- Email: [email protected]
Assessment of progressive collapse of steel structures under seismic loads
Alexandria Engineering Journal (2018) 57, 3825–3839
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Assessment of progressive collapse of steel structures under seismic loads Yara M. Mahmoud, Maha M. Hassan *, Sherif A. Mourad, Hesham S. Sayed Department of Structural Engineering, Cairo University, Gamaa Street, P.O. Box: 268 Orman-Egypt, Giza, Egypt Received 13 April 2017; revised 31 October 2017; accepted 19 February 2018 Available online 07 December 2018
KEYWORDS Progressive collapse; Steel moment resisting frames; Braced frames; Alternate path method; Nonlinear dynamic analysis; Seismic loads
Abstract Progressive collapse involves a series of failures that lead to partial or total collapse of a structure. It is generally initiated by loss of one or more vertical load carrying elements. This loss is caused by abnormal loads such as bombings, gas explosion, earthquakes. . .etc. Progressive collapse due to seismic actions has not received much attention in spite of its importance and repeated occurrences. In the current study, it is intended to investigate the progressive collapse potential of steel moment resisting and braced frames designed according to Egyptian local standards due to damage caused by seismic actions. One first-storey column is fully removed at arbitrary locations within the building using alternate path method recommended in the UFC guidelines in order to study consequences and check safety of adjacent members. 3-D nonlinear dynamic analyses are employed using SAP2000 is employed in the performed parametric study. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction According to ASCE 7-10 [1], progressive collapse is defined as ‘‘the spread of an initial local failure from element to element, eventually resulting in the collapse of an entire structure or a disproportionately large part of it”. Column loss can be triggered by natural hazards such as earthquakes, hurricanes, floods and tornadoes, or accidental actions such as explosions of a service system, or bombings due to terrorist action. Since the event to Ronan Point apartment tower progressive collapse in 1968, many codes and standards presented several approaches to mitigate progressive collapse. The first standard to address progressive collapse was ANSI standard [2]. How* Corresponding author. E-mail address: [email protected] (M.M. Hassan). Peer review under responsibility of Faculty of Engineering, Alexandria University.
ever, only a warning regarding hazards associated with progressive collapse was included. National Building Code of Canada (NBC) [3] includes general statement regarding the need of structural integrity and provides recommendation for good layout, continuity of reinforcement, and structural mechanisms to resist progressive collapse after local loss of support. ASCE 7-10 [1] assigned a section entitled ‘‘General Structural Integrity” presenting brief qualitative requirements. In addition, this section provides general qualifications guidelines for design to prevent progressive collapse phenomenon. Design requirements and guidelines necessary to reduce potential of progressive collapse for new and existing facilities were detailed in The Unified Facilities Criteria (UFC) [4] for structures experiencing localized structural damage through unforeseeable events. The UFC considers two design approaches the direct design approach and the indirect design approach. The direct design approach includes alternate load path method (ALPM) and specific local resistance method (SLRM). There
https://doi.org/10.1016/j.aej.2018.02.004 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
3826 are four procedures for alternate path method: linear static (LS), linear dynamic (LD), nonlinear static (NS), and nonlinear dynamic (ND) methods. The last method is also recommended by FEMA 356 [5] for seismic analysis and design of structures. In addition to provisions in different design codes and standards, several research efforts are available addressing the progressive collapse behavior of buildings. Marjanishvili et al. [6] modeled a 9-storey moment resisting frame using SAP2000 and analyzed the model considering the loss of edge column scenario through linear and nonlinear static and dynamic analyses. The authors recommended depending nonlinear dynamic analysis rather than nonlinear static analysis procedure. Hyun et al. [7] analyzed two-dimensional 2-storey and 3-storey frames for scenario including loss of an intermediate column using OpenSees program. Analysis results showed that the dynamic amplification fctor can be larger than two as recommended by GSA and DoD guidelines. Sasani et al. [8] experimentally and analytically evaluated the progressive collapse of actual reinforced concrete structures and reported the development of a vierendeel action as a dominant mechanism in redistribution of loads. Fu [9] studied the response of a multi-storey steel braced building considering consecutive column removal scenarios using 3-dimensional finite element models. It was observed that different column removal sequences produce different plasticity formations. Accordingly, the author recommended several measures to mitigate progressive collapse in future designs. Tavakoli et al. [10] studied the ability of steel moment resisting frames, designed based on seismic Iranian codes, to resist progressive collapse with different damaged columns under seismic loading. It was observed that the considered buildings were able to resist progressive collapse for scenarios including loss of first-storey columns. Elshaer et al. [11] investigated the capacity of multistory reinforced concrete structures, designed according to the Egyptian code [12], to resist progressive collapse using the alternate load path method specified in the UFC guidelines. To assess the potential for progressive collapse, three-dimensional non-linear dynamic analysis was performed using the ’Applied Element Method’. The authors considered studying several parameters like location of removed column, case of loading and the consideration of the slabs. For each loading scenario, it was assumed that a primary structural component was removed during an earthquake. It was concluded that reinforced concrete buildings designed according Egyptian code meet the UFC guidelines requirements. In addition, authors reported that loss of column due to earthquake was more critical for progressive than due to gravity loads. Moreover, considering the slabs in progressive collapse analysis was found to be of high importance to take in the major catenary effect developed by the slabs. Tavakoli and Hasani [13] studied the seismic progressive collapse capacity of steel special moment resisting frames. Analyses showed that the potential of progressive collapse depend on the removed column, number of stories and earthquake characteristics. Shi et al. [14] studied the influence of considering composite slabs on the progressive collapse resistance of steel moment frames. The authors reported that existence of floor increases the ductility of structure and its progressive collapse resistance. Chuquitaype et al. [15] studied the contribution of gravity frames in the mitigation of collapse in steel buildings subjected to extreme loading conditions such as earthquake and blast scenarios.
