Advertisement

Asian Journal of Civil Engineering

, Volume 19, Issue 3, pp 295–307 | Cite as

Effects of finite element modeling and analysis techniques on response of steel moment-resisting frame in dynamic column removal scenarios

  • F. Kiakojouri
  • M. R. Sheidaii
Original Paper
  • 240 Downloads

Abstract

Due to the high cost of the experimental progressive collapse tests, numerical simulation has been widely used by researchers. Finite element method is applied in the majority of numerical progressive collapse studies. In this paper, the influences of finite element modeling and analysis techniques including solution procedure, mesh size, element type, column removal time (CRT), damping, strain rate and output-related issues on nonlinear dynamic column removal response of a steel framed structure are evaluated in detail. According to the results, mesh size and column removal time have major influence on the structural response in column removal scenarios, while influences of solution procedure and damping ratio on the maximum response are negligible. Considering the strain-rate effects results in lower response and the rate of decline mainly depends on column removal time. Results also show that special emphasis should be laid on the accuracy of saving outputs, because a long interval causes significant change in the estimated response and may lead to misleading conclusions.

Keywords

Progressive collapse Dynamic column removal Nonlinear analysis Mesh dependency Strain rate 

Introduction

In structural engineering, progressive collapse is defined as the spread of initial local failure from structural member to member, eventually resulting in the collapse of an entire structure or a large part of it. The underlying characteristic of progressive collapse is that the final state of collapse is disproportionately larger than the initial local failure (Ellingwood et al. 2007). Progressive collapse can be initiated by abnormal loads such as aircraft impact, design error, construction error, fire, explosions, hazardous materials, vehicular collision, and accidental overload (Ellingwood et al. 2007).

Historically, progressive collapse attracted the attention of researchers from the failure of Ronan Point, a 22-story residential apartment at London, UK, in 1968. Research in progressive collapse has gained momentum after 11 September 2001. In the aftermath, efforts were made to reform the current building code and publish new guidelines and codes (GSA 2003, 2013; DoD 2005, 2009).

Due to the high cost of the experimental progressive collapse tests, numerical simulation has been widely used by researchers. However, experimental progressive collapse study can be found in the literature, especially on reinforced concrete substructures (Lu et al. 2016; Ren et al. 2016). Moreover, there are few experimental tests on steel framed structures mostly on existing buildings (Song et al. 2014) and connections behavior in collapse scenario (Yang and Tan 2012). These research works are mainly static-type experiments. Exceptions can be found in Song and Sezen (2013) and Song et al. (2014).

Numerical study of progressive collapse is performed either by building and structural analysis software packages such as ETABS (Mohamed 2015; Chiranjeevi and Simon 2016), SAP2000 (Kaewkulchai and Williamson 2006; Sheidaii and Jalili 2015), Perform 3D (Tavakoli and Alashti 2013; Kang and Kim 2014) and OpenSees (Kim and Kim 2009; Kim et al. 2009), or by general purpose finite element packages such as Abaqus (Fu 2013; Tavakoli and Kiakojouri 2014), LS-DYNA (Kwasniewski 2010; Agarwal and Varma 2014), ANSYS (Pirmoz 2011; Valipour and Bradford 2012) and ADINA (Pujol and Smith-Pardo 2009; Zhacng et al. 2010). While it is easier to set up a model in first group (due to good preprocessing ability of these softwares), they are not perfect codes for progressive collapse analysis, for example these softwares could not easily simulate the cracking, damage, strain rate and distributed plasticity and also provide limited outputs compared to the second group. Therefore, for precise progressive collapse analysis, using general purpose finite element packages is preferable.

Due to the poor preprocessing ability of general purpose finite element packages and long analysis time, most of the authors prefer 2D macro models using beam element. A good exception is provided by Kwasniewski (2010), in which a detailed 3D finite element macro model using shell elements is presented. One-, two- and three-dimensional substructure models are developed and compared by Liu (2010) to numerical study of progressive collapse. According to the obtained results, the global response of the one-dimensional beam element model is close to that corresponding to the 2D shell or the 3D solid models.

The mesh size has major effects on not only the computational time, but also on the accuracy of the results in nonlinear dynamic finite element collapse analysis (Jiang et al. 2015). Usually, the mesh has been refined around critical regions (e.g., connections and damaged spans) to ensure that the stress and strain gradients in such regions are precisely captured (Alashker et al. 2011). When shell or solid elements are used, fully integrated elements are preferable to ensure that hourglass modes do not contaminate the obtained numerical results (Alashker et al. 2011).

