 2004.
10. Federal Emergency Management Agency, “The Oklahoma City Bombing: Improving Building Performance through Multi-hazard Mitigation,” FEMA 277, Washington, DC, August 1996.
11. Crawford, J. E. and L. J. Malvar, "User's and Theoretical Manual for K&C Concrete Model," Karagozian & Case, Burbank, CA, TR-97-53.1, December 1997.
12. Malvar, L. J. and J. E. Crawford, “Recommended Static and Dynamic Properties of Steel Reinforcing Bars,” TR-97-41.1, Karagozian & Case, Glendale, CA, September 1992.
13. “Connection Test Summaries,” SAC Joint Venture, Sacramento, CA, SAC-96-02. 14. ConWep Hyde, D. W. “User’s Guide for Microcomputer Programs ConWep and FunPro, Applications of
TM 5-855-1, ‘Fundamentals of Protective Design for Conventional Weapons,’” Instruction Report SL-88-1, Department of the Army, Waterways Experiment Station, Corps of Engineers, Vicksburg, MS 1988.
6.0 ACKNOWLEDGEMENT The analytic modeling techniques used in this paper have been developed and validated under a steel blast
effects testing program sponsored by the Defense Threat Reduction Agency (DTRA) under the direction of Mr. Douglas Sunshine.
Figure 1. Explosive threat similar to the Oklahoma City Murrah building bombing.
G
F
31
6
First Story Column G3
24 5
G
F
31
6
First Story Column G3
24 5
3
G
FFirst story column G3
2
43
G
FFirst story column G3
2
4
(a) Rendering. (b) HFPB FE mesh.
Figure 2. Structural model of Column G3.
Y
X Z
Figure 3. Column and girder sizes for the FE mesh.
Figure 4. FE mesh details at the first story joint.
W24×130
W18× (Varies)
W24×76
W14×228 Col
W14×119 Col
W14×95 Col
W14×95 Col
W14×68 Col
W14×68 Col
W21×68 Exterior Girder
10-inch Concrete Wall
W21×112
Column G3
Interior girder
Typical joiststubs
Pinned connection exhibit merged shear tabs
All moment connections exhibit merged cover plates and shear tabs
Exterior girders
(a) Finite element mesh showing concrete wall. (b) Finite element model, not showing concrete wall.
Figure 5. FE mesh details at the column base.
Figure 6. Girder and boundary conditions.
Column G3
Ground interior girder
Continuum elements of the basement wall Base plate embedded
in basement wall
Ground interior girder
Column G3
Exterior girders
Typical joist stubs
Rigid and constrained end blocks
Y-direction linear translational spring
Figure 7. Explosive location and airblast loading to cladding debris
Figure 8. Deformed shape of the FE mesh at 2 ms showing the debris impacting the
column.
7 foot offset
12.5-foot standoff
Marble cladding debris
(a) t = 2 ms. (b) t = 4 ms.
(c) t = 8 ms. (d) t = 18 ms.
Figure 9. Deformed shape of Column G3 showing fringes of horizontal displacement (Global-Y).
(a) Column nodes.
(b) Displacement history in the column strong axis direction (Global-X).
(c) Displacement history in the column weak axis direction (Global-Y).
Figure 10. Response of Column G3 at the first story.
(a) Side view of column deformation. (b) Isometric view of base deformation.
Figure 11. Damage to the column showing fringes of von-Mises effective plastic strain.
(a) Fringes of horizontal displacement (b) Fringes of von-Mises effective plastic strain. (Global-X).
Figure 12. Damage to the first story connection.
(a) Girder nodes at web midline. (b) Displacement history.
Figure 13. Response of girders.
(a) Nodes at story levels. (b) Vertical displacement history.
Figure 14. Vertical global response of the frame.
(a) Frontal view of frame. (b) Side view of frame.
Figure 15. Final displaced shape of the substructure model.