Y.M. Mahmoud et al. In Egypt, research efforts addressing progressive collapse of structures designed according to local standards are rare. In this paper, steel moment resisting frames and braced frames will be studied against progressive collapse due to column loss following major earthquake events according to UFC guidelines. A parametric study employing nonlinear dynamic analysis is performed using SAP2000 software program [16]. Parametric study results for moment resisting and braced frames are compared and conclusions are drawn. 2. Methodology 2.1. Description of models As shown in Fig. 1, XX3-D finite element models are created using SAP2000 software program. The performed parametric study include both moment resisting and braced frames. All the models consist of five equal bays in both directions and five storeys high. Bay width and floor height are equal to 6 m and
a. Moment Resisting Frame
b. Braced Frame Fig. 1
3D view for example models.
Progressive collapse of steel structures under seismic loads
Fig. 2
Stress-strain curve for St-37 as defined in SAP2000.
Fig. 3
Example beam plastic hinge definition.
3827
3828 Table 1
Y.M. Mahmoud et al. Sectional properties of I-beam columns and beams for moment resisting frame models.
Levels
Columns
Perimeter beams
Interior beams
1–2
Web: Flange:
500 12 350 24
400 12 250 22
250 8 150 12
3–5
Web: Flange:
500 12 300 20
300 10 200 18
250 8 150 12
Table 2
Sectional properties of I-beam columns, beams and bracing members for braced frame models.
Levels
Columns
1–2
Web: Flange: Web: Flange:
3–5
500 12 300 28 500 12 250 24
Beams
Bracing members
250 8 150 12 250 8 150 12
Box 200 200 8
Acceleration (m/sec2)
2.00 1.50 1.00 0.50 0.00 -0.50 -1.00 -1.50 0
2
4
6
8
10
12
14
16
18
20
Time (Second) Fig. 4
Generated acceleration time history.
3.5 m, respectively, for all the models. As shown in Fig. 1, floor system for the different models consists of a 120 mm reinforced concrete slab with characteristic strength of concrete cube equal to 25 MPa. Perimeter frames are designed to resist gravity and lateral loads while interior frames resist gravity load only. St 37-2 is used for different steel beams and columns. Hence, the considered yield strength (fy) is 240 N/mm2 and ultimate strength (fu) is 360 N/mm2. Fig. 2 shows the stressstrain curve as defined in SAP2000 program. Model nonlinearity is modeled using concentrated plastic hinges at ends of beams and columns. Fig. 3 shows the definition of an example plastic hinge in beam element. Accordingly, different elements are designed according to the Egyptian Code of Practice for Steel Construction and Bridges [17]. Member sizes for moment resisting and braced frames are presented in Tables 1 and 2. 2.2. Loads and modelling The response of studied structures under sudden column removal is assessed using nonlinear dynamic analysis method. Loads are computed as 120% of the dead loads, 50% of live loads, in addition to seismic loads in order to study the effect of losing a column during an earthquake event. The self-weight
of the structure is considered directly using SAP2000 software program. Meanwhile, super-imposed dead and live loads are taken equal to 1.5 kN/m2 and 3.0 kN/m2, respectively. Wall loads are considered at perimeter beams to consider a 250 mm width brick wall. Time history analysis is performed by defining full excitation in X-axis direction in addition to 30% of the excitation in Y-axis direction. Study models are considered to be located in Cairo, Egypt. Response spectrum curve parameters include design peak ground acceleration of 0.15 g, importance factor (cI) equal to 1 and type B sub-soil group. SeismoArtif program [19] is used to generate acceleration time history records conforming to Type-1 response spectrum curve defined in ECP [18]. Fig. 4 shows sample time history record. Column removal is assumed to occur upon reaching the maximum peak ground acceleration. To simulate the instantaneous column removal, the column is replaced with its equivalent forces. The equivalent load is first assigned using a uniform time history function. This corresponds to the initial case where the column is still in place and functioning at its full capacity. Afterwards, the column is suddenly removed using a step function. The addition of uniform time history and column loss functions are employed to simulate column loss scenario. Fig. 5 shows the time history function used to define the sudden loss of column and its definition in SAP2000. The per-
Progressive collapse of steel structures under seismic loads
Fig. 5
Time history function definition for column removal.
0
Different column removal scenarios. Type of structure
Location of removed column
Scenario 1 Scenario 2 Scenario 3
Moment resisting frames
Corner column Edge column Interior column
Scenario 4 Scenario 5 Scenario 6 Scenario 7
Braced frames
Corner column Edge column Interior column Edge column and adjacent bracing
formed parametric study includes several runs while considering different scenarios for column removal as listed in Table 3. 3. Results and discussion Results will be exhibited in the next sections for the seven listed scenarios in Table 3. Focus will be given to changes in straining actions and deflection values for joints around the removed column. 3.1. Scenario 1, moment resisting Frames-Corner column removal Corner column at the ground floor is removed from the moment resisting frames structure. The maximum deflection
0 Deflection (cm)
Table 3
3829
10
20
30
40
-3
-6
-9
-12
Time (Second)
Fig. 6a Deflection history in Z direction for a beam just above the removed corner column in MRF structure.
in an element just above the removed column was 104 mm as shown in Fig. 6a. A redistribution of major moments in the adjacent beams was observed as shown in Fig. 6b. The maximum value for bending moment developed in the beams reached 1.05 times beam capacity. Plastic hinges were formed in beams after the column removal. The value of maximum plastic rotation is 0.00982 rad which doesn’t exceed the UFC guidelines, so according to the UFC guidelines the structure is considered safe. Figs. 6c–6f show the formation of plastic hinges at the different planes of one of the models. As can be seen, the 3-D representation of the steel moment resisting frame captured the degree of indeterminacy of the structure resulting in deflection values smaller than the reported values in case of 2-D representation of the frame.
