The effect of oblique blast loadings on moment and braced frames in steel structures

Abstract

Due to the increasing use of vehicle bombs on attacking important buildings by terrorist organizations around the world, it is necessary to design buildings with more resistance against blast loads. In this research, numerical studies have been done for three-dimensional structural models of special moment frames, concentrically braced frames, and eccentrically braced frames with 3, 5, and 10 stories. The nonlinear dynamic method is applied for analyzing the models under two different levels of straight and oblique blast loadings based on the UFC 3-340-02. The plastic hinge rotations, ductility ratios, performance levels, and flexural moments in the models are obtained from the analysis and compared with each other. According to the results, it can be said that the eccentrically braced frame systems generally show better performances than other systems under blast loadings. Also due to different shock directions, the values of column plastic rotations and bending moments under oblique blast loadings are less than straight ones.

Keywords

oblique explosion special moment frame/concentrically braced frame/eccentrically braced frame frames steel structure

Introduction

Nowadays, due to the increase in terrorist attacks around the world, building design against blast loadings has been of particular interest especially in some sensitive structures and vital arteries. Design of blast-resistant structures as a necessity is not only applied for the government and military organizations but also is applied for civilian’s safety against terrorist threats.

The expected performance of buildings against explosion has effects on the design economy and long-term exploitation of a project. The importance of blast effects on structures has led to developing guidelines in the design of structures and urban areas against blast loadings. TM 5-855-1 manual which was provided by the US army department for designing and analyzing structures subjected to conventional weapon effects in 1986 can be considered as one of the pioneers of these guidelines. This manual was prepared and completed from the early 50s (Ngo et al., 2007). TR 87-57 manual was then provided by US air force engineering in 1989 to analyze and design non-nuclear blast-resistant structures. In proceeding, TM 5-1300 manual was prepared by US Department of the Army, Navy, and Air Force in 1990. It was widely used by military and civil engineers to design blast-resistant structures. Finally, UFC 3-340-02 manual was published by the US Department of Defense (2008). This guideline is the updated version of TM 5-1300 and is more comprehensive than the previous guidelines. UFC 3-340-02 (US Department of Defense, 2008) is now mostly used as the main basis of design and research in blast-resistant design fields.

When an explosion occurs, the energy is suddenly released in a very short time (milliseconds) as thermal radiations and expanding shock waves in the air. These waves propagate with ultrasonic speed and form a wave front. The explosion wave forces are the main cause of building damage. When an object is located in the path of the wave front, its surface pressure rises from ambient pressure to a peak overpressure in a very short time. The magnitude and distribution of blast loads on the structure surface vary greatly with the following factors (American Institute of Steel Construction (AISC), 2004; Bangash and Bangash, 2006; Federal Emergency Management Agency (FEMA), 2003a, 2003b):

The shape and geometry of the structure

Location of the detonation relative to the structure

Explosive properties (type of material, the amount of energy released, and quantity of explosive)

The amplification of the pressure pulse because of its reflection from the ground or structure surface

The pressure–time variation curve for blast in free-field is shown in Figure 1. The pressure reaches rapidly from ambient pressure to pick overpressure $P_{SO}^{+}$ and then decreases to the ambient pressure in time $t_{O}^{+}$ which is called the positive phase duration. The negative phase is followed, with the time duration $t_{O}^{-}$ and the maximum negative pressure value, $P_{SO}^{-}$ (Bangash and Bangash, 2009; US Department of Defense, 2008). The negative phase is longer compared to the positive phase, and the peak values of the under ambient pressures are generally lower compared to the peak positive overpressures (FEMA, 2003b). The negative phase is often less important than the positive phase in the design of blast-resistant structures.

Figure 1.

Free-field pressure–time variation (US Department of Defense, 2008).

Scaling law is used to predict the properties of blast waves. The most common form of blast scaling law is cube-root scaling law that was first derived by Hopkinson in 1915 and then formulated by Cranz in 1926 (US Department of Defense, 2008). Scaling law provides parametric correlations between a particular explosion and a standard charge of the same substance, as follows

Z_{G} = \frac{R}{\sqrt[3]{W}}

(1)

where R is the distance from the center of the explosive source and W is the total weight of a standard explosive, such as TNT, that can represent the explosive energy.