Most of the published numerical progressive collapse analyses are based on alternate path method with sudden column loss at the first floor level. The alternate path is a threat-independent method, which means this method ignores the triggering event and considers structural response after the local failure. In recent years, more researchers have focused on progressive collapse due to certain triggering event such as blast (Fu 2013; Tavakoli and Kiakojouri 2013a), impact (Kaewkulchai and Williamson 2006; Kang and Kim 2014) and fire (Agarwal and Varma 2014; Tavakoli and Kiakojouri 2015). Although some authors propose that threat-independent approaches underestimate the dynamic response, the standard procedure in guidelines and codes focus on the threat-independent approaches (Kiakojouri et al. 2016).

The influence of step size on column removal response is investigated by Gerasimidis and Baniotopoulos (2011). Two algorithms were used for the solution of the column loss: the β-Newmark and the Hilbert–Hughes–Taylor. Based on the results, the response of the structures changes when the solution procedure changes. These differences are more critical when the time step size of the methods is high, especially when it is close to the time duration of the column removal. The results also show that the response of the structure is underestimated when the step sizes are not low enough. As the time step size reached values close to zero, two algorithms produced the same results, showing that low time step size values are vital for the reliability of both the algorithms (Gerasimidis and Baniotopoulos 2011).

Generally, progressive collapse analysis is performed in rate-independent analysis, but the influence of strain-rate effects should not be neglected when the column is removed instantaneously according to some researches (Tavakoli and Kiakojouri 2013a; Chen et al. 2016). Based on their results, the capacity of structures increase meaningfully when the strain-rate effect is considered.

The effect of damping ratio on nonlinear dynamic analysis response and dynamic increase factor (DIF) in nonlinear analysis of structures against column removal are investigated by Mashhadi and Saffari (2016). The results of the analysis reveal that DIF is decreased with increasing damping ratio (Mashhadi and Saffari, 2016). According to Jiang et al. (2017), the influence of damping on progressive collapse of steel frames under a localized fire is negligible in the range of damping ratio from 0 to 10%. On the other hand, the effect of strain rate on the structural performance of steel frames is significant for the cases involving dynamic buckling (Jiang et al. 2017). The study by Li et al. (2018) showed that, for a column instability-induced collapse mode, the impact of the damping is larger than the influences of the strain rate on the structural response. However, for the failure-induced collapse, the effects of the strain rate are larger than the damping (Li et al. 2018).

According to GSA guideline, it is preferable to remove the column instantaneously, and the duration for removal must be less than one-tenth of the period associated with the structural response mode for the vertical motion of the bays above the removed column (GSA, 2013). Numerical study of the effects of duration of column removal is the subject of some papers. According to results, sudden column removal provides larger structural response (Tavakoli and Kiakojouri 2013b; Chen et al. 2016). Furthermore, some authors suggest that the decision about using either sudden column removal or gradual column removal depends on the type of triggering event (Tavakoli and Kiakojouri 2013b).

Although thousands of papers on numerical study of progressive collapse can be found in the literature, a comprehensive study of the influences of finite element modeling and analysis on the obtained response is rare. In this paper, the effects of finite element modeling parameters and analysis techniques including solution procedure, mesh size, element type, column removal time (CRT), damping, strain rate and output related issues are considered in numerical modeling and the results are discussed in detail with special emphasis on evaluation of column removal point (CRP) displacements. The obtained results provide the rationale for finite element modeling and analysis of steel moment-resisting frames in dynamic column removal scenarios.

Primary design, loading and finite element modeling

Primary design

The numerical model is a four-story steel moment-resisting frame, the floor height of which is 3.2 m and span length is 5 m as shown in Figs. 1 and 2. This building has special steel moment frame system and designed by commercial program ETABS (Habibullah 2013) based on seismic criteria of Iranian code of practice for seismic design of buildings (2014). The building is designed for a very high seismic zone of Iran that has design acceleration of 0.35g, where g is the gravitational acceleration. The considered R-factor (response modification factor) is 7.5, based on Iranian code of practice for seismic resistant design of buildings. This building is considered as standard residential (importance factor is 1) and assumed to be on soil type 3 according to Iranian code of practice (Standard no. 2800). The considered dead load and live load are 6.5 and 2 kPa, respectively.
Fig. 1

Plan of the building and the selected frame for progressive collapse analysis

Fig. 2

Elevation of structure and column removal cases

The structural members are made of St37 steel having a yield stress of Fy = 240 MPa. The other adopted material properties were: Young’s modulus, E = 210 GPa, Poisson coefficient, ν = 0.3 and density ρ = 7800 kg/m3. The nonlinear behavior of steel is modeled by bilinear behavior with strain hardening (see Fig. 3).
Fig. 3

Bilinear stress–strain curve of steel

Finite element modeling

Progressive collapse analysis is performed using general purpose finite element package Abaqus 6.14. Both explicit and implicit methods are applied in this numerical study and results are compared. All members are modeled by beam elements in Abaqus (see Fig. 4). Because the global response of the frame in the column removal scenario is the main interest, beam element is used in this study. All beam elements in Abaqus library are beam-column elements, which means they allow axial, bending and torsional deformation. The beam properties are input by defining the cross section from the Abaqus cross-sectional library. At each increment of the analysis, the stress in the cross section of beam elements is numerically integrated and the responses are defined as the analysis proceeds (SIMULIA 2014).
Fig. 4