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Y.M. Mahmoud et al.
3.2. Scenario 2, moment resisting Frames-Edge column removal Edge column at the ground floor is removed from the moment resisting frames structure. The maximum deflection in an element just above the removed column is 204 mm as shown in Fig. 7a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 7b. The maximum value
Fig. 6b
Fig. 6c
for bending moment developed in the beams reached 1.16 times beam capacity. Plastic hinges were formed in beams after the column removal as shown in Fig. 7c. The value of maximum plastic rotation is 0.00315 which doesn’t exceed the UFC guidelines, so according to the UFC guidelines the structure is considered safe.
Maximum bending moments in beams due to removal of corner column in MRF structure.
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in XZ plane (Y = 0).
Progressive collapse of steel structures under seismic loads
3831
Fig. 6d
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in XZ plane (Y = 3000).
Fig. 6e
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in YZ plane (X = 3000).
3.3. Scenario 3, moment resisting Frames-Interior column removal Interior column at the ground floor is removed from the moment resisting frames structure. The maximum deflection at joint above the removed column is 250 mm as shown in
Fig. 8a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 8b. The maximum value for bending moment developed in the beams reached 1.02 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 8c. The value of maximum plastic rotation is 0.00276 which doesn’t exceed the
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Y.M. Mahmoud et al.
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in YZ plane (X = 0).
Fig. 6f
0 0
5
10
15
20
25
Deflection (cm)
-5
the forces in the brace exceeded the maximum capacity and bracing members failed to resist the straining actions developed due to column loss upon application of earthquake load. 3.5. Scenario 5, Braced Frames-Edge column removal
-10
-15
-20
-25 Time (second)
Fig. 7a Deflection history in Z direction for an element just above the removed edge column in MRF structure.
UFC guidelines, so according to the UFC guidelines the structure is considered safe. 3.4. Scenario 4, Braced Frames-Corner column removal Corner column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is found equal to 335 mm as shown in Fig. 9a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 9b. The maximum value for bending moment developed in the beams reached 1.45 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 9c. The value of maximum plastic rotation is 0.0078. After the column removal,
Edge column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is 207 mm as shown in Fig. 10a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 10b. The maximum value for bending moment developed in the beams reached 1.13 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 10c. The value of maximum plastic rotation is 0.0056. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss. 3.6. Scenario 6, Braced Frames-Interior column removal Interior column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is 105 mm as shown in Fig. 11a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 11b. The maximum value for bending moment developed in the beams reached 0.86 times beam capacity. No plastic hinges are formed in beams after the column removal as shown in Fig. 11c. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss.
Progressive collapse of steel structures under seismic loads
Fig. 7b
3833
Maximum bending moments in beams due to removal of edge column in MRF structure.
Fig. 7c
Deformed shape due to removal of edge column in MRF structure.
3.7. Scenario 7, Braced Frames-Edge column with adjacent bracing removal Edge column with adjacent bracing at the ground floor are removed from braced frames structure. The maximum deflection at joint above the removed column is 54 mm as shown in Fig. 12a. A redistribution of major moments in the adjacent beams was observed as shown in Fig. 12b. The maximum value
for bending moment developed in the beams reached 0.92 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 12c. The value of maximum plastic rotation is 0.0018. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss.
3834
Y.M. Mahmoud et al. 4. Conclusions
0 0
5
10
15
Deflection (cm)
-5 -10 -15 -20 -25 -30
Time (second)
Fig. 8a Deflection history in Z direction for an element just above the removed interior column in MRF structure.
Fig. 8b
In this study, the progressive collapse of steel structures are investigated using nonlinear dynamic procedure recommended in the UFC guidelines. The performed work has provided an assessment of the progressive collapse of moment resisting frames and braced frames while implementing considering several parameters. The behavior of 5-storey moment resisting frame and braced frame under different column removal scenarios was investigated using a 3-D finite element modelling technique. Observations regarding the progressive collapse behavior of such structures was drawn while focusing on
Maximum bending moments in beams due to removal of interior column in MRF structure.
Fig. 8c
Deformed shape due to removal of interior column in MRF structure.
Progressive collapse of steel structures under seismic loads
3835 0
0
0
0
1
2
3
4
2
3
4
5
-5
-10 Deflection (cm)
1
5 Deflection (cm)
-5
-15 -20
-10 -15
-25 -20
-30 -35
-25
Time (second)
Fig. 9a Deflection history in Z direction for an element just above the removed corner column in Braced Frame structure.
Fig. 9b
Time (second)
Fig. 10a Deflection history in Z direction for an element just above the removed edge column in Braced Frame structure.
Maximum bending moments in beams due to removal of corner column in Braced Frame structure.
Fig. 9c
Deformed shape due to removal of corner column in Braced Frame structure.
3836
Y.M. Mahmoud et al.
Fig. 10b
Maximum bending moments in beams due to removal of edge column in Braced Frame structure.