Determination of the blast parameters and appropriate relations for calculating the maximum blast overpressure has been the purpose of many scientific researches until now. For the first time, estimations of the peak overpressure due to the spherical blast were introduced by Brode (1955), as follows

\begin{array}{l} P_{S O} = \frac{0.975}{Z} + \frac{1.455}{Z^{2}} + \frac{5.85}{Z^{3}} - 0.019 bar \\ (0.1 bar < P_{S O} < 10 bar) \end{array}

(2)

P_{SO} = \frac{6.7}{Z} + 1 bar (P_{SO} > 10 bar)

(3)

where Z is the scaled distance.

Another famous equation was introduced by Newmark and Hansen (1961)

P_{SO} = 6784 \frac{W}{R^{3}} + {(63 \frac{W}{R^{3}})}^{\frac{1}{2}} bar

(4)

Also, Henrych (1979) introduced the following equation to calculate the maximum blast pressure (bar)

\begin{array}{l} P_{S O} = \frac{14.072}{Z} + \frac{5.54}{Z^{2}} + \frac{0.357}{Z^{3}} \\ + \frac{0.00625}{Z^{4}} (0.05 < Z < 0.3) \end{array}

(5)

P_{SO} = \frac{6.194}{Z} + \frac{0.326}{Z^{2}} + \frac{2.132}{Z^{3}} (0.3 < Z < 0.1)

(6)

P_{SO} = \frac{6.662}{Z} + \frac{4.05}{Z^{2}} + \frac{3.288}{Z^{3}} (0.1 < Z < 10)

(7)

According to the researches in the field of blast wave parameters, some curves have been presented in TM 5-1300 (US Department of the Army, Navy, and Air Force, 1990) and UFC 3-340-02 (US Department of Defense, 2008) to calculate the blast pressure, impulse, duration, and other effective parameters in the positive and negative phases.

The unconfined explosion based on the location of the detonation relative to the structure can be classified into the free air burst, air burst, and surface burst. Free air burst is an explosion which occurs in free air above a structure. Shock waves propagate radially away from the center of the detonation and strike the structure without any amplification. Air burst is an explosion which occurs at the nearest height above the ground surface, so the ground reflected wave may affect the initial wave. The interaction point between the initial wave and other reflected wave (from the ground and or structure surface) is called Mach height. A surface burst is an explosion which occurs when the detonation is located near or on the ground, so the initial shock is amplified at the point of detonation due to the ground reflection (Figure 2). A comparison among blast wave parameters in different explosions indicates that at the same distance from a detonation of the same explosive weight, blast pressure, impulse, duration, and other effective parameters for the surface burst are larger than other types of burst (US Department of Defense, 2008).

Figure 2.

Surface burst blast environment (US Department of Defense, 2008).

In this study, the explosion is considered to be a kind of surface burst. The equations and curves that are presented in UFC 3-340-02 (US Department of Defense, 2008) will be used to determine all the required parameters for the blast loading pattern on the front walls, roof, side walls, and rear walls of the structure.

Since the existing steel structures are usually designed for gravity and seismic loads, it is necessary to evaluate their performances under blast loadings in hazard zones. The explosion effects on the members or connections of steel structures have been investigated by many researchers, for example, it can be referred to Saedi Daryan et al. (2011), Guzas and Earls (2011), Urgessa and Arciszewski (2011), and many other researchers. However, the global behavior of steel frames with different lateral systems is less investigated under the blast loadings. The main scope in this study is concentrated to investigate the global behavior of steel structures with different lateral resistant systems such as special moment frame (SMF), concentrically braced frame (CBF), and eccentrically braced frame (EBF) under blast loadings.

Study method

Selected models

To investigate steel structures’ performance under the oblique blast loadings, analytical studies have been carried out on three-dimensional (3D) structural models of SMFs, CBFs, and EBFs with different numbers of stories (3, 5, and 10). All the models have the same rectangular plans with 5 m spans and 3.2 m height (Figure 3). Figure 4 shows the location of braces in the CBF and EBF model plans. The models have been selected based on FEMA 356 (FEMA, 2000b) and FEMA 357 (FEMA, 2000a) to behave in the immediate occupancy (IO) performance level under seismic loads. Sections for selected models are presented in Tables 1 to 3.

Figure 3.

Floor plan.

Figure 4.

Locations of braces in CBF and EBF models.

Table 1.

Sections for SMF models.