Beam element in Abaqus

In the modeling of steel, the elastic part is defined by Young’s modulus and Poisson’s ratio. The plastic part is defined as the true stress versus logarithmic strain. Abaqus calculates values of yield stress from the current values of strain, approximating the stress–strain behavior of steel with a series of straight lines to simulate the actual behavior. In this study, a bilinear model was used. Therefore, the material behaves as a linear elastic material up to the yield stress of the steel. Then, it goes into the strain hardening until reaching the ultimate stress. Figure 3 shows the bilinear stress–strain curve of steel that is used in this study.

Two different column removal scenarios are considered in the numerical study. In Scenario 1, the corner column in the first story is suddenly removed, while in Scenario 2 the center column in the first story is used for dynamic column removal. These scenarios are shown in Fig. 2.

Unless otherwise specified, all results reported in this paper were obtained using linear beam formulation with the size of 0.25 m, 5% damping, implicit analysis and automatic incrementation.

Verification of the finite element model

Due to the lack of published dynamic full-scale progressive collapse test, a two-dimensional static experimental verification was performed to ensure the accuracy of the finite element model. Such an approach has been widely used by other researchers (Szyniszewski and Krauthammer 2012; Tavakoli and Hasani 2017). For this purpose, the test results presented by Sadek et al. (2010) are used for validation of the developed numerical model. In this test, a hydraulic ram was employed to apply a vertical load on the column removal point of the two-dimensional steel moment-resisting frame (Fig. 5). The simulation result is compared with the experimental results in Fig. 6. As shown in this figure, the numerical finite element model captured the linear and nonlinear steel frame resistance with good accuracy. The good agreement between the numerical and experimental test results validated the simulation approach to represent the actual behavior of the steel moment-resisting frames under column loss scenarios.
Fig. 5

Experimental configuration utilized by Sadek et al. (2010)

Fig. 6

Comparison of experimental results with the employed FE simulations by Abaqus

Procedure for implicit progressive collapse analysis

Numerical analysis methods may be classified as either explicit or implicit. Implicit method is one in which the calculation of the current value in one step is based on the values calculated in the previous step. This method is unconditionally stable even for large steps. The most important disadvantage of the implicit FEA is that this approach requires the calculation of the inverse of stiffness matrixes, and calculation of an inverse matrix is computationally expensive and time-consuming, especially for nonlinear problem and complicated models (Wu and Gu 2012; SIMULIA 2014).

In this paper, for implicit progressive collapse analysis, a three-step procedure is used. In the first step, vertical loads (1.2DL + 0.5LL) are applied to all members statically. In the second step, the remove command from the Abaqus library is used for dynamic column removal. This step is dynamic and has a time duration equal to 0.01 s. By changing this value, the influence of column removal time is investigated. In the third step, the structural response after column removal is monitored. The duration of this step is 1 s. These three steps are shown in Fig. 7.
Fig. 7

Procedure for implicit column removal analysis

Procedure for explicit progressive collapse analysis

In an explicit finite element analysis, instead of solving for displacement, the solution is based on acceleration and, therefore, there is no need for inversion of the stiffness matrixes. The explicit method is conditionally stable. Therefore, small time steps should be employed. This time step basically depends on the order of the smallest value of the ratio of the element length to the speed of the wave in the material. These characteristics make this method practical for the phenomena like blast and impact (Wu and Gu 2012; SIMULIA 2014).

Although the procedure mentioned for implicit dynamic column removal is very useful and practical (see Fig. 7), it cannot be used for explicit column removal analysis, because an explicit analysis after an implicit analysis (static gravity loading) is not allowed in FEA packages due to the different nature of the two approaches. Moreover, the remove command is not available in Abaqus/explicit. Therefore, the following procedure is used for explicit analysis. First, the reaction forces acting on a column are calculated. Then the column is replaced by concentrated load equivalent of its calculated forces. To simulate the phenomena of dynamic column loss, the column forces are removed after a certain time has elapsed, as shown in Fig. 8. A similar procedure is used by (Kim and Kim 2009) and a detailed discussion can be found in Tavakoli and Kiakojouri (2013b).
Fig. 8

Applied load for explicit dynamic column removal analysis

In this study, as shown in Fig. 8, the loads (vertical gravity loads and reactions) increased linearly for 3 s until they reached their maximum amounts and then remained constant for 2 s. The concentrated forces were suddenly removed at 5 s to simulate the dynamic column loss.