Fig. 10c
Deformed shape due to removal of edge column in Braced Frame structure. 0
deflection and straining action values. Main conclusions regarding each of the considered structures include:
The largest displacement is observed in case of interior column. This can be attributed for: The better catenary action developed in perimeter frames due to the rigid beam-column connections. Meanwhile, interior frames have pinned beam-column connections. Beam sections used in perimeter frames have larger member sizes compared to beams used in interior
Deflection (cm)
4.1. For the moment resisting frames
0
1
2
3
4
5
-2 -4 -6 -8
-10 -12 Time (second)
Fig. 11a Deflection history in Z direction for an element just above the removed interior column in Braced Frame structure.
Progressive collapse of steel structures under seismic loads
Fig. 11b
3837
Maximum bending moments in beams due to removal of interior column in Braced Frame structure.
a. Along axis (2) @ Y=6000
Deformed shape due to removal of interior column in Braced Frame structure.
frames. This results in increasing progressive-collapse capacity of the perimeter frames. The displacement in the scenario including loss of edge column is larger than that in the scenario including loss of corner column. This is due to the higher straining actions formed in the beams causing higher plastic rotations causing larger displacement of the joint above the removed column.
0 0
5
10
15
20
-1 Deflection (cm)
Fig. 11c
b. Along Axis (1) @ Y=0
-2 -3 -4 -5
4.2. For the braced frames -6
The maximum displacement is observed in the case of the corner column removal followed by the case of the edge column removal. This can be attributed to the fact that joint above the removed column is more restrained in the case
Time (second)
Fig. 12a Deflection history in Z direction for an element due to the removal of an edge column with adjacent bracing member in Braced Frame structure.
3838
Fig. 12b
Y.M. Mahmoud et al.
Maximum bending moments in beams due to removal of edge column with adjacent bracing in Braced Frame structure.
a. Along axis (1) @ Y=0 Fig. 12c
b. Along Axis (6) @ Y=30000
Deformed shape due to removal of edge column with adjacent bracing in Braced Frame structure.
of the interior column as it is connected by four beams while the joint above the corner column is connected by two beams only. The least displacement is observed in the case of edge column and bracing removal. Based on the above study, best practical advice to reduce the potential of progressive collapse is to consider performance-based design practices and to avoid local damage failures that may affect the whole structure. Meanwhile, the conducted work can be extended through: comparing forces developing at interface between beams and floor supporting slabs, investigating progressive collapse behavior of different bracing systems such as cross bracing and eccentric bracing configurations, and examining the behavior of steel structures with irregular layouts, different heights, spans, and loads.
References [1] ASCE SEI/ASCE 7–05, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Washington, DC, 2005. [2] ANSI A58.1-72,-82, Minimum Design Loads for Buildings and Other Structures, American National Standards Institute (ANSI), New York, N.Y, 1972–1982. [3] NBCC, National Buildings Code of Canada, National Research Council, Canada, 2005. [4] UFC, Design of Buildings to Resist Progressive Collapse, UFC 4-023, Unified Facilities Criteria, Department of Defense (DoD), Washington, D.C, 2013. [5] FEMA 356 AA, Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, D.C, 2000.
Progressive collapse of steel structures under seismic loads [6] S. Marjanishvili, E. Agnew, Comparison of various procedures for progressive collapse analysis, J. Perform. Construct. Facilit. ASCE 20 (4) (2006) 364–374. [7] A. Hyun-Su Kim, K.I. Jinkoo, An Da-Woon, Development of integrated system for progressive collapse analysis of building structures considering dynamic effect, Adv. Eng. Softw. J. 40 (1) (2009) 1–8. [8] M. Sasani, S. Sagiroglu, Progressive collapse resistance of hotel San Diego, J. Struct. Eng. 134 (3) (2008) 478–488. [9] F. Fu, Progressive collapse analysis of high-rise building with 3D finite element modeling method, J. Constr. Steel Res. 65 (6) (2009) 1269–1278. [10] H.R. Tavakoli, 3-D Nonlinear Static Progressive Collapse Analysis of Multi-story Steel Braced buildings, Civil Engineering, Babol University of Technology, 2012. [11] A. Elshaer, H. Mostafa, Hatem, H. Salem, Progressive collapse assessment of multistory reinforced concrete structures subjected to seismic actions, KSCE J. Civ. Eng. 21 (2016), https://doi.org/10.1007/s12205-016-0493-6. [12] ECP 203 – 2007, The Egyptian Code of Practice for Design and Construction of Reinforced Concrete Structures, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2007.
3839 [13] H.R. Tavakoli, A.H. Hasani, Effect of Earthquake characteristics on seismic progressive collapse potential in steel moment resisting frame, J. Earthq. Struct. 12 (5) (2017) 529–541. [14] F. Shi, L. Wang, S. Dong, progressive collapse assessment of the steel moment-frame with composite floor slabs based on membrane action and energy equilibrium, Open Construct. Build. Technol. J. 11 (2017) 200–215. [15] C. Chuquitaype, A.Y. Elghazouli, R. Enache, Contribution of secondary frames to the mitigation of collapse in steel buildings subjected to extreme loads, J. Struct. Infrastruct. Eng. 12 (2014) 1. [16] SAP2000, SAP 2000 Advanced Structural Analysis Program, Version 14, Computers and Structures, Inc. (CSI), Berkeley, CA, USA, 2009. [17] ECP 205-2007, The Egyptian Code of Practice for Steel Construction – Allowable Stress Design, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2007. [18] ECP 201-2011, The Egyptian Code of Practice for Loads and Forces in Structural Works and Buildings, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2012. [19] SIMQKE, Dario A. Gasparini, Erik H. Vanmarcke, ‘‘Users’ Manual and Documentation”, Massachusetts Institute of Technology, 1976.
