Weak axis response of steel I-sections subjected to close-in detonations

Journal of Constructional Steel Research 160 (2019) 189–206

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Journal of Constructional Steel Research

Weak axis response of steel I-sections subjected to close-in detonations Hezi Y. Grisaro a,⁎, Jeffrey A. Packer a, Michael V. Seica a,b a b

Department of Civil & Mineral Engineering, University of Toronto, 35 St. George Street, Toronto, ON M5S 1A4, Canada Explora Security Ltd, 3-4 Talina Centre, Bagleys Lane, London SW6 2BW, United Kingdom

a r t i c l e

i n f o

Article history: Received 7 March 2019 Received in revised form 16 May 2019 Accepted 17 May 2019 Available online xxxx Keywords: I-section Wide-flange section Blast load Close-in detonation Numerical simulation CFD modelling Autodyn

a b s t r a c t The response of I-shaped, or wide-flange, sections subjected to close-in detonations has been evaluated through numerical simulations. A simulation approach for close-in detonation, which includes two stages, is suggested. The first stage includes the modelling of the detonation process through computational fluid dynamics (CFD) and the second stage includes only the free vibrations of the structural member. The suggested approach is validated by a comparison with two experimental results for close-in detonations. Then, a parametric study for Isections with their weak axis subjected to close-in detonations has been performed. Various spherical charges and standoff distances have been studied, with scaled distances in the range of 0.15–0.29 m/kg1/3. Bare members and members strengthened with stiffeners have been simulated. The influence of charge and standoff distance, and the addition of stiffeners on several parameters affecting deformation and folding angles, has been studied. The effect of localized pressure confined between the flanges and the stiffeners at the midspan, which can lead to increased total and local deformations, is illustrated. Finally, an alternative strengthening method, in which the flanges are connected with bars, is presented as an optional stiffening technique. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Blast loads on structures The requirement for protection of structures to extreme loadings, such as blast loads resulting from external explosions, is receiving more attention these days. More specifically, the response of structures to blast loads generated by an explosive detonation has been discussed in many papers, books and design manuals (e.g. [1–3]). While much attention has been given for blast load and response for the far-field range [1,4,5], close-in and contact detonations are more challenging to deal with due to the complicated high-pressure environment [6–8]. A possible scenario for a close-in detonation can be an explosive in a backpack or satchel and detonated within a short distance from a structural element. When the scaled distance becomes smaller, the response is dominated by increased local damage combined with the global response of the structural element, whereas under the far-field conditions the response is mostly controlled by global deformation. In all cases, the structural capacity of the affected element can be compromised partially or totally. The spatial pressure distribution in a close-ranged explosion scenario is more likely to be non-uniform, making the prediction of the blast loads and the structural response more challenging; while for a far-field explosion the pressure distribution is approximately uniform [4]. In addition, in the near-field, even a small amount of explosive ⁎ Corresponding author. E-mail address: [email protected] (H.Y. Grisaro).

https://doi.org/10.1016/j.jcsr.2019.05.025 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

may cause severe damage and response [6,9]. The charge shape (e.g. spherical, hemispherical, cubic, cylindrical, etc.) may significantly affect the pressure distribution at a short distance from the charge, too [6]. The predictions and modelling of close-in detonations are very challenging due to their characterizations mentioned above. In general, there are three main approaches for predicting the blast load overpressure parameters: • Empirical diagrams in design manuals, such as in the UFC 3–340-02 [3], or other empirical equations such as the Kingery and Bulmash equations [10], which are very common. Such diagrams are often used for spherical or hemispherical charges. • Numerical simulations. • Experiential data for specific cases. The most commonly used approach is the empirical one (first one) since it is a relatively quick and simple tool. However, while it predicts reasonable values for far-field conditions, it is less accurate for nearfield, as also deduced from previous studies [6,11,12]. The main reason for its lesser accuracy is because, in the near-field regime, two types of waves are generated: (i) from detonation products of the explosive and air; and (ii) by a more-distant blast wave that involves atmospheric air only. The detonation products also impinge on the structure in the near-field and affect the resulting reflected pressure [6]. In addition, empirical methods usually consider spherical or hemispherical charge shapes, and the solutions are mainly for one-dimensional flow in a radial direction. However, the charge shape may significantly affect the

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pressure environment in the near-field, as explained by Mazurkiewicz et al. [11] and others (although in the current study only a spherical charge shape is considered). Rigby et al. [12] also state that empirical methods are less suitable for the near-field regime for the same reasons. Thus, in the near-field regime, the other two approaches are more accurate and, hence, recommended. As important or even critical structural members, the response of steel rectangular hollow section (RHS) members to blast loads has been dealt with in several previous studies, either as tubular unfilled members or filled with concrete [1,4,6,9,13], or for I-sections [5,14,15]. In some cases, the steel member was covered with cladding (for example, made of metal [4] or bricks [16]). When there is a cladding covering steel columns, the blast load will act only on the cladding, and the actual pressure on the column will mainly be generated as a reaction force imposed by the cladding over its length [4]. On the other hand, when no cladding is installed and a bare column is subjected to a close-in detonation, the blast load can flow around the section and load it from various directions [17]. 1.2. I-sections subjected to close-in detonation The response of I-sections has been experimentally investigated before, as described in the following. Nassr et al. performed experiments in which I-section columns, covered with cladding, were subjected to explosive detonations with relatively far-field loading about both their strong and weak axes [5]. They showed the global flexural response of these elements to the blast loads. In a follow-up study, another series of tests were performed using a different reaction structure, which enabled the application of axial load to the members [18]. As expected, it was found that the axial force may affect the response of the members to blast loads. In both studies, the blast pressure generated by the explosions was relatively uniform over the height of the column, mainly due to the effect of the cladding. Magallanes et al. [16] presented a single experiment on an I-section subjected to close-in detonation. However, most of the details were not presented, possibly due to classification issues. They showed the distortion of the section near the support, which may affect the residual capacity of the section. Denny and Clubley [19] tested bare I-sections in an air-blast tunnel. They monitored the pressure and impulse for various angles of incidence and found that detonations with an angle of incidence of approximately 60 degrees to the strong axis of the section would yield the maximum impulse on the section. This means that it is in-between weak and strong axis loading of the column. Mazurkiewicz et al. [11] tested and analyzed I-section columns loaded about their weak axis, subjected to close-in detonations. In their experiments and analysis, the charges were close to the column and the ground, resulting in relatively high damage to the columns such that their webs were totally destroyed, thus leaving a large hole in the column. Krishnappa et al. [14] performed similar experiments. However, they did not report the charge weights and standoff distances due to security concerns, and most of their tests resulted in excessive damage and breaching of the sections, so the structural response could not be studied. The potential failure modes of I-section members subjected to blast loads were presented by Astaneh-Asl [20] as follows: overall buckling, local buckling, distortion of cross section, shear failure of column ends, fracture of tension flange, failure of column splices, failure of base-plate or anchor bolt assembly, and fracture of foundations. A principal failure mode for close-in detonation is distortion of the cross section resulting in the local bending (folding) of the flanges and web, as presented in Fig. 1. This typical distortion was also reported by others [20–22]. The distortion of the cross section may affect the residual capacity of the member after the blast. This aspect is important especially for columns, for which the axial load capacity is an important parameter for design. The purpose of the current study is to investigate intentional bombing of building columns by relatively small explosives which may potentially cause disproportionate damage to the structure and