Results and discussion

Explicit versus implicit

Displacements of CRP by the two considered methods are shown in Figs. 9 and 10 for Scenario 1 and Scenario 2, respectively. A very good agreement between the two methods can be observed in these figures. Almost identical responses in terms of maximum displacement are observable. According to the results, the time step should be significantly lower than the CRT. Additional studies show that in an explicit column removal analysis, better results are achieved when the incrementation size is lower than CRT/200. A similar suggestion is also reported in the literature (Gerasimidis and Baniotopoulos, 2011).
Fig. 9

Comparison of explicit and implicit analyses (displacement of CRP in Scenario 1)

Fig. 10

Comparison of explicit and implicit analyses (displacement of CRP in Scenario 2)

As mentioned before, in an implicit analysis, a larger time step is allowed. Figure 11 shows the influence of time increment size on the dynamic response of CRP in Scenario 2. In this case, the results do not change for time steps smaller than 0.001 s. Therefore, the increment size smaller than CRT/10 is satisfactory. In the other sections of this study, automatic incrementation is used and the required size is automatically calculated by Abaqus.
Fig. 11

Influence of increment size on dynamic response of CRP in Scenario 2 (implicit analysis)

These calculations were performed on 4 processors Intel Core-i7 with 16 GB RAM. The analysis time for the implicit method is two to three times larger than that required for explicit analysis, depending on column removal cases. It should be noticed that the procedures for loading and column removal are different in the two mentioned methods, as shown in Figs. 7 and 8. For explicit analysis, a considerable amount of calculations is needed before column removal, and by manipulating this time the explicit method becomes even more efficient.

Element type and mesh dependency

In linear static finite element analysis using beam elements, the size of the elements does not affect the results of the analysis. On the other hand, for nonlinear dynamic analysis, the solution is highly dependent on the mesh configuration, and the influences of mesh size should be considered in the analysis when nonlinearity is expected. Abaqus offers a wide range of beam elements including linear, quadratic or cubic interpolation. In this paper, B21 (linear interpolation Timoshenko beam element) and B22 (quadratic interpolation Timoshenko beam element) with four different mesh sizes are used for progressive collapse analysis.

Figures 12 and 13 show the time history of CRP displacement using linear (interpolation) beam element for Scenario 1 and Scenario 2, respectively. The analysis is repeated for four different mesh sizes including 0.1-, 0.25-, 0.5- and 1-m elements. As expected, by reducing the mesh size the maximum displacement of CRP is increased. However, for mesh size smaller than 0.25 m, the results do not change significantly. This mesh size is used in the other sections of this paper. It should be noticed that the influence of mesh size is more relevant for Scenario 1, in which more nonlinearity is anticipated.
Fig. 12

Influence of mesh size on CRPs displacement in Scenario 1 using linear beam formulation (B21)

Fig. 13

Influence of mesh size on CRP displacement in Scenario 2 using linear beam formulation (B21)

Figures 14 and 15 show the influences of element type on dynamic response of CRP. When quadratic interpolation element is used, a bigger mesh size can be used. The obtained response using a 0.25-m linear element is almost equal to that one obtained with a 0.5-m quadratic beam element. The authors suggest that the mesh size equal to height of the beam section for linear beam formulation is a good primary guess. For quadratic beam element, this size could be increased twice. Table 1 summarizes the maximum response for all discussed mesh sizes and element types. Figure 16 summarizes the influences of mesh size and element type in terms of the number of elements for each beam member. Figure 17 shows the displacement, rotation and von Mises stress counters at maximum displacement in Scenario 1. The 0.25-m linear beam elements are used in this figure. Detailed comparisons of different scenarios, state of plastic zones and forces in adjacent members are outside the scope of this paper and the reader can find a detailed discussion in Kim and Kim (2009) and Tavakoli and Kiakojouri (2014).
Fig. 14

Influence of element type on CRP displacement in Scenario 1

Fig. 15

Influence of element type on CRP displacement in Scenario 2

Table 1

Influences of mesh size and element type on the maximum displacement of CRP

Type

Linear (B21)

Quadratic (B22)

Size (m)

0.1

0.25

0.5

1

0.1

0.25

0.5

1

Scenario 1a

98

96

91

86

99

98

96

92

Scenario 2a

60

58

56

54

60

60

59

57

aMaximum displacements in millimeters

Fig. 16

Influences of number of element for each member on the dynamic response

Fig. 17

Counter in Scenario 1: a displacement, b rotation and c von Mises stress

Column removal time

According to GSA guidelines (2013), it is preferable to remove the column instantaneously. However, in numerical modeling of progressive collapse, dynamic column removal should be performed in a certain period of time. In this study, four different time intervals including 0.001, 0.01, 0.1 and 0.5 s are considered. According to the results, influences of CRT on dynamic response of the model are very important. By increasing the CRT, displacements of CRP meaningfully decrease. Figure 18 shows the influence of CRT on the displacement of CRP in Scenario 1. Abaqus predicted 48-mm vertical displacement when the column was removed in 0.5 s and 92 mm for 1 ms in the Scenario 1. The results have also shown that when the velocity of column removal reaches a certain rate, the final results do not change much. Figure 19 shows the influence of CRT on the displacement of CRP in Scenario 2. The same results also have been reported by Tavakoli and Kiakojouri (2013b) and Chen et al. (2016).
Fig. 18