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Assessment of progressive collapse of steel structures under seismic loads Yara M. Mahmoud, Maha M. Hassan *, Sherif A. Mourad, Hesham S. Sayed Department of Structural Engineering, Cairo University, Gamaa Street, P.O. Box: 268 Orman-Egypt, Giza, Egypt Received 13 April 2017; revised 31 October 2017; accepted 19 February 2018 Available online 07 December 2018
KEYWORDS Progressive collapse; Steel moment resisting frames; Braced frames; Alternate path method; Nonlinear dynamic analysis; Seismic loads
Abstract Progressive collapse involves a series of failures that lead to partial or total collapse of a structure. It is generally initiated by loss of one or more vertical load carrying elements. This loss is caused by abnormal loads such as bombings, gas explosion, earthquakes. . .etc. Progressive collapse due to seismic actions has not received much attention in spite of its importance and repeated occurrences. In the current study, it is intended to investigate the progressive collapse potential of steel moment resisting and braced frames designed according to Egyptian local standards due to damage caused by seismic actions. One first-storey column is fully removed at arbitrary locations within the building using alternate path method recommended in the UFC guidelines in order to study consequences and check safety of adjacent members. 3-D nonlinear dynamic analyses are employed using SAP2000 is employed in the performed parametric study. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction According to ASCE 7-10 [1], progressive collapse is defined as ‘‘the spread of an initial local failure from element to element, eventually resulting in the collapse of an entire structure or a disproportionately large part of it”. Column loss can be triggered by natural hazards such as earthquakes, hurricanes, floods and tornadoes, or accidental actions such as explosions of a service system, or bombings due to terrorist action. Since the event to Ronan Point apartment tower progressive collapse in 1968, many codes and standards presented several approaches to mitigate progressive collapse. The first standard to address progressive collapse was ANSI standard [2]. How* Corresponding author. E-mail address: [email protected] (M.M. Hassan). Peer review under responsibility of Faculty of Engineering, Alexandria University.
ever, only a warning regarding hazards associated with progressive collapse was included. National Building Code of Canada (NBC) [3] includes general statement regarding the need of structural integrity and provides recommendation for good layout, continuity of reinforcement, and structural mechanisms to resist progressive collapse after local loss of support. ASCE 7-10 [1] assigned a section entitled ‘‘General Structural Integrity” presenting brief qualitative requirements. In addition, this section provides general qualifications guidelines for design to prevent progressive collapse phenomenon. Design requirements and guidelines necessary to reduce potential of progressive collapse for new and existing facilities were detailed in The Unified Facilities Criteria (UFC) [4] for structures experiencing localized structural damage through unforeseeable events. The UFC considers two design approaches the direct design approach and the indirect design approach. The direct design approach includes alternate load path method (ALPM) and specific local resistance method (SLRM). There
https://doi.org/10.1016/j.aej.2018.02.004 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
3826 are four procedures for alternate path method: linear static (LS), linear dynamic (LD), nonlinear static (NS), and nonlinear dynamic (ND) methods. The last method is also recommended by FEMA 356 [5] for seismic analysis and design of structures. In addition to provisions in different design codes and standards, several research efforts are available addressing the progressive collapse behavior of buildings. Marjanishvili et al. [6] modeled a 9-storey moment resisting frame using SAP2000 and analyzed the model considering the loss of edge column scenario through linear and nonlinear static and dynamic analyses. The authors recommended depending nonlinear dynamic analysis rather than nonlinear static analysis procedure. Hyun et al. [7] analyzed two-dimensional 2-storey and 3-storey frames for scenario including loss of an intermediate column using OpenSees program. Analysis results showed that the dynamic amplification fctor can be larger than two as recommended by GSA and DoD guidelines. Sasani et al. [8] experimentally and analytically evaluated the progressive collapse of actual reinforced concrete structures and reported the development of a vierendeel action as a dominant mechanism in redistribution of loads. Fu [9] studied the response of a multi-storey steel braced building considering consecutive column removal scenarios using 3-dimensional finite element models. It was observed that different column removal sequences produce different plasticity formations. Accordingly, the author recommended several measures to mitigate progressive collapse in future designs. Tavakoli et al. [10] studied the ability of steel moment resisting frames, designed based on seismic Iranian codes, to resist progressive collapse with different damaged columns under seismic loading. It was observed that the considered buildings were able to resist progressive collapse for scenarios including loss of first-storey columns. Elshaer et al. [11] investigated the capacity of multistory reinforced concrete structures, designed according to the Egyptian code [12], to resist progressive collapse using the alternate load path method specified in the UFC guidelines. To assess the potential for progressive collapse, three-dimensional non-linear dynamic analysis was performed using the ’Applied Element Method’. The authors considered studying several parameters like location of removed column, case of loading and the consideration of the slabs. For each loading scenario, it was assumed that a primary structural component was removed during an earthquake. It was concluded that reinforced concrete buildings designed according Egyptian code meet the UFC guidelines requirements. In addition, authors reported that loss of column due to earthquake was more critical for progressive than due to gravity loads. Moreover, considering the slabs in progressive collapse analysis was found to be of high importance to take in the major catenary effect developed by the slabs. Tavakoli and Hasani [13] studied the seismic progressive collapse capacity of steel special moment resisting frames. Analyses showed that the potential of progressive collapse depend on the removed column, number of stories and earthquake characteristics. Shi et al. [14] studied the influence of considering composite slabs on the progressive collapse resistance of steel moment frames. The authors reported that existence of floor increases the ductility of structure and its progressive collapse resistance. Chuquitaype et al. [15] studied the contribution of gravity frames in the mitigation of collapse in steel buildings subjected to extreme loading conditions such as earthquake and blast scenarios.