Performance level	Peripheral beam	Central beam	Peripheral column	Central column	Story	Model type
IO	IPE400	IPE300	BOX450X30	BOX250X15	1–2	SMF 3
IO	IPE400	IPE270	BOX450X30	BOX200X15	3	SMF 3
IO	IPE360	IPE360	BOX450X30	BOX300X20	1–2	SMF 5
IO	IPE360	IPE360	BOX450X30	BOX250X15	3
IO	IPE300	IPE300	BOX450X30	BOX250X15	4–5
IO	IPE400	IPE400	BOX450X30	BOX350X20	1–5	SMF 10
IO	IPE360	IPE360	BOX300X20	BOX300X20	6–10	SMF 10

IO: immediate occupancy; SMF: special moment frame.

Table 2.

Sections for CBF models.

Performance level	Brace	Peripheral beam	Central beam	Peripheral column	Central column	Story	Model type
IO	2U140	IPE240	IPE240	BOX450X30	BOX200X10	1–2	CBF 3
IO	2U120	IPE240	IPE240	BOX450X30	BOX200X10	3	CBF 3
IO	2U200	IPE270	IPE270	BOX450X30	BOX250X15	1–3	CBF 5
IO	2U180	IPE270	IPE270	BOX450X30	BOX200X10	4–5	CBF 5
IO	2U300	IPE270	IPE270	BOX400X30	BOX250X15	1–5	CBF 10
IO	2U300	IPE240	IPE240	BOX400X30	BOX250X15	6–7
IO	2U220	IPE240	IPE240	BOX250X15	BOX250X15	8–10

IO: immediate occupancy; CBF: concentrically braced frame.

Table 3.

Sections for EBF models.

Performance level	Brace	Central beam	Peripheral column	Central column	Story	Model type
IO	2U140	IPE240	BOX450X30	BOX200X10	1–2	EBF 3
IO	2U140	IPE240	BOX450X30	BOX200X10	3	EBF 3
IO	2U220	IPE270	BOX450X30	BOX250X15	1–3	EBF 5
IO	2U200	IPE270	BOX450X30	BOX200X10	4–5	EBF 5
IO	2U320	IPE270	BOX400X30	BOX250X15	1–5	EBF 10
IO	2U320	IPE240	BOX400X30	BOX250X15	6–7
IO	2U220	IPE240	BOX250X15	BOX250X15	8–10

IO: immediate occupancy; EBF: eccentrically braced frame.

Blast loading

Two different cases of blast loading are considered. Load case 1 is equivalent to 500 kg of TNT at a distance of 10 m from the structure and load case 2 is equivalent to 1000 kg of TNT at a distance of 20 m from the structure. To investigate the effect of shock direction, the detonation has been located in front of the small side of the plan in one case and at the corner of the plan in the other case as shown in Figure 5.

Figure 5.

Location of the detonation.

The assumptions for the blast loading are as follows:

The positive phase of the blast pressure generated by a surface burst subjected to front side of the structure is applied for analyses. The negative pressure phase effects are ignored due to its insignificant value.

Since the dimensions and height of the selected structures are larger compared to the distance of the explosion point, calculation of the effective pressures on the side walls, rear wall, and roof shows that the effects of explosion on these walls are insignificant compared to their effects on the front wall. Therefore, the mentioned effects are ignored.

Distribution of the effective load for subjected beams and columns has been conservatively calculated based on the assumption that the side walls of the structure are strong enough to bear and distribute the exerted loads.

In the considered models, load is distributed invariably up to Mach height and is reduced with the increase in height.

The blast loading parameters have been calculated for two load cases of explosion according to UFC 3-340-02 (US Department of Defense, 2008). The pressure–time patterns for different load cases are shown in Figures 6 and 7.

Figure 6.

Pressure–time curve for straight blast loading.

Figure 7.

Pressure–time curve for oblique blast loading.

Material properties

Rapid variation in stress–strain rate under impact loadings (such as blast loading) influences on the mechanical properties of the materials. The effects of increasing strain can be observed as the increase in yield stress and ultimate stress of structural steel (Ngo et al., 2007; US Department of Defense, 2008). Figure 8 shows a typical stress–strain curve of structural steel under impact loadings. In this research, a simplified bilinear elasto-plastic curve has been considered (Figure 9). Based on UFC 3-340-02 (US Department of Defense, 2008), the dynamic increase factor (DIF) has been considered 1.2 for yield stress and 1.05 for ultimate stress. The mechanical properties of structural steel for selected models are presented in Table 4.

Figure 8.

Typical stress–strain curves for steel.

Figure 9.