Fig. 1. Typical folding of flanges due to blast load acting on the weak axis.

progressive collapse of the building. This paper examines the response of I-sections subjected to close-in detonations by numerical simulations. An approach to reduce the computational cost of these simulations is suggested. This approach is validated through comparison with available experimental data and is then used for a parametric study on the response of I-sections subjected to close-in detonations from spherical charges onto their weak axis. The influence of strengthening methods, which include stiffeners and transverse bars, is illustrated. Lastly, conclusions from the current study are drawn. 2. Numerical simulation method and validation In this section, a validation of the modelling approach employed is presented and validated for close-in detonations. To consider the nonuniform pressure distribution along the member span and around its section, a Computational Fluid Dynamics (CFD) modelling approach which includes the detonation process, the formation of the blast waves and the Fluid-Structure Interaction (FSI) to transfer the load to the structural member, is required for appropriate modelling. One challenge is the necessary computational time and resources. Hours of simulation time are needed for a few milliseconds of the blast wave propagation. In real life, the required time for the structural response of a member can be in the order of magnitude of tens or hundreds of milliseconds (e.g. [1,4]). Hence, a high computational cost is required to perform just a single simulation (e.g. [9]), and it would be demanding to perform a parametric study. Ngo et al. mentioned that, in some of the cases, they used approximations for a non-uniform initial velocity distribution, for representing the realistic non-uniform pressure distribution to avoid using CFD modelling [9]. When they tried to perform the calculations using CFD modelling, the authors could only perform the simulation up to the first peak deflection value due to the high cost of computational resources. Therefore, an alternative approach is suggested in the current study, consisting of two stages: • In the first stage, a simulation of the structure with CFD and FSI modelling is performed for the first few milliseconds. • In the second stage, after enough time has elapsed, and all pressures have already been reflected from the structural member, the CFD component is ignored and then the free-vibration component of the response is modelled up to tens or hundreds of milliseconds relatively easily. Table 1 Simulation data. Simulation IDa [6]

Concrete infill

Charge mass (kg)

Clear distance – centre of charge to RHS member (mm)

Scaled distance – centre of charge to RHS member (m/kg1/3)

C3 C5

No Yes

2.603 2.601

100 150

0.12 0.15

a

The simulation IDs correspond to the test IDs in Ref. [6].

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Fig. 2. Simulation ‘C5’ details: (a) Overview (dimensions in mm), (b) Full model (air is not shown), (c) Meshing details.

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Table 2 TNT JWL EOS parameters. ρ0 (gr/cm3)

A1 (kPa)

A2 (kPa)

R1

R2

w

e (MJ/kg)

1.51

3.712·108

3.231·106

4.15

0.95

0.3

4.635

Note that the transition time between the two stages should be late enough in order to account for all significant reflection and blast flows around the section. This issue is discussed further in Sections 2.4 and 3.3. The validation of the suggested approach is done by comparison with experimental data. Since there are no suitable experiments with Isections having the required details for close-in detonations to be used for a comparison of the structural response, the experiments of Remennikov and Uy [6] (in which RHS members, unfilled and concrete-filled were tested) are used for the validation. A validation with a different cross-section type is not ideal. However, it still provides validation for two purposes: • Validation of the damage modes and residual deformations predicted by the numerical simulations. Then, the same material models and parameters are used for the I-section investigation. • Validation of the numerical modelling approach. The suggested Table 3 Steel material model parameters. Parameter

Value

Bulk modulus (GPa) Shear moduluds (GPa) B1 – Basic yield stress (MPa) B2 – Hardening constant (MPa) n – Hardening exponent (−) B3 – Strain rate constant (−) m – Thermal exponent (−) Tmelt – Melting temperture (K) ε_ 0 – Ref. strain rate (1/s) Failure by principal strain (−)

172.5 79.6 400 275 0.493 0.022 1 1811 1 0.225

approach, which consist of two stages, is verified through mesh sensitivity analysis and a study of the transition time between the two stages. In their experiments, cubic-shaped ~2.6 kg TNT charges were detonated from above and close to a 2-m span RHS beam, which was attached to two concrete blocks at its ends. The standoff distances were in the range of 0.05–0.15 m/kg1/3 from the centre of the charge to the face of the member. For the current validation, one unfilled and one concrete-filled beam are used. The numerical simulations were performed using the Ansys Autodyn hydro-dynamic program [23]. The workstation used for the simulations consisted of two Intel Xeon E52687Wv4 3.0 GHz processors with a total of 24 cores and 128 GB DDR4 system memory. An Autodyn licence with 32 parallel computations was used for the calculations. 2.1. Simulation overview An illustration of the simulation for a hollow section with concrete infill (simulation ‘C5’ in Table 1) is presented in Fig. 2. Due to symmetry, only a quarter of the investigated problem was simulated, as shown in the figure. The explosive, the air around the structural member, the steel member (and in the case it is concrete-filled, the concrete inside it), the concrete blocks at the ends and a rigid surface to represent the ground, are modelled. The explosive and the air represent the CFD part of the simulation. This is an Eulerian formulation, which means that the detonation products flow inside it. The RHS beam is modelled using shell elements, while the concrete blocks, the concrete infill and the ground are modelled by solid elements. After a preliminary investigation, it was found that cells not exceeding 5 mm are needed for the Eulerian part in the area close to the charge. Thus, the cell size was chosen as 5 mm and it was then gradually increased towards the air boundaries. As such, a total of 2.07 million cells were modelled in the Eulerian part. The RHS beam and the concrete infill were modelled by 5-mm-size elements, and the concrete block and the ground were modelled by 10-mm-size elements. A total of 67,879 cells

Fig. 3. Pressure propagation for specimen ‘C5’.