Y.M. Mahmoud et al. In Egypt, research efforts addressing progressive collapse of structures designed according to local standards are rare. In this paper, steel moment resisting frames and braced frames will be studied against progressive collapse due to column loss following major earthquake events according to UFC guidelines. A parametric study employing nonlinear dynamic analysis is performed using SAP2000 software program [16]. Parametric study results for moment resisting and braced frames are compared and conclusions are drawn. 2. Methodology 2.1. Description of models As shown in Fig. 1, XX3-D finite element models are created using SAP2000 software program. The performed parametric study include both moment resisting and braced frames. All the models consist of five equal bays in both directions and five storeys high. Bay width and floor height are equal to 6 m and
a. Moment Resisting Frame
b. Braced Frame Fig. 1
3D view for example models.
Progressive collapse of steel structures under seismic loads
Fig. 2
Stress-strain curve for St-37 as defined in SAP2000.
Fig. 3
Example beam plastic hinge definition.
3827
3828 Table 1
Y.M. Mahmoud et al. Sectional properties of I-beam columns and beams for moment resisting frame models.
Levels
Columns
Perimeter beams
Interior beams
1–2
Web: Flange:
500 12 350 24
400 12 250 22
250 8 150 12
3–5
Web: Flange:
500 12 300 20
300 10 200 18
250 8 150 12
Table 2
Sectional properties of I-beam columns, beams and bracing members for braced frame models.
Levels
Columns
1–2
Web: Flange: Web: Flange:
3–5
500 12 300 28 500 12 250 24
Beams
Bracing members
250 8 150 12 250 8 150 12
Box 200 200 8
Acceleration (m/sec2)
2.00 1.50 1.00 0.50 0.00 -0.50 -1.00 -1.50 0
2
4
6
8
10
12
14
16
18
20
Time (Second) Fig. 4
Generated acceleration time history.
3.5 m, respectively, for all the models. As shown in Fig. 1, floor system for the different models consists of a 120 mm reinforced concrete slab with characteristic strength of concrete cube equal to 25 MPa. Perimeter frames are designed to resist gravity and lateral loads while interior frames resist gravity load only. St 37-2 is used for different steel beams and columns. Hence, the considered yield strength (fy) is 240 N/mm2 and ultimate strength (fu) is 360 N/mm2. Fig. 2 shows the stressstrain curve as defined in SAP2000 program. Model nonlinearity is modeled using concentrated plastic hinges at ends of beams and columns. Fig. 3 shows the definition of an example plastic hinge in beam element. Accordingly, different elements are designed according to the Egyptian Code of Practice for Steel Construction and Bridges [17]. Member sizes for moment resisting and braced frames are presented in Tables 1 and 2. 2.2. Loads and modelling The response of studied structures under sudden column removal is assessed using nonlinear dynamic analysis method. Loads are computed as 120% of the dead loads, 50% of live loads, in addition to seismic loads in order to study the effect of losing a column during an earthquake event. The self-weight
of the structure is considered directly using SAP2000 software program. Meanwhile, super-imposed dead and live loads are taken equal to 1.5 kN/m2 and 3.0 kN/m2, respectively. Wall loads are considered at perimeter beams to consider a 250 mm width brick wall. Time history analysis is performed by defining full excitation in X-axis direction in addition to 30% of the excitation in Y-axis direction. Study models are considered to be located in Cairo, Egypt. Response spectrum curve parameters include design peak ground acceleration of 0.15 g, importance factor (cI) equal to 1 and type B sub-soil group. SeismoArtif program [19] is used to generate acceleration time history records conforming to Type-1 response spectrum curve defined in ECP [18]. Fig. 4 shows sample time history record. Column removal is assumed to occur upon reaching the maximum peak ground acceleration. To simulate the instantaneous column removal, the column is replaced with its equivalent forces. The equivalent load is first assigned using a uniform time history function. This corresponds to the initial case where the column is still in place and functioning at its full capacity. Afterwards, the column is suddenly removed using a step function. The addition of uniform time history and column loss functions are employed to simulate column loss scenario. Fig. 5 shows the time history function used to define the sudden loss of column and its definition in SAP2000. The per-
Progressive collapse of steel structures under seismic loads
Fig. 5
Time history function definition for column removal.
0
Different column removal scenarios. Type of structure
Location of removed column
Scenario 1 Scenario 2 Scenario 3
Moment resisting frames
Corner column Edge column Interior column
Scenario 4 Scenario 5 Scenario 6 Scenario 7
Braced frames
Corner column Edge column Interior column Edge column and adjacent bracing
formed parametric study includes several runs while considering different scenarios for column removal as listed in Table 3. 3. Results and discussion Results will be exhibited in the next sections for the seven listed scenarios in Table 3. Focus will be given to changes in straining actions and deflection values for joints around the removed column. 3.1. Scenario 1, moment resisting Frames-Corner column removal Corner column at the ground floor is removed from the moment resisting frames structure. The maximum deflection
0 Deflection (cm)
Table 3
3829
10
20
30
40
-3
-6
-9
-12
Time (Second)
Fig. 6a Deflection history in Z direction for a beam just above the removed corner column in MRF structure.
in an element just above the removed column was 104 mm as shown in Fig. 6a. A redistribution of major moments in the adjacent beams was observed as shown in Fig. 6b. The maximum value for bending moment developed in the beams reached 1.05 times beam capacity. Plastic hinges were formed in beams after the column removal. The value of maximum plastic rotation is 0.00982 rad which doesn’t exceed the UFC guidelines, so according to the UFC guidelines the structure is considered safe. Figs. 6c–6f show the formation of plastic hinges at the different planes of one of the models. As can be seen, the 3-D representation of the steel moment resisting frame captured the degree of indeterminacy of the structure resulting in deflection values smaller than the reported values in case of 2-D representation of the frame.