Influence of CRT on displacement of CRP in Scenario 1

Fig. 19

Influence of CRT on displacement of CRP in Scenario 2

Despite guideline recommendation, CRT in a real scenario is basically dependent on the triggering event. For example, positive phase duration in blast load can range from less than 1 ms to tens of milliseconds. Moreover, it should be noticed that the actual column loss (in terms of maximum displacement or damage) may occur at free vibration after blast loads. In the impact scenario, the duration of the event is even longer. Kinney equation (Eq. 1) can be used for the estimation of the positive phase duration in a blast (Kinney and Graham 1985):
$$ t_{\text{p}} = W^{{\frac{1}{3}}} \frac{{980\left( {1 + \left( {\frac{Z}{0.54}} \right)^{10} } \right)}}{{\left( {1 + \left( {\frac{Z}{0.02}} \right)^{3} } \right)\left( {1 + \left( {\frac{Z}{0.74}} \right)^{6} } \right)\sqrt {1 + \left( {\frac{Z}{6.9}} \right)^{2} } }}, $$
(1)
where W is the charge weight in kg and Z is the scaled distance and defined as follows:
$$ Z = \frac{R}{{W^{{\frac{1}{3}}} }}, $$
(2)
where R is the standoff distance and W is the weight of the explosive material.

Moreover, there are examples of triggering events (e.g., fire) where “instantaneous” column removal is not rational for them. Therefore, while abrupt column loss usually provides larger structural response, it is not the most rational simulation for every column loss scenario and special attention should be paid to the nature of the triggering event to prevent overestimation of the structural response.

Strain-rate effects

The influences of rating on the increase of yield stress are well known. Generally, progressive collapse analysis is performed in rate-independent approaches. But the recent studies show that this effect can be important (Tavakoli and Kiakojouri 2013a; Chen et al. 2016; Li et al. 2018). It should be noticed that, while progress of failure is rate independent in most collapse mechanisms, the immediate response of the structures under certain triggering events such as blast and impact is highly rate dependent (Tavakoli and Kiakojouri 2013a). Therefore, considering these effects even in threat-independent alternate load path progressive collapse analysis is useful. In this paper, the strain-rate effects are included by using the Cowper–Symond equation (Abramowicz and Jones 1984):
$$ \sigma_{\text{dyn}} = \sigma_{\text{y}} \left( {1 + \left( {\frac{{\dot{\varepsilon }}}{D}} \right)^{{\frac{1}{n}}} } \right), $$
(3)
where σdyn is the dynamic yield stress, σy the static yield stress, D a rate-dependent constant and n a positive dimensionless parameter. D can be used as an estimation of the sensitivity of the rate effects and it is dependent on the static flow stress, and n defines the slope of the logarithm curve and is a measure of the hardening characteristics of the material (Boh et al. 2004). In this study, D = 40 s−1 and n = 5 are used (Abramowicz and Jones 1984; Boh et al. 2004).
According to the results, considering the strain-rate effects changes the responses meaningfully. The amount of change depends on the CRT. By decreasing the CRT, rate effects are intensified. In the case of CRT equal to 0.5 s, rate-dependent response is 98% of rate-independent response (in Scenario 1); on the other hand, for CRT equal to 0.001, this ratio is only about 86%. Figures 20 and 21 show rate-dependent displacement of CRP in Scenario 1 and Scenario 2, respectively. Rate-dependent time-history of axial force in the adjacent column is shown in Fig. 22 for two different CRTs. The results of rate-dependency analysis are summarized in Table 2.
Fig. 20

Influence of strain rate on vertical displacement time-history of CRP (Scenario 1)

Fig. 21

Influence of strain rate on vertical displacement time history of CRP (Scenario 2)

Fig. 22

Influence of strain rate on reaction force of adjacent column (Scenario 2)

Table 2

Summary of rate-dependency analysis

CRT (s)

Rate-independent

Rate-dependent

0.001

0.01

0.1

0.5

0.001

0.01

0.1

0.5

Scenario 1a

99

96

60

48

85

84

58

47

Scenario 2a

63

58

33

30

55

52

33

30

aMaximum displacements at CRP in millimeters

Damping

Three different damping ratio including 2, 5 and 10% are used in the numerical modeling. Based on the results, the influences of damping on maximum displacement of CRP are very small. The similar results also have been reported by Jiang et al. (2017) for threat-dependent progressive collapse. In Scenario 1, the difference between the response with 2.5 and 10% damping is only about 2%. In scenario 2, this difference is even smaller. Figures 23 and 24 show CRP displacement time history for Scenario 1 and Scenario 2 using various damping ratios, respectively. In progressive collapse analysis, unlike seismic analysis, maximum response develops generally after few cycles and, therefore, during these few cycles, influences of damping are very small and can be safely ignored. In other words, this phenomenon more or less is similar to the impact or blast and as we know in such phenomena the influences of damping are negligible.
Fig. 23