Bilinear elasto-plastic curve.

Table 4.

Properties of structural steel.

Weight per unit volume	Poisson’s ratio	Modulus of elasticity	Ultimate stress	Yield stress	Blast ultimate stress	Blast yield stress
G (kN/m²)	ν	E (kN/m²)	Fu (kN/m²)	Fy (kN/m²)	Fdu (kN/m²)	Fdy (kN/m²)
76.98	0.3	2.06 E + 08	5.20 E + 05	3.50 E + 05	5.46 E + 05	4.20 E + 05

Acceptance criteria under the blast loading

The acceptable criteria for the structural elements have been considered in three performance levels, IO, life safety (LS), and collapse prevention (CP), according to Table 5. The ductility ratio (µ) is defined as the ratio of the maximum deflection to the equivalent elastic deflection. The ductility ratio must be checked to determine whether the specified rotation can be reached without premature buckling of the member (US Department of Defense, 2008). The hinge rotation (θ) is the other criteria to determine the performance level of the structural elements. As shown in Figure 10, the hinge rotation is the angle between the chord joining the supports and the point on the element where deflection is maximum.

Table 5.

Deformation criteria for a frame structure (Iranian National Building Code, 2013).

Performance level
IO		LS		CP
µ	θ (rad)	µ	θ (rad)	µ	θ (rad)
1.5	0.017	2	0.026	3	0.035

IO: immediate occupancy; LS: life safety; CP: collapse prevention.

Figure 10.

Member end rotations for frames (US Department of Defense, 2008).

Analysis results

The nonlinear direct integration time-history method (Hilber–Hughes–Taylor (HHT)) is applied for analyzing the performance of the models under blast loadings. All the models are analyzed using the finite element software (SAP2000). The HHT method has an acceptable precision and a proper convergence for the nonlinear solution. This method uses a single parameter called alpha which can take values between 0 and −1/3. For alpha = 0, the method is equivalent to the Newmark method with gamma = 0.5 and beta = 0.25, which is the same as the average acceleration method. Using alpha = 0 leads to the most accurate results, but it is often necessary to use a negative value of alpha to encourage a nonlinear solution to converge. For best results, the alpha = −0.1 has been used.

The plastic hinge properties’ definition has been performed based on FEMA 356 (FEMA, 2000b) and FEMA 357 (FEMA, 2000a). The plastic hinge rotation, ductility ratio, and performance levels of the members are obtained from the analysis and compared to each other. The maximum values of plastic hinge rotation, ductility ratio, and performance levels of the critical columns and beams are presented in Tables 6 to 11. The results of 3-, 5-, and 10-story models show that the plastic hinges are mostly formed in the front columns and beams. It can be said that the structure performance is highly depended on the peripheral members (columns and beams) under blast loadings. As an example, the plastic hinge locations and performance levels of the five-story models under the straight and oblique blast (load case 1) are presented in Figure 11. The scale of the images is reduced to show better the local deformation and deflection of structure members.

Table 6.

Results for straight blast loading in SMF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
CP	0.693	0.0195	IO	0.996	0.0023	CP	2.956	0.0231	1	3
CP	0.518	0.0174	IO	0.518	0.0012	CP	1.832	0.0242	2	3
LS	0.516	0.0068	IO	0.869	0.0122	CP	2.119	0.0325	1	5
IO	0.415	0.0	IO	0.156	0.0004	CP	1.037	0.0185	2	5
IO	0.346	0.0	IO	0.159	0.0	IO	0.911	0.0092	1	10
IO	0.165	0.0	IO	0.125	0.0	IO	0.283	0.0032	2	10

CP: collapse prevention; IO: immediate occupancy; LS: life safety; SMF: special moment frame.

Table 7.

Results for straight blast loading in CBF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
IO	0.398	0.0	IO	0.689	0.0016	CP	2.066	0.0195	1	3
IO	0.412	0.0	IO	0.506	0.0	CP	1.538	0.0199	2	3
IO	0.297	0.0	IO	0.180	0.0	LS	1.102	0.0117	1	5
IO	0.308	0.0	IO	0.178	0.0	LS	1.037	0.0162	2	5
IO	0.288	0.0	IO	0.284	0.0026	CP	1.799	0.027	1	10
IO	0.266	0.0	IO	0.179	0.0	CP	1.000	0.0203	2	10

IO: immediate occupancy; CP: collapse prevention; LS: life safety; CBF: concentrically braced frame.