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Y.M. Mahmoud et al.
3.2. Scenario 2, moment resisting Frames-Edge column removal Edge column at the ground floor is removed from the moment resisting frames structure. The maximum deflection in an element just above the removed column is 204 mm as shown in Fig. 7a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 7b. The maximum value
Fig. 6b
Fig. 6c
for bending moment developed in the beams reached 1.16 times beam capacity. Plastic hinges were formed in beams after the column removal as shown in Fig. 7c. The value of maximum plastic rotation is 0.00315 which doesn’t exceed the UFC guidelines, so according to the UFC guidelines the structure is considered safe.
Maximum bending moments in beams due to removal of corner column in MRF structure.
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in XZ plane (Y = 0).
Progressive collapse of steel structures under seismic loads
3831
Fig. 6d
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in XZ plane (Y = 3000).
Fig. 6e
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in YZ plane (X = 3000).
3.3. Scenario 3, moment resisting Frames-Interior column removal Interior column at the ground floor is removed from the moment resisting frames structure. The maximum deflection at joint above the removed column is 250 mm as shown in
Fig. 8a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 8b. The maximum value for bending moment developed in the beams reached 1.02 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 8c. The value of maximum plastic rotation is 0.00276 which doesn’t exceed the
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Y.M. Mahmoud et al.
Deformed shape due to removal of corner column in MRF structure @ t = 30 s in YZ plane (X = 0).
Fig. 6f
0 0
5
10
15
20
25
Deflection (cm)
-5
the forces in the brace exceeded the maximum capacity and bracing members failed to resist the straining actions developed due to column loss upon application of earthquake load. 3.5. Scenario 5, Braced Frames-Edge column removal
-10
-15
-20
-25 Time (second)
Fig. 7a Deflection history in Z direction for an element just above the removed edge column in MRF structure.
UFC guidelines, so according to the UFC guidelines the structure is considered safe. 3.4. Scenario 4, Braced Frames-Corner column removal Corner column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is found equal to 335 mm as shown in Fig. 9a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 9b. The maximum value for bending moment developed in the beams reached 1.45 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 9c. The value of maximum plastic rotation is 0.0078. After the column removal,
Edge column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is 207 mm as shown in Fig. 10a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 10b. The maximum value for bending moment developed in the beams reached 1.13 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 10c. The value of maximum plastic rotation is 0.0056. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss. 3.6. Scenario 6, Braced Frames-Interior column removal Interior column at the ground floor is removed from the braced frames structure. The maximum deflection at joint above the removed column is 105 mm as shown in Fig. 11a. A redistribution of major moments in the adjacent beams is observed as shown in Fig. 11b. The maximum value for bending moment developed in the beams reached 0.86 times beam capacity. No plastic hinges are formed in beams after the column removal as shown in Fig. 11c. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss.
Progressive collapse of steel structures under seismic loads
Fig. 7b
3833
Maximum bending moments in beams due to removal of edge column in MRF structure.
Fig. 7c
Deformed shape due to removal of edge column in MRF structure.
3.7. Scenario 7, Braced Frames-Edge column with adjacent bracing removal Edge column with adjacent bracing at the ground floor are removed from braced frames structure. The maximum deflection at joint above the removed column is 54 mm as shown in Fig. 12a. A redistribution of major moments in the adjacent beams was observed as shown in Fig. 12b. The maximum value
for bending moment developed in the beams reached 0.92 times beam capacity. Plastic hinges are formed in beams after the column removal as shown in Fig. 12c. The value of maximum plastic rotation is 0.0018. After the column removal, the forces in the brace exceeded the maximum capacity and the bracing members failed to resist the straining actions developed due to column loss.
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Y.M. Mahmoud et al. 4. Conclusions
0 0
5
10
15
Deflection (cm)
-5 -10 -15 -20 -25 -30
Time (second)
Fig. 8a Deflection history in Z direction for an element just above the removed interior column in MRF structure.
Fig. 8b
In this study, the progressive collapse of steel structures are investigated using nonlinear dynamic procedure recommended in the UFC guidelines. The performed work has provided an assessment of the progressive collapse of moment resisting frames and braced frames while implementing considering several parameters. The behavior of 5-storey moment resisting frame and braced frame under different column removal scenarios was investigated using a 3-D finite element modelling technique. Observations regarding the progressive collapse behavior of such structures was drawn while focusing on
Maximum bending moments in beams due to removal of interior column in MRF structure.
Fig. 8c
Deformed shape due to removal of interior column in MRF structure.
Progressive collapse of steel structures under seismic loads
3835 0
0
0
0
1
2
3
4
2
3
4
5
-5
-10 Deflection (cm)
1
5 Deflection (cm)
-5
-15 -20
-10 -15
-25 -20
-30 -35
-25
Time (second)
Fig. 9a Deflection history in Z direction for an element just above the removed corner column in Braced Frame structure.
Fig. 9b
Time (second)
Fig. 10a Deflection history in Z direction for an element just above the removed edge column in Braced Frame structure.
Maximum bending moments in beams due to removal of corner column in Braced Frame structure.
Fig. 9c
Deformed shape due to removal of corner column in Braced Frame structure.
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Y.M. Mahmoud et al.
Fig. 10b
Maximum bending moments in beams due to removal of edge column in Braced Frame structure.