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were modelled for these Lagrangian parts for the concrete infill and 28,279 cells for the simulation of the unfilled hollow section. Numerical gauges were placed on the top of the RHS beam to monitor the beam deflections, and on the Eulerian part in various locations to monitor the pressure environment. The data for the two simulations are shown in Table 1.

where γ = 1.4 is the heat capacity ratio. The initial conditions included the air in a standard condition at a temperature of 15 °C, density of ρ = 1.225 kg/m3 and pressure of p = 101.332 kPa. These data correspond to an internal energy per unit mass of e = 2.068·105 J/kg. The steel RHS beam was modelled by Linear EOS, and the widely used Johnson-Cook strength model [23,27] as follows:

2.2. Material models

σ y ¼ B1 þ B2 ε p n

The TNT explosive is modelled by the JWL equation of state (EOS) [23,24], as follows:     ρ0 ρ0 wρ wρ p ¼ A1 1− e−R1 ρ þ A2 1− e−R2 ρ þ wρe; R1 ρ0 R2 ρ 0

ð1Þ

where p is the pressure, ρ is the density, ρ0 is a reference density, e is the internal energy per unit mass, and A1, A2, R1, R2 and w are constants. The material parameters are given in Table 2. These parameters are suggested by Autodyn [23,25] for TNT and are widely used. The only parameter that was changed is the reference density ρ0 to match the reported mass by Remennikov and Uy [6]. The air was modelled by the ideal gas equation of state [23,26] as follows: p ¼ ðγ−1Þρe;

ð2Þ

   
 T−T room m  ; 1 þ B3 ln ε_ p 1− T melt −T room

ð3Þ

where σy is the effective yield stress, B1 is the basic yield stress under static conditions, B2 and n are the hardening constant and exponent, re spectively, B3 is the strain rate constant, ε_ p = ε_ p/ε_ 0 is the normalized effective plastic strain rate, ε_ p is the strain rate, ε_ 0 is the reference strain rate under static conditions, Troom and Tmelt are the reference and melting temperatures, respectively, and m is the thermal exponent. The first term corresponds to the static strain-hardening conditions, the second to the strain-rate effects in a dynamic event, and the third considers the effect of the temperature. The modelling parameters are given in Table 3 and were chosen to best fit the steel material data of the RHS beam given in [6,9]. The strain rate constant was chosen from the Autodyn recommendations for mild steel and was also found to fit experimental data in previous studies [28]. The bulk and shear modulus were calculated based on the reported modulus of elasticity and the Poisson's ratio. A failure criterion was employed in the simulation for the steel based on a principal strain of 0.225, taken from material tests reported by [6]. To visually illustrate the rupture of the material, an erosion criterion by material failure was used in the numerical simulation for the steel. The concrete-infill (in the case where it was used) was simulated using the Riedel-Hiermaier-Thoma (RHT) material model [29] available in Autodyn [23], which has been widely used in other studies [30–32]. In this model, the concrete is considered by three ultimate surfaces – the elastic limit, the failure, and the residual surfaces. For further details about the RHT model, the reader is referred to [33]. Previous studies suggested modifications for the RHT concrete model parameters to get more-realistic results. Therefore, the parameters suggested by Tu and Lu [33] have been used herein. The concrete block and the ground were modelled by rigid material models to simplify the analysis. 2.3. Boundary and contact conditions The RHS beam was assumed to be fully bonded to the concrete block because, in the experiment, it was anchored inside it. A gravitational acceleration of 9.81 m/s2 was applied to the model to allow the concrete blocks to return to their initial position on the ground and to also allow their rotation during the response, as in the experiment. Ngo et al. [9] used values of 0.2 and 0.3 for the static and dynamic coefficients of friction, respectively, between the infill concrete and the RHS beam, and Ritchie et al. [1] used a coefficient of friction of 0.25. Thus, it was decided that the friction between the concrete infill and the RHS steel beam would be modelled with a static and dynamic friction coefficient of 0.25 in the current simulation. Contact between the Eulerian CFD part and the Lagrangian parts was enabled to allow pressure reflections. ‘Flow out’ boundary conditions were applied to the Eulerian part at three of its six edges (Fig. 2) to allow the air and explosive products to flow outside the numerical model without reflections. No boundary conditions were applied to the two symmetry planes. Also, no boundary conditions were applied to the ground plane of the Eulerian part to allow reflections of pressure from the ground. 2.4. Results and validation

Fig. 4. Overpressure (a) and impulse (b) over the beam span for simulation ‘C5’.

An illustration of the pressure propagation for simulation of specimen ‘C5’ is presented in Fig. 3, which shows a section through the

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Fig. 5. Qualitative comparison of the residual deformation of specimen ‘C3’ with the experimental results of Remennikov and Uy [6].

middle of the RHS member. The blast wave arrives at, and is reflected from, the RHS specimen at ~0.1 ms after detonation. Afterwards, the wave propagates around the section and reflects from the ground at ~0.2 ms. Additional reflections of the blast wave from the bottom face of the RHS member and the concrete blocks can be also seen in the figure. The most important question in the current simulation approach is the decision on the transition time in which the first stage of the

simulation is terminated, according to the suggested modelling approach. This time should be late enough such that all pressure loads are reflected from the steel member, such that the Eulerian part is not needed any more in the simulation. Fig. 4 shows the overpressuretime history and the peak impulse (by integration with respect to time) at 10 mm from the top surface of the RHS beam at various locations along the span (measurement exactly on the surface was very difficult due to the movement of the RHS mesh and the contact algorithm).

Fig. 6. Comparison of the residual deformation of simulation ‘C5’ with experimental data.

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195

Fig. 7. Deformation-time history of simulation ‘C5’ and a comparison with the reported residual deformation.

Fig. 8. W150 × 22 section – dimensions in mm.

It can be seen that the overpressure and impulse have very high values, but the high values are localized at the midspan zone and they decrease as the distance from the midspan point increases. The overpressure and impulse at ~400 mm from the midspan point are much lower, such that their values cannot be clearly read in the figure. The main finding from this figure is that, from approximately 0.2 ms after detonation, the impulse reached its peak values at all significant locations. Hence, it can be claimed that, after ~0.2 ms, the Eulerian formulation in the model, which includes the CFD calculations, is not needed anymore since it provides relatively small pressures which will not affect the results significantly. After the removal of the Eulerian part, the simulation would be much faster, and the free vibrations of the structure can be analyzed. Nevertheless, to consider any further possible pressure reflections, it was decided that the first stage of the simulation would be run up to 5 ms, which is much longer then needed before the Eulerian part could be removed from the simulation. A similar phenomenon regarding the pressure distribution and values was observed for simulation of specimen ‘C3’. After the removal of the Eulerian component, the second stages of simulations ‘C3’ and ‘C5’ were performed, and the simulations could

Fig. 9. Strengthening methods considered in the simulations: (a) Bare member, (b) Stiffeners @200 mm, (c)Stiffeners @100 mm; and (d) Bars @100 mm.