Table 8.

Results for straight blast loading in EBF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
IO	0.398	0.0	IO	0.71	0.0016	CP	2.087	0.018	1	3
IO	0.412	0.0	IO	0.253	0.0	CP	0.504	0.0213	2	3
IO	0.297	0.0	IO	0.191	0.0	LS	0.932	0.01	1	5
IO	0.308	0.0	IO	0.192	0.0	LS	0.881	0.0138	2	5
IO	0.302	0.0	IO	0.237	0.0	LS	0.994	0.0137	1	10
IO	0.268	0.0	IO	0.042	0.0	IO	0.089	0.0065	2	10

IO: immediate occupancy; CP: collapse prevention; LS: life safety; EBF: eccentrically braced frame.

Table 9.

Results for oblique blast loading in SMF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
LS	0.693	0.0103	IO	0.869	0.0042	LS	1.989	0.0188	1	3
LS	0.518	0.008	IO	0.497	0.0026	LS	1.3	0.017	2	3
IO	0.516	0.0011	IO	0.731	0.0106	LS	1.61	0.0242	1	5
IO	0.321	0.0	IO	0.178	0.003	LS	0.625	0.0093	2	5
IO	0.202	0.0	IO	0.127	0.0	IO	0.487	0.0046	1	10
IO	0.142	0.0	IO	0.075	0.0	IO	0.158	0.0	2	10

LS: life safety; IO: immediate occupancy; SMF: special moment frame.

Table 10.

Results for oblique blast loading in CBF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
IO	0.398	0.0	IO	0.614	0.0032	LS	1.504	0.0155	1	3
IO	0.412	0.0	IO	0.414	0.0002	LS	1.11	0.014	2	3
IO	0.297	0.0	IO	0.148	0.0002	IO	0.614	0.0093	1	5
IO	0.308	0.0	IO	0.142	0.0	IO	0.575	0.0083	2	5
IO	0.288	0.0	IO	0.303	0.0033	LS	1.165	0.014	1	10
IO	0.266	0.0	IO	0.03	0.0011	LS	0.06	0.0107	2	10

IO: immediate occupancy; LS: life safety; CBF: concentrically braced frame.

Table 11.

Results for oblique blast loading in EBF models.

Beam			Corner column			Central column			Blast case	Number of stories
Performance level	µ	θp	Performance level	µ	θp	Performance level	µ	θp	Blast case	Number of stories
IO	0.398	0.0	IO	0.614	0.0033	LS	1.997	0.0137	1	3
IO	0.412	0.0	IO	0.414	0.0002	LS	1.124	0.0135	2	3
IO	0.297	0.0	IO	0.148	0.0002	IO	0.487	0.005	1	5
IO	0.308	0.0	IO	0.142	0.0	IO	0.455	0.0065	2	5
IO	0.302	0.0	IO	0.303	0.0033	IO	0.578	0.0071	1	10
IO	0.268	0.0	IO	0.03	0.0011	IO	0.071	0.0013	2	10

IO: immediate occupancy; LS: life safety; EBF: eccentrically braced frame.

Figure 11.

Performance level for five-story models in load case 1.

In Figures 12 to 17, the maximum plastic rotation of the central column of the frame fronting the explosion is compared in different stories of 3-, 5-, and 10-story models. The results indicate that the values of plastic hinge rotations for three- and five-story models with SMF systems are higher than those of CBF and EBF systems. The stiffness of the braced frames is generally higher than the moment frames. Thus, the deformations are increased in moment frames compared to the braced frames. Also, according to the selecting and designing of the models based on IO performance level, the EBF systems are more stiffened than the CBF systems. The increase in the stiffness in EBF three- and five-story models compared to the CBF systems leads to reduce the plastic hinge rotation of columns in EBF models compared to the CBF models.

Figure 12.

Plastic rotation of the central column for three-story models in blast case 1.

Figure 13.

Plastic rotation of the central column for five-story models in blast case 1.

Figure 14.

Plastic rotation of the central column for 10-story models in blast case 1.

Figure 15.

Plastic rotation of the central column for three-story models in blast case 2.

Figure 16.

Plastic rotation of the central column for five-story models in blast case 2.

Figure 17.

Plastic rotation of the central column for 10-story models in blast case 2.

In 10-story models with SMF systems, the values of plastic hinge rotations are less than those of CBF and EBF models. It is because of the bigger sections which satisfy the requirements of IO performance level in SMF models compared to the CBF and EBF models.