Influence of damping on vertical displacement time history of CRP (Scenario 1)

Fig. 24

Influence of damping on vertical displacement time history of CRP (Scenario 2)

Request and saving of outputs

According to the GSA guideline, the duration of the analysis shall be until the maximum displacement is reached or one cycle of vertical motion occurs at the CRP (GSA 2013). To study the influences of analysis time on dynamic response, the duration of analysis is increased to 5 s after column loss. According to results, it is unnecessary to continue the analysis further than 1 s after column removal. Figure 25 shows the time history of CRP in longer time after loss of the column. Since in dynamic progressive collapse analysis, maximum displacement of CRP is the major interest, and unlike seismic analysis the maximum response always develops in few cycles, continuing the analysis after 1  s (that include several cycles of vibration for steel moment-resisting frames) is unnecessary. For special purposes, for example when permanent displacement is needed for comparison to static pushdown analysis, the overdamped response can be used instead of time-consuming long analysis (e.g., see Fig. 24).
Fig. 25

Increasing the analysis duration

One of the most important issues in any dynamic time history analysis is the frequency of saving the results. Long interval in saving outputs causes significant change in estimated response and may lead to misleading conclusions. Figure 26 shows CRP displacement time history in Scenario 1 for three saving schemes. Influences of the number of output steps on the axial force of adjacent column are shown in Fig. 27 for Scenario 1. As shown in this figure, using long intervals for output time steps can lead to errors up to 19% in estimated CRPs maximum displacement. Therefore, it is recommended that saving the outputs should be performed for each one or two analysis increments. Using longer interval for saving output may lead to loss of accuracy and invalid estimated structural response.
Fig. 26

Influences of number of output time steps on estimated CRP displacements in Scenario 1

Fig. 27

Influences of number of output time steps on the estimated axial force of adjacent column in Scenario 1

Conclusions

In this paper, the effects of finite element modeling and analysis parameters including solution procedure, mesh size, element type, column removal time, damping, strain rate and output-related issues are discussed in detail with special emphasis on the evaluation of column removal points’ displacements in nonlinear dynamic column removal scenarios. The following conclusions are drawn:
  • In this study, progressive collapse analysis is performed using both explicit and implicit approaches. A very good agreement between the two methods is observed. The results also show that the time step should be significantly lower than the CRT in both procedures.

  • Mesh dependency and element type analysis shows that for sufficiently fine mesh, quadratic and linear interpolation beam elements produce the same result. When the quadratic beam element is used, larger element size can be used. Moreover, suggestions are provided for effective mesh size using different elements.

  • In progressive collapse analysis, unlike seismic analysis, maximum response develops generally after few cycles of vibration and, therefore, influences of damping can be safely ignored. Current results show that even for very large damping ratio, maximum response does not change meaningfully.

  • Despite guideline recommendation, duration of column removal in a real scenario basically depends on the triggering event. Therefore, while sudden column removal provides larger structural response, it is not a rational assumption in every collapse scenario and special attention should be paid on the nature and characteristic of triggering event to prevent overestimation of the structural response.

  • Results also show that including the strain-rate effects changes the responses meaningfully and decreases displacement of the column removal point. The amount of change depends on the column removal time; by decreasing the time of column removal, the rate effects are increased.

  • According to results, using long intervals for output time steps can lead to significant errors in the estimated responses. It is recommended that saving the outputs should be performed for every one or two analysis increments. Using longer interval in saving outputs may lead to invalid estimation of structural response.

Further study is still required to investigate the effects of finite element modeling and analysis techniques on progressive collapse response of other steel framed structures, specially braced frames and frames with shear wall. Moreover, extensive study is still needed to gain a further understanding of the relation between threat-related parameters such as column removal time and strain rate to specific triggering event.