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Fig. 10. Details for simulation of 5-kg TNT at 500 mm (simulation ‘W-5-500-N-N’).

be calculated up to 100 ms after detonation. Validation of the results was achieved by qualitatively comparing the residual deformation of both simulations with the experimental data. For simulation ‘C5’, an additional quantitative comparison of the deflected shape, which was reported by Remennikov and Uy [6], is presented. The qualitative comparison of the residual deformation of specimen ‘C3’ with the experimental picture from [6] is presented in Fig. 5. The simulation shows a similar failure mode as in the experiment, characterized by: (i) breaching of the top and bottom surfaces of the RHS beam at midspan; (ii) bending down of the top surface; and (iii) a similar pattern

of deformation outwards of the side surfaces. In addition, the beam impacted the ground in both the experimental and numerical cases. For specimen ‘C5’, both qualitative and quantitative comparisons are performed. The comparison of the residual deformation of specimen ‘C5’ with the experimental results is illustrated in Fig. 6. Qualitatively, both show the same failure mode, which includes extended local plastic deformation at the midspan. In addition, the residual plastic deformation between the steel tube edges in the outwards direction was measured in the experiment to be 158 mm, while the residual vertical deformation of the top RHS surface relative to its initial position was 152 mm. By comparison, the residual plastic deformation between the

Table 4 Simulation plan and analysis results. IDa

W (kg)

R (mm)

Z (m/kg1/3)

Stiffeners

Barsb

δtotal,max (mm)

δtotal,res (mm)

T (ms)

δlocal,max (mm)

δlocal,res (mm)

θmax (deg)

θres (deg)

W-5-500-N-N W-5-500-200-N

5.00 5.00

500 500

0.292 0.292

None None

58.9 57.0

45.5 45.5

7.4 7.8

32.2 19.7

22.1 17.0

62.1 16.1

42.8 14.8

W-5-500-100-N

5.00

500

0.292

None

41.1

31.1

8.0

9.0

7.7

5.4

4.7

W-10-500-N-N W-10-500-200-N

10.00 10.00

500 500

0.232 0.232

None None

122.6 127.9

111.7 113.6

6.9 6.7

48.8 33.1

39.8 28.8

98.0 32.3

91.4 31.0

W-10-500-100-N

10.00

500

0.232

None

103.4

87.7

7.1

16.9

14.9

13.1

12.8

W-5-250-N-N W-5-250-200-N

5.00 5.00

250 250

0.146 0.146

None None

171.8 223.7

163.5 212.7

5.3 5.0

61.5 71.4

54.3 66.4

133.9 45.6

131.8 39.6

W-5-250-100-N

5.00

250

0.146

None

193.0

181.7

5.7

44.9

42.1

21.8

18.7

W-1.08-300-N-N W-1.08-300-200-N

1.08 1.08

300 300

0.292 0.292

None None

25.5 25.8

16.7 16.4

6.2 7.0

17.3 13.3

12.1 10.9

20.3 7.0

3.6 4.9

W-1.08-300-100-N

1.08

300

0.292

None

16.8

9.3

7.8

5.7

4.2

1.6

0.9

W-5-397-N-N W-5-397-200-N

5.00 5.00

397 397

0.232 0.232

None None

88.8 92.5

75.9 76.9

7.6 7.4

43.6 29.1

32.3 25.9

76.1 26.2

67.5 25.0

W-5-397-100-N

5.00

397

0.232

None

73.1

60.1

7.8

14.8

13.1

11.4

10.8

W-5-250-N-6 W-5-250-N-12

5.00 5.00

250 250

0.146 0.146

None @200 mm @100 mm None @200 mm @100 mm None @200 mm @100 mm None @200 mm @100 mm None @200 mm @100 mm None None

176.0 184.1

164.4 171.6

5.1 5.3

61.5 71.4

54.3 66.4

133.9 45.6

131.8 39.6

W-5-250-N-18

5.00

250

0.146

None

d = 6 mm, @100 mm d = 12 mm, @100 mm d = 18 mm, @100 mm

177.6

165.2

5.5

44.9

42.1

21.8

18.7

a b

ID legend: W-Charge mass (kg)-Standoff distance (mm)-Spacing of stiffeners (mm), or ‘N’ if no stiffeners-Diameter of bars (mm), or ‘N’ if no bars. d denotes bar diameter.

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steel tube edges in the numerical model was 156.1 mm, which is in very good agreement with the experimental value. The deflection-time history (δ) of the top RHS surface, relative to its initial position (and after deducting the rigid body vertical deflection of the concrete blocks) is presented in Fig. 7. The peak deflection δmax is predicted to be 173.8 mm and the residual deformation δres is in the range of 140– 155 mm. Thus, it can be concluded that good agreement is obtained both qualitatively and quantitively with the experimental results. In summary, the results demonstrate the motivation to use the twostage modelling approach for close-in detonations. This approach is adopted in the following sections to investigate weak-axis loading of I-sections subjected to close-in detonations. 3. Simulation of I-sections subjected to close-in detonation 3.1. Simulation overview After validation of the suggested modelling approach, the response of I-section members is evaluated in this section. All case studies are based on a W150 × 22 section and its dimensions are shown in Fig. 8. The explosive is a spherical TNT charge detonated at its centre and the beam span is 2 m. Although the charge shape may affect the pressure environment in the near-field, a spherical shape was considered to be relevant and hence was selected as part of the scope of the current study. In some cases, the member was strengthened in an attempt to improve its response to blast loading. Three types of strengthening were used, as depicted in Fig. 9. Stiffeners, made of steel plate with the same plate thickness as the web (5.8 mm), were modelled. Two spacing distances were used, 100 and 200 mm, thus creating two options for strengthening. The third option for strengthening included the use of bars connected between the flanges, spaced at 100 mm intervals and with diameters of 6, 12 and 18 mm. The motivation for using bars as a strengthening method is explained in sections 4.2 and 4.3. In all simulations it was assumed that the stiffeners and the bars were properly welded to the section and for this reason a fully bonded contact was applied between them. The material model for the stiffeners and the bars was the same as that for the I-section. The vertical projection of the centre of the charge was located in between two stiffeners or bars, at the midspan of the beam. Hence, the total number of stiffeners or bars was always an even number. A representative case study for a 5-kg TNT charge placed at 500 mm between the centre of the charge and the top edge of the flange is illustrated in Fig. 10 (simulation ‘W-5-500-N-N’ in Table 4). Due to symmetry, as in the validation process, only a quarter of the model was