Moreover, the maximum plastic hinge rotation values for three- and five-story models have been observed in the columns of the middle stories. The reason is that according to the blast load pattern, the intensity of the blast load at lower stories (less than Mach height) is almost the same. Also, with increasing the height (according to the seismic design), the sections of upper stories are gradually reduced compared to the lower stories. Thus, in three- and five-story models, middle stories are more vulnerable.

In 10-story models unlike 3- and 5-story models, the values of plastic hinge rotations in the middle stories decrease and the maximum rotations occur in lower stories. This is due to the fact that in the middle stories of high-rise buildings, the intensity of the blast load is gradually reduced and the lower stories are affected by the maximum blast loads. In the upper stories of 10-story models, while the exerted load decreases, the plastic hinge rotations increase due to the reduction in the cross section of the members. According to the results, the plastic hinge rotation of the columns depends on the loading pattern and the cross section of the members at height.

In Figures 18 to 26, the maximum plastic rotation of the central column in the fronting frame is compared for oblique and straight blast loadings. The results indicate that the values of plastic rotation in oblique blast loadings are less than its values in straight ones. The general pattern of plastic hinges in the columns is the same for oblique and straight blast loadings despite the different shock directions.

Figure 18.

Comparison of plastic hinges’ rotation for the central column in three-story SMF models.

Figure 19.

Comparison of plastic hinges’ rotation for the central column in three-story CBF models.

Figure 20.

Comparison of plastic hinges’ rotation for the central column in three-story EBF models.

Figure 21.

Comparison of plastic hinges’ rotation for the central column in five-story SMF models.

Figure 22.

Comparison of plastic hinges’ rotation for the central column in five-story CBF models.

Figure 23.

Comparison of plastic hinges’ rotation for the central column in five-story EBF models.

Figure 24.

Comparison of plastic hinges’ rotation for the central column in 10-story SMF models.

Figure 25.

Comparison of plastic hinges’ rotation for the central column in 10-story CBF models.

Figure 26.

Comparison of plastic hinges’ rotation for the central column in 10-story EBF models.

The maximum values of the bending moments due to the elastic and plastic rotations of the central columns in 3-, 5-, and 10-story models are presented in Figures 27 to 35. Three-story models with CBF and EBF systems have nearly the same bending moment values. The values of the bending moments in columns with plastic hinges are nearly identical. This is due to the elasto-plastic behavior which is considered for the moment–rotation curves in the nonlinear hinges. For example, in the first floors of five-story models due to the formation of the nonlinear hinges and elasto-plastic relations between moment and rotation, the values of the bending moments are nearly identical.

Figure 27.

Moment comparison for the central columns in three-story SMF models.

Figure 28.

Moment comparison for the central columns in three-story CBF models.

Figure 29.

Moment comparison for the central columns in three-story EBF models.

Figure 30.

Moment comparison for the central columns in five-story SMF models.

Figure 31.

Moment comparison for the central columns in five-story CBF models.

Figure 32.

Moment comparison for the central columns in five-story EBF models.

Figure 33.

Moment comparison for the central columns in 10-story SMF models.

Figure 34.

Moment comparison for the central columns in 10-story CBF models.

Figure 35.

Moment comparison for the central columns in 10-story EBF models.

The maximum values of bending moments for 3- and 5-story models are observed in CBF systems and for 10-story models are observed in SMF systems. Comparison of the results for oblique and straight blast loadings indicates that due to the different shock directions, the bending moment under oblique blast loadings is less than straight ones.

The structures’ performance levels in different lateral resistant systems under straight and oblique blast loadings are illustrated in Figures 36 to 38. The three- and five-story structures with EBF systems have a better performance compared to the structures with SMF and CBF systems under blast loads. This is due to the lower rotation values of the members and higher performance levels. Furthermore, in 10-story models, structures with SMF lateral resistant systems have a better performance compared to the structures with EBF and CBF systems. But it should be noted that the better performance in 10-story models is due to the stronger sections, which satisfies the requirements of IO performance level, in SMF models compared to the CBF and EBF models. Moreover, using SMF system only in tall buildings is not a cost-effective plan.

Figure 36.

Comparison of performance levels for three-story models.

Figure 37.

Comparison of performance levels for five-story models.

Figure 38.

Comparison of performance for levels 10-story models.