Fig. 10c
Deformed shape due to removal of edge column in Braced Frame structure. 0
deflection and straining action values. Main conclusions regarding each of the considered structures include:
The largest displacement is observed in case of interior column. This can be attributed for: The better catenary action developed in perimeter frames due to the rigid beam-column connections. Meanwhile, interior frames have pinned beam-column connections. Beam sections used in perimeter frames have larger member sizes compared to beams used in interior
Deflection (cm)
4.1. For the moment resisting frames
0
1
2
3
4
5
-2 -4 -6 -8
-10 -12 Time (second)
Fig. 11a Deflection history in Z direction for an element just above the removed interior column in Braced Frame structure.
Progressive collapse of steel structures under seismic loads
Fig. 11b
3837
Maximum bending moments in beams due to removal of interior column in Braced Frame structure.
a. Along axis (2) @ Y=6000
Deformed shape due to removal of interior column in Braced Frame structure.
frames. This results in increasing progressive-collapse capacity of the perimeter frames. The displacement in the scenario including loss of edge column is larger than that in the scenario including loss of corner column. This is due to the higher straining actions formed in the beams causing higher plastic rotations causing larger displacement of the joint above the removed column.
0 0
5
10
15
20
-1 Deflection (cm)
Fig. 11c
b. Along Axis (1) @ Y=0
-2 -3 -4 -5
4.2. For the braced frames -6
The maximum displacement is observed in the case of the corner column removal followed by the case of the edge column removal. This can be attributed to the fact that joint above the removed column is more restrained in the case
Time (second)
Fig. 12a Deflection history in Z direction for an element due to the removal of an edge column with adjacent bracing member in Braced Frame structure.
3838
Fig. 12b
Y.M. Mahmoud et al.
Maximum bending moments in beams due to removal of edge column with adjacent bracing in Braced Frame structure.
a. Along axis (1) @ Y=0 Fig. 12c
b. Along Axis (6) @ Y=30000
Deformed shape due to removal of edge column with adjacent bracing in Braced Frame structure.
of the interior column as it is connected by four beams while the joint above the corner column is connected by two beams only. The least displacement is observed in the case of edge column and bracing removal. Based on the above study, best practical advice to reduce the potential of progressive collapse is to consider performance-based design practices and to avoid local damage failures that may affect the whole structure. Meanwhile, the conducted work can be extended through: comparing forces developing at interface between beams and floor supporting slabs, investigating progressive collapse behavior of different bracing systems such as cross bracing and eccentric bracing configurations, and examining the behavior of steel structures with irregular layouts, different heights, spans, and loads.
References [1] ASCE SEI/ASCE 7–05, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Washington, DC, 2005. [2] ANSI A58.1-72,-82, Minimum Design Loads for Buildings and Other Structures, American National Standards Institute (ANSI), New York, N.Y, 1972–1982. [3] NBCC, National Buildings Code of Canada, National Research Council, Canada, 2005. [4] UFC, Design of Buildings to Resist Progressive Collapse, UFC 4-023, Unified Facilities Criteria, Department of Defense (DoD), Washington, D.C, 2013. [5] FEMA 356 AA, Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, D.C, 2000.
Progressive collapse of steel structures under seismic loads [6] S. Marjanishvili, E. Agnew, Comparison of various procedures for progressive collapse analysis, J. Perform. Construct. Facilit. ASCE 20 (4) (2006) 364–374. [7] A. Hyun-Su Kim, K.I. Jinkoo, An Da-Woon, Development of integrated system for progressive collapse analysis of building structures considering dynamic effect, Adv. Eng. Softw. J. 40 (1) (2009) 1–8. [8] M. Sasani, S. Sagiroglu, Progressive collapse resistance of hotel San Diego, J. Struct. Eng. 134 (3) (2008) 478–488. [9] F. Fu, Progressive collapse analysis of high-rise building with 3D finite element modeling method, J. Constr. Steel Res. 65 (6) (2009) 1269–1278. [10] H.R. Tavakoli, 3-D Nonlinear Static Progressive Collapse Analysis of Multi-story Steel Braced buildings, Civil Engineering, Babol University of Technology, 2012. [11] A. Elshaer, H. Mostafa, Hatem, H. Salem, Progressive collapse assessment of multistory reinforced concrete structures subjected to seismic actions, KSCE J. Civ. Eng. 21 (2016), https://doi.org/10.1007/s12205-016-0493-6. [12] ECP 203 – 2007, The Egyptian Code of Practice for Design and Construction of Reinforced Concrete Structures, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2007.
3839 [13] H.R. Tavakoli, A.H. Hasani, Effect of Earthquake characteristics on seismic progressive collapse potential in steel moment resisting frame, J. Earthq. Struct. 12 (5) (2017) 529–541. [14] F. Shi, L. Wang, S. Dong, progressive collapse assessment of the steel moment-frame with composite floor slabs based on membrane action and energy equilibrium, Open Construct. Build. Technol. J. 11 (2017) 200–215. [15] C. Chuquitaype, A.Y. Elghazouli, R. Enache, Contribution of secondary frames to the mitigation of collapse in steel buildings subjected to extreme loads, J. Struct. Infrastruct. Eng. 12 (2014) 1. [16] SAP2000, SAP 2000 Advanced Structural Analysis Program, Version 14, Computers and Structures, Inc. (CSI), Berkeley, CA, USA, 2009. [17] ECP 205-2007, The Egyptian Code of Practice for Steel Construction – Allowable Stress Design, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2007. [18] ECP 201-2011, The Egyptian Code of Practice for Loads and Forces in Structural Works and Buildings, Housing and Building Research Center, Building and Physical Planning, Giza, Egypt, 2012. [19] SIMQKE, Dario A. Gasparini, Erik H. Vanmarcke, ‘‘Users’ Manual and Documentation”, Massachusetts Institute of Technology, 1976.