197

simulated. As explained before, each simulation included an Eulerian part to simulate the explosive and the air, and the steel member. The dimensions of the Eulerian part are shown in Fig. 10. A restraint on velocity in all directions was applied to the member end at all nodes to provide a fixed boundary condition. Numerical gauges, placed in various locations over the steel member and the Eulerian part, were set to capture the deformation and pressure time-histories. After a mesh sensitivity analysis had been performed (see Section 3.2), the cell sizes for the Eulerian part and the steel member were selected to be 10 mm, which yielded 907,500 and 4,735 cells for the Eulerian and Lagrangian parts (for a bare member without stiffeners or bars) in the model, respectively (in the symmetric model, since a full model would be quadrupled). The explosive TNT charge was modelled by the JWL equation of state as explained in Section 2.2 but using a density of 1.63 g/cm3 instead, which is a characteristic value for TNT. The air and the steel were modelled by the same material models as described in Section 2.2. 3.2. Mesh sensitivity analysis A mesh sensitivity analysis was performed for the Eulerian part, which includes the air and the TNT explosive charge. As noted above, a cell size of 10 mm corresponds to 907,500 cells, while a cell size of 7.5 mm corresponds to 2,166,780 cells. The use of a 7.5 mm mesh is therefore very expensive in terms of computational resources and a parametric study could not be performed in a reasonable time on the given workstation. However, two analyses for a 5-kg TNT charge located at standoff distances of 250 and 500 mm (simulations ‘W-5-500-N-N’ and ‘W-5-250-N-N’ in Table 4, respectively) were performed also for this 7.5 mm cell size to check the influence of the mesh size, up to 5 ms after detonation. The parameter used for the comparison was the total vertical deflection of the web at the midspan (δtotal in Fig. 1) which is expected to be the largest deflection of the web along the span. Fig. 11 shows the comparison of the vertical deflection-time history for these two mesh sizes. It can be observed from the figure that the results are almost identical up to ~2 ms and, beyond that, there is some difference between them. For a 500 mm standoff distance, the peak deflections for the coarse (10 mm) and fine (7.5 mm) meshes are 58.9 and 55.3 mm, respectively, with a difference between them of only 7%. For the 250 mm standoff distance, the peak deflections for the coarse and fine meshes are 171.7 and 166.4 mm, respectively, with a difference between them of just 3%. At all other times (than the time of the peak deformations) the differences are clearly much lower. These errors are considered to be within acceptable limits and, to also 60

180 160

5kg@250mm

50

140

40

80

5kg@500mm

60

30

Transion me

(mm)

100

total

total

(mm)

120

20

40 7.5 mm 20 0

10

One phase - simulation Two stages

10 mm

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (ms) Fig. 11. Total vertical deflection of the web at midspan section using different mesh sizes, for 5 kg charge at 500 mm and 250 mm.

0

5

10

15

20

25

30

35

40

45

50

Time (ms) Fig. 12. Comparison between the suggested two-stage approach and one-phase simulation.

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Fig. 13. Residual deformations at 50 ms after detonation.

balance accuracy with expensive computational resources and time, it was decided that a 10 mm mesh size be used in all subsequent analyses. 3.3. Transition time between the two stages Similar to the validation process, the transition time between the two stages was decided to be 5 ms after detonation. Simulation of a 5kg TNT charge at 500 mm (‘W-5-500-N-N’) was chosen to further verify the transition time. As in the validation process, the overpressure dropped to zero and the impulse reached its peak value before 1 ms after the detonation. An additional validation of this transition time was achieved by calculating the overall response by only one-phase simulation; i.e. without removing the Eulerian part. This was a very expensive simulation which took days to complete with the given workstation. The total vertical deflection of the web at the midspan was then compared between the one-phase simulation and the simulation with two stages which involved removing the Eulerian part, at 5 ms after the detonation. Fig. 12 shows a comparison of this deformation

derived from these two approaches. As expected, both curves are identical up to 5 ms because they are extracted from the same simulation. Then, from 5 ms to 50 ms, there is a good agreement between the two curves, which verifies that the removal of the Eulerian part is acceptable at the time selected. 4. Parametric study and discussion A parametric study has been performed for I-section members subjected to close-in detonations causing weak-axis bending. The main goals of the parametric study are to investigate the response of a given I-section member to different threats, and to assess the improvement in performance of a member by particular strengthening methods. Two alternatives for I-section strengthening are presented: (i) the use of welded plates, at close and more-distant spacings, between the flanges; and (ii) the use of bars between the flanges. The parametric study consists of different combinations of charges and stand-off distances, the addition of stiffening plates with two spacing options, and

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199

Fig. 13 (continued).

the addition of stiffening bars. The first and second stages in the suggested approach were calculated up to 5 and 50 ms after detonation, respectively. The results are presented and discussed in the following sections.

Eighteen simulations were performed, as listed in Table 4. Various combinations of charge mass (W), standoff (R) and scaled distances (Z), and sections strengthened with either stiffeners or bars, were modelled, as shown in the table. A 1.08-kg TNT charge at 300 mm and