It can be said that the structures with EBF lateral resistant systems have a better performance compared to the other systems under the blast loading. Also, the results indicate that due to the different shock directions, the structures under oblique blast loadings have a better performance compared to the straight blast loadings.

Conclusion

Analysis and comparison of the results due to the first mode of straight/oblique explosion effect lead to the following conclusions:

Plastic hinge rotations of the structural members have more effect on determining the performance level compared to the ductility ratio of the members, especially in more intense blasts.

Due to the different shock directions, the columns’ plastic rotations and bending moments in oblique blast loadings are less than their values in straight ones.

Short buildings are more vulnerable compared to tall buildings (especially in the first mode of explosion). The reason is that the blast forces are larger than the earthquake forces in short buildings. However, if the second and third blast modes (occurrence of progressive collapse phenomenon, etc.) are considered, tall buildings will be more vulnerable.

Stiffness factor is one of the effective parameters in the performance of the structures under blast loading. Thus, CBF and EBF lateral resistant systems have a better performance compared to the SMF systems under the blast loading.

Three- and five-story models (short buildings), EBF lateral resistant systems, due to the lower rotations of the members, have a better performance compared to the structures with SMF and CBF lateral resistant systems.

Peripheral components of the structure including the columns have an important role in determining the performance level of the structure. The peripheral walls of the structure that are connected to the peripheral columns increase the effective load-bearing area of these columns.

It is recommended that the structures’ peripheral columns are properly isolated from the peripheral walls so that the exerted blast loads on the peripheral walls can be transferred to the other columns and structural components through the roof diaphragm. Consequently, the performance level of the structure can be improved under the blast loading.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

American Institute of Steel Construction (AISC) (2004) Facts for Steel Buildings, Blast and Progressive Collapse. Chicago, IL: AISC, pp. 1–13.

Bangash

NYH

Bangash

(2006) Explosion-Resistant Buildings. Berlin, Heidelberg: Springer-Verlag, pp. 67–101.

Bangash

NYH

Bangash

(2009) Shock, Impact and Explosion. Berlin, Heidelberg: Springer-Verlag, pp. 388–393.

Brode

(1955) Numerical solution of spherical blast waves. Journal of Applied Physics 26: 766–775.

Federal Emergency Management Agency (FEMA) (2000a) Global topics report on the pre-standard and commentary for the seismic rehabilitation of buildings. FEMA 357. Available at: https://www.wbdg.org/ccb/DHS/ARCHIVES/fema357.pdf

Federal Emergency Management Agency (FEMA) (2000b) Pre-standard and commentary for the seismic rehabilitation of buildings. FEMA 356. Available at: https://law.resource.org/pub/us/code/bsc.ca.gov/sibr/gov.fema.fema356.pdf

Federal Emergency Management Agency (FEMA) (2003a) Primer for design of commercial buildings to mitigate terrorist attacks. FEMA 427. Available at: http://www.fema.gov/media-library-data/20130726-1455-20490-6114/fema427.pdf

Federal Emergency Management Agency (FEMA) (2003b) Reference manual to mitigate potential terrorist attacks against building. FEMA 426. Available at: http://www.fema.gov/media-library/assets/documents/2150

Guzas

Earls

(2011) Simulating blast effects on steel beam-column members: applications. Computers & Structures 89: 2149–2161.

10.

Henrych

(1979) The Dynamics of Explosion and Its Use, vol. 1. Amsterdam: Elsevier Scientific Publishing Company.

11.

Iranian National Building Code (2013) Part 21: passive defense. Tehran, Iran: Ministry of Road and Urban Development.

12.

Newmark

Hansen

(1961) Design of Blast Resistant Structures, Shock and Vibration Handbook, vol. 3. New York: McGraw-Hill.

13.

Ngo

Mendis

Gupta

. (2007) Blast loading and blast effects on structures - an overview. EJSE Special Issue: Loading on Structures 7: 76–91.

14.

Saedi Daryan

Ziaei

Sadrnejad

(2011) The behavior of top and seat bolted angle connections under blast loading. Journal of Constructional Steel Research 67: 1463–1474.

15.

Urgessa

Arciszewski

(2011) Blast response comparison of multiple steel frame connections. Finite Elements in Analysis and Design 47: 668–675.

16.

US Department of Defense (2008) Unified facilities criteria: structures to resist the effects of accidental explosions. UFC 3-340-02, 5 December. Washington, DC. Available at: https://www.wbdg.org/ccb/DOD/UFC/ufc_3_340_02.pdf