References

  1. Abramowicz, W., & Jones, N. (1984). Dynamic axial crushing of square tubes. International Journal of Impact Engineering, 2(2), 179–208.CrossRefGoogle Scholar
  2. Agarwal, A., & Varma, A. H. (2014). Fire induced progressive collapse of steel building structures: The role of interior gravity columns. Engineering Structures, 58, 129–140.CrossRefGoogle Scholar
  3. Alashker, Y., Li, H., & El-Tawil, S. (2011). Approximations in progressive collapse modeling. Journal of Structural Engineering, 137(9), 914–924.CrossRefGoogle Scholar
  4. Boh, J. W., Louca, L. A., & Choo, Y. S. (2004). Strain rate effects on the response of stainless steel corrugated firewalls subjected to hydrocarbon explosions. Journal of Constructional Steel Research, 60(1), 1–29.CrossRefGoogle Scholar
  5. Chen, J., Shu, W., & Huang, H. (2016). Rate-dependent progressive collapse resistance of beam-to-column connections with different seismic details. Journal of Performance of Constructed Facilities, 04016086.Google Scholar
  6. Chiranjeevi, M. D., & Simon, J. (2016). Analysis of reinforced concrete 3d frame under blast loading and check for progressive collapse. Indian Journal of Science and Technology, 9(30), 1–6.CrossRefGoogle Scholar
  7. DoD. (2005). Unified facilities criteria: Design of buildings to resist progressive collapse. UFC 4-023-03. US Department of Defense: Washington, DC.Google Scholar
  8. DoD. (2009). Unified facilities criteria: Design of buildings to resist progressive collapse. UFC 4-023-03. US Department of Defense: Washington, DC.Google Scholar
  9. Ellingwood, B. R., Smilowitz, R., Dusenberry, D. O., et al. (2007). Best practices for reducing the potential for progressive collapse in buildings. Gaithersburg: National Institute of Standards and Technology.CrossRefGoogle Scholar
  10. Fu, F. (2013). Dynamic response and robustness of tall buildings under blast loading. Journal of Constructional Steel Research, 80, 299–307.CrossRefGoogle Scholar
  11. Gerasimidis, S., & Baniotopoulos, C. (2011). Steel moment frames column loss analysis: The influence of time step size. Journal of Constructional Steel Research, 67, 557–564.CrossRefGoogle Scholar
  12. GSA. (2003). Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, DC: General Service Administration.Google Scholar
  13. GSA. (2013). Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, DC: General Service Administration.Google Scholar
  14. Habibullah, A. (2013). ETABS-three dimensional analysis of building systems, users manual. Berkeley, California: Computers and Structures Inc.Google Scholar
  15. Jiang, B., Li, G. Q., Li, L., & Izzuddin, B. A. (2017). Simulations on progressive collapse resistance of steel moment frames under localized fire. Journal of Constructional Steel Research, 138, 380–388.CrossRefGoogle Scholar
  16. Jiang, B., Li, G. Q., & Usmani, A. (2015). Progressive collapse mechanisms investigation of planar steel moment frames under localized fire. Journal of Constructional Steel Research, 115, 160–168.CrossRefGoogle Scholar
  17. Kaewkulchai, G., & Williamson, E. B. (2006). Modeling the impact of failed members for progressive collapse analysis of frame structures. Journal of Performance of Constructed Facilities, 20(4), 375–383.CrossRefGoogle Scholar
  18. Kang, H., & Kim, J. (2014). Progressive collapse of steel moment frames subjected to vehicle impact. Journal of Performance of Constructed Facilities, 29(6), 04014172.CrossRefGoogle Scholar
  19. Kiakojouri, F., Jahedi Delivand, A., & Sheidaii, M.R. (2016). Blast-induced progressive collapse: Threat-independent or threat-dependent approach? 4 th International Congress on Civil Engineering, Architecture and Urban Development, Tehran, Iran, 27–29 December.Google Scholar
  20. Kim, J., & Kim, T. (2009). Assessment of progressive collapse-resisting capacity of steel moment frames. Journal of Constructional Steel Research, 65(1), 169–179.CrossRefGoogle Scholar
  21. Kim, H. S., Kim, J., & An, D. W. (2009). Development of integrated system for progressive collapse analysis of building structures considering dynamic effects. Advances in Engineering Software, 40(1), 1–8.CrossRefzbMATHGoogle Scholar
  22. Kinney, G. F., & Graham, K. J. (1985). Explosive shocks in air. New York Tokyo: Springer Verlag Berlin Heidelberg.CrossRefGoogle Scholar
  23. Kwasniewski, L. (2010). Nonlinear dynamic simulations of progressive collapse for a multistory building. Engineering Structures, 32, 1223–1235.CrossRefGoogle Scholar
  24. Li, L. L., Li, G. Q., Jiang, B., & Lu, Y. (2018). Analysis of robustness of steel frames against progressive collapse. Journal of Constructional Steel Research, 143, 264–278.CrossRefGoogle Scholar
  25. Liu, J. L. (2010). Preventing progressive collapse through strengthening beam-to-column connection, Part 2: Finite element analysis. Journal of Constructional Steel Research, 66(2), 238–247.CrossRefGoogle Scholar