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a 5-kg TNT charge at 397 mm were selected to yield the same scaled distances as 5-kg TNT at 500 mm (Z = 0.292 m/kg1/3) and 10-kg TNT at 500 mm (Z = 0.232 m/kg1/3), respectively. Fig. 13 shows the residual deformation at 50 ms after the detonation for each case, as well as a view from the midspan to the end of the beam (sections ‘A-A' in Fig. 13). This view illustrates the final distorted shape of the cross-section of the member. It can be qualitatively seen that, in all cases, significant local deformation can be observed at the midspan, which is characterized by deflection of the web and folding of the flanges. The tips of the top flanges (which were the closest to the charge) were bent outwards in all cases. However, the tips of the flanges at the bottom, which were at the opposite side of the charge, were bent inwards for the bare specimens (‘W-5-500-N-N’, ‘W-10-500-N-N’, ‘W-5-250-N-N’, ‘W-1.08-300N-N’, and ‘W-5-397-N-N’); whereas for the strengthened specimens they almost did not deform or deformed outwards, which is in the opposite direction when comparing their behaviour to that of the bare-specimen flanges. In addition, for the strengthened members, the folding angle of the flanges was always smaller than for the bare specimens. An example of the pressure propagation for simulation ‘W-5-500-NN’ is presented in Fig. 14. The figure shows the reflection of the pressure from the web and flanges, as well as the propagation around the section. It emphasizes the importance of the use of CFD modelling for I-sections subjected to close-in detonations because the pressure waves reflect in various directions around the shape of the section, and this effect cannot be easily captured by approximated pressure boundary conditions, without CFD modelling. To quantitively assess the structural response, three parameters were chosen: the total (δtotal) and local (δlocal) vertical deformations of the web at the midspan section, and the folding angle of the top flanges (θ). These parameters are schematically presented in Fig. 1. For each simulation, the following output parameters are presented in Table 4: the maximum total deformation of the web δtotal,max, the residual total deformation δtotal,res (estimated by best fitting curve from 40 and 50 ms in the time-history analysis), the period of vibration, T, of the total deformation (estimated as the time interval between two maximum deformation points), the residual local deformation δlocal,res (estimated by the difference between the total deformation at the midpoint of the web and the deformation of the point where the flange and the web connect), and the residual folding angle of the top flanges θres (estimated using the same approach as for δtotal,res). The period of vibration, T, of the total deformation ranged from 5 and 8 ms in all cases. No correlation was found for this parameter with the scaled distance, or for a given charge and standoff distance. Thus, it will not be further discussed in this section. 4.1. Effect of charge and standoff distance The effect of charge and standoff distance was determined by comparing the response of the same structural member to various blast Pressure (kPa) 23.59e3

Pressure (kPa) 235.9e2 Pressure propagation around the section

Reflection from top surface

101.3

40 Time=0.16 ms

Time=0.46 ms

Fig. 14. Pressure propagation (simulation ‘W-5-500-N-N’).

Fig. 15. Time-history of the: (a) Total deformation, (b) Local deformation, and (c) Folding angle, for bare members subjected to various detonations.

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loads. It was performed for the bare member and for a member strengthened with stiffeners. Accordingly, the results from three groups of simulations (viz. without stiffeners, with stiffeners spaced @200 mm, and with stiffeners spaced @100 mm) can be plotted together to study the effect of charge and standoff distance.

4.1.1. Bare members Fig. 15 shows an example for a comparison of the time-history of the total (δtotal) and local deformations (δlocal), and the folding angle (θ), for bare members (without stiffeners or bars), subjected to different scenarios of explosive charges and standoff distances. As can be seen from Fig. 15 and Table 4, for smaller scaled distances (Z), the peak and residual deflections were higher, for a given member. Note that two pairs of results have the same scaled distance each (‘W-5-500-N-N’ and ‘W-1.08-300-N-N’; ‘W-10-500-N-N’ and ‘W-5-397-N-N’). In both cases, the member subjected to the larger charge mass caused larger deformations. This can be explained by the fact that in all cases the loading can be characterized as impulsive because the ratio of the positivephase pressure duration (which is less than 0.5 ms) to the period of oscillation (which is in the range of 5–8 ms; see Table 4) is less than 0.1 [34]. Thus, for detonations having the same scaled distance, the peak overpressure and the scaled impulse are expected to be similar. Since, in the case of impulsive loading, the response is governed by the absolute impulse, in two cases in which the scaled impulse is similar the absolute impulse will be higher when the charge mass is larger, and as a result so will the deformation. It can also be observed that the local deformation and the folding angle reached their residual value (or oscillated around it) relatively early in time. This means that the local damage at the midspan occurred quickly after the pressure reflected from the surface. A similar phenomenon, in which the local damage occurred within the first millisecond after the detonation while the global deformation controlled the response afterwards, is reported by Ngo et al. [9]. The residual total and local deformations, and the residual folding angle for each case are presented in Table 4 and their scaled form (with respect to the cube root of the charge mass) are plotted versus the scaled distance in Fig. 15. They all show an approximate linear trend of the scaled parameters with the scaled distance. Linear curve fitting has been approximated using the least-squares method. The suggested empirical equations take the following form: y ¼ c1 Z þ c2 ;

ð4Þ

where y is the scaled variable on the vertical axis, Z is the scaled distance, and c1 and c2 are empirical coefficients. The values for c1 and c2, and the coefficient of correlation r2 are given in Table 5. It should be noted that the suggested equations are based on a limited amount of calculation points.

4.1.2. Members with stiffeners A similar comparison was performed for members with stiffeners placed at 200- and 100-mm intervals. Time-history analyses of the same parameters and their residual values were determined using the same procedure and they are listed in Table 4 and are plotted in Fig. 16. The same phenomenon as in the bare members can be seen here, viz. as the scaled distance becomes smaller, the deformations increase for a given member, while for the same scaled distance the case with the higher charge mass yields higher deflections. The local deformation and folding angle reached their residual values quickly, similar to the bare members. Again, linear curve fitting was performed for the members with stiffeners and the equations are also plotted in Fig. 16. The suggested empirical coefficients and the correlation coefficient r2 are listed in Table 5 for these cases.

201

Table 5 Suggested linear curve-fitting coefficients.a Coefficientsa

δtotal,res/W1/3 (mm/kg1/3) c1

Bare Stiffeners @200 mm Stiffeners @100 mm a

c2

δlocal,res/W1/3 (mm/kg1/3) r2

c1

c2

θres (deg) r2

c1

c2

r2

−504.6 167.4 0.97 −131.2 50.1 0.98 −754.9 247.7 0.87 −691.9 218.2 0.95 −188.0 62.5 0.87 −209.4 73.1 0.85 −621.3 190.2 0.95 −134.5 41.7 0.89 −111.2 36.1

0.92

General formula: Parameter = C1Z + C2, where Z is in m/kg1/3.

4.2. Effect of adding stiffeners The effect of strengthening by adding stiffeners on the performance of the member is analyzed by comparing a member with and without stiffeners subjected to detonations of given charge mass and standoff distance. Accordingly, five comparisons can be illustrated for each charge and standoff distance combinations. As was done in the previous section, similar time-history analyses for the total and local deformations, and the folding angle are performed. The results from these analyses, viz. the total (δtotal,res) and local (δlocal,res) residual deformations, and the residual angles of flange rotation (θres), are presented for each case using bar diagrams in Fig. 17. Based on the quantitative residual parameters presented in Fig. 17, and the qualitative residual deformations shown in Fig. 13, the following observations are noted. For the 5 kg charge located at 500 mm (Z = 0.292 m/kg1/3), the 10 kg charge located at 500 mm (Z = 0.232 m/kg1/3), and the 5 kg charge located at 397 mm (Z = 0.232 m/kg1/3), the addition of stiffeners @200 mm spacing hardly affects the residual total deformations. However, the addition of stiffeners reduced the local deformation and significantly reduced the folding angle of the flanges. In these cases, the addition of stiffeners @100 mm intervals also reduced the total deformations in addition to the local deformations and the folding angle. Next, for the 1.08 kg charge located @300 mm (Z = 0.292 m/kg1/3), the damage, in terms of both total and local deformations, was relatively insignificant for the beam with stiffeners placed @200 mm spacing or without stiffeners, whereas the residual folding angle of the flanges was approximately the same. The addition of stiffeners @100 mm intervals reduced all deformations and the folding angle to negligible values. Lastly, for the 5 kg charge located @250 mm (Z = 0.146 m/kg1/3), an opposite trend from the other cases was observed for both the total and local deformations. Unexpectedly, from Fig. 17(c), it can be observed that the total and local deformations were larger for the member with stiffeners placed @200 mm spacing than those for the member without stiffeners. For the member with stiffeners placed @100 mm spacing, the residual total deformation was higher than that for the bare member but was still lower than that for the member with stiffeners placed @ 200 mm intervals; the residual local deformation was lower than that for the member without stiffeners or with stiffeners placed @200 mm intervals. The explanation for this result stems from the fact that, in this case, the scaled distance is the smallest. The CFD model indicates that the pressure waves were ‘trapped’ inside the rectangular area, defined by the flanges and the stiffeners. Thus, a more concentrated load, of likely higher intensity due to local wave reflections, was applied to the member. As a result, even though the global stiffness of the member might be somewhat higher due to the addition of the stiffeners which prevent the warping of the cross section, the actual loading characteristics were different and more localized in the midspan zone as compared to the bare member case, leading to an increase in the local deformations of the web panels at the centre of the beam, bound by stiffeners. Additional reasoning for this explanation can be demonstrated by comparing the deflection profile at 50 ms after detonation. Fig. 18 illustrates the deflection profiles of the central axis of the web along the member

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span, for the current charge and standoff distance, for members with and without stiffeners. It can be seen that the total deformation at the midspan was larger for the members with stiffeners. In addition, the localized larger deformations can be seen between the stiffeners at the midspan. However, when comparing the deflections outside the midspan region (e.g. farther than 300 mm from the midspan point) the deflections of the members with stiffeners are smaller than those for the bare member. The spacing of the stiffeners is also of interest here. The clear distance between the two flanges is 139 mm. When the spacing between two stiffeners is 200 or 100 mm, the rectangular plate between the flanges and the stiffeners, has clear dimensions of 139 × 194 mm and 139 × 94 mm, respectively. Therefore, the shorter span direction in the first case (stiffeners @200 mm) is perpendicular to the flanges, while in the second case (stiffeners @100 mm) it is parallel to the flanges. Fig. 19 illustrates the direction of the shorter span, and hence the main load path, to the plate supports. For the case when stiffeners are placed @200 mm intervals, the load path in the web is similar to that for the bare beam, whereas placing the stiffeners @100 mm spacing reduced the span of the web panels by approximately 35%. As can be seen in Fig. 13, the local distortion of the beam cross section is smaller in simulation ‘W-5-250-100-N’ than that in simulation ‘W-5-250-200N’ which supports the explanation above. This effect of the localized pressures ‘trapped’ in between the flanges and the stiffeners has led to the investigation of an additional solution for strengthening the member to avoid confining the pressure, especially in the midspan area. The solution suggested includes the installation of round bars spaced @100 mm intervals between the flanges, adjacent to the flange edges, as illustrated in Fig. 9. In this way, the flange angle of bending would still be restrained but the pressures would not be concentrated in the closed spaces created in between the stiffeners. The use of transverse bars between I-section flanges as a building concept is described in CSA S16 [35] for a type of composite I-section column, in which the steel is partially encased in concrete, between the flanges only. The CSA S16 Commentary mentions that the steel links restrain the flanges from local buckling and provide limited confinement to the concrete [35]. Thus, this flange-tying technique is already included as a fabrication concept in structural steel design standards, and it is used here as a concept for blast resistance to provide blast pressure relief. An analysis using this suggested solution is presented in the next section. 4.3. Effect of adding bars

Fig. 16. Scaled (a) Residual total and (b) Local deformations, and (c) Residual folding angle, versus scaled distance.

For practical reasons, it was decided to connect the face of the bars 20 mm away from the flange edge to provide sufficient space for bar welding, above and below the web. Three diameters (d) of bars were used in the simulations: 6, 12 and 18 mm. Bars with a diameter of 18 mm may be too large because this size is approximately three times the web and flange thickness; therefore, it is provided here only as a theoretical approach. As mentioned in Section 2.2, the same material model used for the I-section steel was applied for the bars in the numerical simulation. The residual deformation at 50 ms after the detonation is presented for each case in Fig. 13. Qualitatively, the use of bars restrained the flange folding angles at midspan, in comparison with a bare member. Some of the thinner bars with a diameter of 6 mm (d = 6 mm) located between the flanges directly exposed to the blast pressures (top flanges) failed in tension, whereas some of the bars located between the bottom flanges deformed significantly (see cross-section A-A of member ‘W-5-250-N-6’ in Fig. 13). In addition to a higher level of restraint against flange folding, the use of bars with diameters of 12 mm and 18 mm prevented the failure of the top bars in tension. However, while the bottom flanges were almost undeformed with 6 mm bars, in the cases of 12 mm and 18 mm bars they deformed outwards. The deformed web impacted the bars in these two latter cases and a minimal

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Fig. 17. Residual parameters for a given charge mass and standoff distance, for various member types.

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Fig. 17 (continued).

local failure can be observed due to this impact in the case of 18 mm bars (see cross-section A-A of member ‘W-5-250-N-18’ in Fig. 13). Quantitatively, the residual total and local deformations, and folding angle are presented in bar diagrams in Fig. 17(c). Two comparison are made: (i) between a bare member and a member with bars; (ii) between a member with bars and a member with stiffeners. From Fig. 17c one can see that the addition of bars caused some increase of the residual total and local deformations compared to a bare member. However, the folding angle was reduced significantly. While the use of bars with d = 6 mm reduced the folding angle from 132 degrees to 111 degrees, the use of bars with d = 12 mm reduced this angle to 60 degrees – a significant reduction. The use of bars with d = 18 mm, further reduced the residual angle to only 55 degrees. When comparing the performance of the members with bars to those with stiffeners, it is evident that the folding angle was lower for the members with stiffeners. Nevertheless, the use of members with bars still reduced the angle by more than 50% in comparison with bare members, while the total deformation was somewhat lower than that of the members with stiffeners. In summary, the use of members with 12 mm bars still results in an acceptable performance for flange rotation/distortion. It should be noted

Fig. 18. Deformation profile through the web mid-plane, for 5 kg at 250 mm, at 50 ms after detonation.