  26. Lu, X., Lin, K., Li, Y., et al. (2016). Experimental investigation of RC beam-slab substructures against progressive collapse subject to an edge-column-removal scenario. Engineering Structures, 149, 91–103.CrossRefGoogle Scholar
  27. Mashhadi, J., & Saffari, H. (2016). Effects of damping ratio on dynamic increase factor in progressive collapse. Steel and Composite Structures, 22(3), 677–690.CrossRefGoogle Scholar
  28. Mohamed, O. A. (2015). Calculation of load increase factors for assessment of progressive collapse potential in framed steel structures. Case Studies in Structural Engineering, 3, 11–18.CrossRefGoogle Scholar
  29. Pirmoz, A. (2011). Performance of bolted angle connections in progressive collapse of steel frames. The Structural Design of Tall and Special Buildings, 20(3), 349–370.CrossRefGoogle Scholar
  30. Pujol, S., & Smith-Pardo, J. P. (2009). A new perspective on the effects of abrupt column removal. Engineering Structures, 31(4), 869–874.CrossRefGoogle Scholar
  31. Ren, P., Li, Y., Lu, X., et al. (2016). Experimental investigation of progressive collapse resistance of one-way reinforced concrete beam–slab substructures under a middle-column-removal scenario. Engineering Structures, 118, 28–40.CrossRefGoogle Scholar
  32. Sadek, F., Main, J. A., Lew, H. S., Robert, S. D., Chiarito, V. P., & El-Tawil, S. (2010). An experimental and computational study of steel moment connections under a column removal scenario. NIST Technical Note, 1669.Google Scholar
  33. Sheidaii, M. R., & Jalili, S. (2015). Comparison of the progressive collapse resistance of seismically designed steel shear wall frames and special steel moment frames. International Journal of Engineering-Transactions C: Aspects, 28(6), 871–879.Google Scholar
  34. SIMULIA (2014). Abaqus theory and analysis manual. Version 6.10, Hibbitt. Pawtucket (RI): Karlsson and Sorensen, Inc.Google Scholar
  35. Song, B. I., Giriunas, K. A., & Sezen, H. (2014). Progressive collapse testing and analysis of a steel frame building. Journal of Constructional Steel Research, 94, 76–83.CrossRefGoogle Scholar
  36. Song, B. I., & Sezen, H. (2013). Experimental and analytical progressive collapse assessment of a steel frame building. Engineering Structures, 56, 664–672.CrossRefGoogle Scholar
  37. Standard no. 2800, Iranian code of practice for seismic resistant design of buildings (2014) Standard no. 2800. 4th edition. Building and Housing Research Center.Google Scholar
  38. Szyniszewski, S., & Krauthammer, T. (2012). Energy flow in progressive collapse of steel framed buildings. Engineering Structures, 42, 142–153.CrossRefGoogle Scholar
  39. Tavakoli, H. R., & Alashti, A. R. (2013). Evaluation of progressive collapse potential of multi-story moment resisting steel frame buildings under lateral loading. Scientia Iranica, 20(1), 77–86.Google Scholar
  40. Tavakoli, H. R., & Hasani, A. H. (2017). Effect of Earthquake characteristics on seismic progressive collapse potential in steel moment resisting frame. Earthquake and Structures, 12(5), 529–541.Google Scholar
  41. Tavakoli, H. R., & Kiakojouri, F. (2013a). Influence of sudden column loss on dynamic response of steel moment frames under blast loading. International Journal of Engineering, Transactions B: Applications, 26(2), 197–206.CrossRefGoogle Scholar
  42. Tavakoli, H. R., & Kiakojouri, F. (2013b). Numerical study of progressive collapse in framed structures: a new approach for dynamic column removal. International Journal of Engineering, Transaction A: Basics, 26(7), 685–692.Google Scholar
  43. Tavakoli, H. R., & Kiakojouri, F. (2014). Progressive collapse of framed structures: Suggestions for robustness assessment. Scientia Iranica. Transaction A. Civil Engineering, 21(2), 329–338.Google Scholar
  44. Tavakoli, H. R., & Kiakojouri, F. (2015). Threat-independent column removal and fire-induced progressive collapse: numerical study and comparison. Civil engineering infrastructures journal, 48(1), 121–131.Google Scholar
  45. Valipour, H. R., & Bradford, M. (2012). An efficient compound-element for potential progressive collapse analysis of steel frames with semi-rigid connections. Finite Elements in Analysis and Design, 60, 35–48.CrossRefGoogle Scholar
  46. Wu, S. R., & Gu, L. (2012). Introduction to the explicit finite element method for nonlinear transient dynamics. Wiley.Google Scholar
  47. Yang, B., & Tan, K. H. (2012). Robustness of bolted-angle connections against progressive collapse: Experimental tests of beam-column joints and development of component-based models. Journal of Structural Engineering, 139(9), 1498–1514.CrossRefGoogle Scholar
  48. Zhacng, Y. M., Sun, C. J., Su, Y. P., et al. (2010). Finite element analysis of vertical continuous collapse of six-story frame structure. In Applied Mechanics and Materials, 34, 1800–1803.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUrmia UniversityUrmiaIran

Personalised recommendations