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Flanges

Flanges

Web

Web Stiffeners 100

152

152

200

205

Short loading path

Short loading path

(a)

(b) Fig. 19. Short loading path for member with stiffeners (a) @200 and (b) @100 mm.

that, in the current models, the bars were fully bonded to the flanges therefore assuming that weld failure was not critical, a condition which should be ensured in practice. 5. Summary and conclusions The results of a research study of the response of I-sections to closein detonations, using numerical simulations are presented. Due to the non-uniform and complicated nature of the pressure environment around the target, the main challenge for this kind of problem is the need to simulate the detonation process through CFD modelling. Such modelling requires a high amount of computational time and resources. An alternative approach which consists of two stages of analysis is suggested herein. In the first stage, the detonation process is simulated using CFD modelling and, after sufficient time, the second stage, in which the CFD part is removed and the free vibrations of the structural member are analyzed, is initiated. This approach is validated through comparison with experimental data of RHS beams subjected to closein detonations. Then, the simulation is used to study the response of Isections subjected to close-in detonations causing bending about the weak axis. Aside from evaluating the behaviour of bare members, three strengthening methods were investigated: stiffeners at close and far spacing, and bars with various diameters at close spacing. After the approach had been verified and a mesh sensitivity analysis had been performed, a parametric study was conducted for various charge mass values and standoff distances. The total and local deformations of the web at midspan, and the folding angle of the flanges, as well as the visual residual deformations and failure modes were determined and compared. The following conclusions can be drawn from the current study: • The postulated two-stage numerical modelling approach provides a very good method for simulating the response of steel I-sections to close-in detonations, while significantly reducing the computation effort compared to single-stage modelling. This modelling approach allows the challenges in simulating structural response for close-in detonations to be overcome. • In general, as the scaled distance becomes smaller, the total and local member deformations and folding angle of the flanges become larger for a given member, as expected; however, for two different charges having the same scaled distance, the larger charge mass produces higher deflections. This occurs because the absolute impulse is the dominant parameter in the structural response and, for the same scaled distance, the absolute impulse is higher for a larger charge mass. • Empirical linear functions were fitted to scaled deformation parameters as functions of the scaled distance, which allows prediction of residual damage for the given cases. • In most cases, the addition of stiffeners has little effect on the total deformation. However, the addition of stiffeners significantly reduces the flange folding angle (i.e. the local cross-section

distortion) in all cases, in turn leading to an increased residual member capacity. • At small scaled distances, even though the addition of stiffeners reduces the folding angle of the flanges, blast pressure causes increased local, and hence total midspan deformations. This result is unexpected, and it occurs due to the ‘entrapment’ of pressure which accumulate at the midspan in the confined space between the flanges and the stiffeners. • The larger total deformations observed for members at small scaled distances can be mitigated with transverse bars instead of stiffeners, to provide a pressure relief pathway along the member. This represents a good solution for reducing the flange folding angle at small scaled distances, without the increase in the total deflections at midspan. The use of bars with a diameter of 12 mm provided reasonable results for the size of I-sections investigated. The use of transverse bars for blast mitigation is thus advocated as a novel reinforcement method. Acknowledgements Financial support for this study has been provided by the Lyon Sachs Research Fund, University of Toronto. References [1] C.B. Ritchie, J.A. Packer, M.V. Seica, X.-L. Zhao, Behaviour and analysis of concretefilled rectangular hollow sections subject to blast loading, J. Constr. Steel Res. 147 (2018) 340–359, https://doi.org/10.1016/J.JCSR.2018.04.027. [2] T. Krauthammer, Modern Protective Structures, CRC Press, 2008. [3] U.S Army Corps of Engineers, Unified Facilities Criteria (UFC) - Structures to Resist the Effects of Accidental Explosions (UFC 3-340-02), 2008. [4] C.B. Ritchie, J.A. Packer, M.V. Seica, X.-L. Zhao, Behavior of steel rectangular hollow sections subject to blast loading, J. Struct. Eng. ASCE 143 (2017), 04017167. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001922. [5] A.A. Nassr, A.G. Razaqpur, M.J. Tait, M. Campidelli, S. Foo, Experimental performance of steel beams under blast loading, J. Perform. Constr. Facil. ASCE. 26 (2012) 600–619, https://doi.org/10.1061/(ASCE)CF.1943-5509.0000289. [6] A.M. Remennikov, B. Uy, Explosive testing and modelling of square tubular steel columns for near-field detonations, J. Constr. Steel Res. 101 (2014) 290–303, https:// doi.org/10.1016/J.JCSR.2014.05.027. [7] H. Zhang, Z. Li, C. Wu, Investigation of blast effects on double-skinned composite steel tubular columns, Int. J. Prot. Struct. 6 (2015) 403–418, https://doi.org/10. 1260/2041-4196.6.3.403. [8] W. Wang, C. Wu, J. Li, Numerical simulation of hybrid FRP-concrete-steel doubleskin tubular columns under close-range blast loading, J. Compos. Constr. 22 (2018), 04018036. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000871. [9] T. Ngo, D. Mohotti, A. Remennikov, B. Uy, Numerical simulations of response of tubular steel beams to close-range explosions, J. Constr. Steel Res. 105 (2015) 151–163. [10] C.N. Kingery, G. Bulmash, Air Blast Parameters From TNT Spherical Air Burst and Hemispherical Surface Burst, US Army Ballistic Research Laboratory technical report ARBRL-TR 02555, Maryland, USA, 1984. [11] L. Mazurkiewicz, J. Malachowski, P. Baranowski, Blast loading influence on load carrying capacity of I-column, Eng. Struct. 104 (2015) 107–115, https://doi.org/10. 1016/J.ENGSTRUCT.2015.09.025. [12] S.E. Rigby, O.I. Akintaro, B.J. Fuller, A. Tyas, R.J. Curry, G.S. Langdon, D.J. Pope, Predicting the response of plates subjected to near-field explosions using an energy equivalent impulse, Int. J. Impact Eng. 128 (2019) 24–36, https://doi.org/10.1016/J. IJIMPENG.2019.01.014.

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