Study on the Anti-Progressive Collapse Behavior of Steel Frame Structures under Close-Range Blast Loading

Abstract

The steel frame structure plays an important role in strategic deployments and is widely used in heavy machinery, metallurgy, military, and other important industries. To study the impact of explosive loads on the anti-progressive collapse performance of steel structures, this paper proposes to establish the vulnerability characteristics of steel frame structures and provides a method for calculating vulnerability characterization indicators. A finite element model is used to analyze the dynamic response of steel frame structures under the action of close-range explosive loads, and factors influencing the anti-progressive collapse of steel frame structures are proposed, including the number of stories and diagonal bracing. A comparison is made between the various column types of steel structures under explosive loads, such as corner columns, long-edge middle columns, short-edge middle columns, inner columns, also in various coupling conditions. The results show that the progressive collapse of steel frame structures is greatly influenced by the position of the explosion and less affected by the amount of explosive material. The simultaneous failure of corner columns and long-edge middle columns is more likely to cause overall structural failure. The addition of diagonal bracing significantly improves the anti-progressive collapse ability and prevents the lateral displacement of steel frame structures; increasing the number of stories provides more alternative load transfer paths for steel frame structures, thereby preventing their collapse.

1. Introduction

During their service life, building structures may be subject to various extreme disasters, such as earthquakes, explosions, impacts, and fires, which may cause critical components of the structure to fail and initiate a series of chain reactions that lead to the failure of adjacent components and ultimately result in the partial or complete collapse of the structure [1]. Terrorist bomb attacks, due to their characteristics of short-lived, high-peak blast loading, random explosion locations, and complex structural damage patterns have become important causes of building collapse. Based on the British specifications for building construction, the General Services Administration (GSA) [2] published its specifications. Recently, referring to recent research results on structural continuous collapse [3,4,5,6], a method for studying the anti-collapse performance of building structures under blast loads was proposed [7].

J.T. Baylot et al. [8] conducted blast load analysis on a 1:4 scale RC frame structure. Gao et al. [9] studied the dynamic response and failure modes of a three-story RC frame structure under different explosion conditions. Jiang et al. [10] analyzed the anti-collapse performance of a single-story planar reinforced concrete frame structure and a single-story spatial concrete frame structure using pseudo-static test methods. Francioli M. [11] established a finite element model for an RC frame structure, conducted nonlinear time-history analysis on a large-span structure, and compared the robustness curves under explosion-only and coupled earthquake–explosion cases. Alok Dua [12] developed a finite element model and proposed an empirical formula to predict the critical failure limit considering the influence of the reinforcement ratio. This study provides important information on the response of reinforced concrete structures to blast loading. Sergey Savin [13] investigated the numerical simulation of the structural response and damage modes of slender-column reinforced concrete frames under the scenario of sudden removal of the corner columns. Suxia Kou [14] addressed the dynamic response of welded steel frame joints when subjected to blast loading, the main influencing factors, and the numerical analysis of three types of joint damage modes. Ni Jinfeng [15] simulated and analyzed the dynamic response of reticulated shell structures under external blast loads using the CONWEP method. Through extensive parameter analysis involving changes in parameters such as explosive equivalent, explosive orientation, vertical position variation, structural form, and material properties, the study investigated the statistical patterns of typical structural responses with varying parameters.

At present, scholars’ studies on explosion loading are mostly focused on the dynamic response of RC frame structures [8,9,10], and there is a lack of research on the performance of steel frame structures in the presence of vertical continuous collapse and on the factors affecting the resistance of steel structures to continuous collapse. Therefore, in this paper, we study the dynamic response of steel frame structures by adding support arrangements and compare the effects of different equivalents and different explosion positions on the performance of steel frame structures under continuous vertical collapse.

2. Vulnerability Characteristics of Steel Structures under Blast Loading

2.1. Determination of the Vulnerability Characteristics

The vulnerability analysis of steel frame structures under explosion load [16] can be carried out using the energy method, the basic idea of which is to evaluate the seismic capacity of a structure by using the energy of the deformation of the structure under an external force.

Zhang Leming [17] obtained the key path of energy flow in a frame structure based on graph theory, compared the relative influence of the removal of different components on the overall strain energy of the structure, and defined the importance of the components:

$$Q_N=\frac{U_n}{U}$$

(1)

“$U_n$” represents the strain energy of the structure after component damage, and “$U$” represents the stored strain energy of the intact structure. The vulnerability index of a steel structure under the action of explosive shock waves is defined as the effective damage rate of the structure. It is represented by the ratios of displacement, bearing capacity, stress, and strain for a damaged unit compared to those for the intact structure under the loading of the explosive shock wave. The ratio of strain energy in the damaged structure and that in the intact structure are represented by $Q_1$ and $Q_2$. Both elastic strain energy and total strain energy can accurately measure the importance of a component under normal loading, reflecting its contribution to load transfer. However, the evaluation method based on energy changes may not provide precise data and can result in conservative assessments of the structure.

This paper used an integral expression to improve the accuracy of structural analysis. The vulnerability of steel frame structures refers to the extent to which they are susceptible to damage or failure when subjected to various adverse conditions such as extreme loads, environmental factors, and unforeseen events. It evaluates the likelihood of structures being damaged or experiencing structural damage when exposed to external forces or hazards, as well as the performance and stability of the structures when they undergo damage or impairment. Steel structures can be susceptible to fatigue damage under the action of impact loads or vibratory loads. The vulnerability integral expression for steel structures, internal spaces, and their substructures is as follows:

$$Q_N=\left\{\begin{array}{cc}0& ∆q_n\le ∆q_{n0}\hfill \\ {\displaystyle \int }\frac{∆q_{n1}-∆q_n}{∆q_{n1}-∆q_{n0}}& ∆q_{n0}<∆q_n<∆q_{n1}\hfill \\ 1& ∆q_{n1}\le ∆q_n\hfill \end{array}\right.$$

(2)

$∆q_n$ is the shock wave overpressure, in MPa; $∆q_{n0}$ is the maximum overpressure for steel structures that cannot be 100% destroyed; $∆q_{n1}$ is the minimum overpressure for steel structures that can be 100% damaged; $Q_N$ is the probability of destruction.

When conducting vulnerability analysis, the size and location of the load need to be determined first. Then, based on the properties of the materials and the geometric shape of the structure, parameters such as stress, strain, and deformation under the action of the load are calculated [18]. Using the principle of energy, the load on the structure is converted into internal energy, and parameters such as plastic deformation energy and residual strength of the structure are calculated. Finally, based on the vulnerability indicators of the structure (such as displacement, strain, plastic deformation energy, etc.), the blast resistance of the structure is evaluated, and corresponding improvement measures are proposed to enhance the safety of the structure.

2.2. Determination of the Peak Overpressure of the Air Blast Wave

When subjected to an air blast wave, a steel frame structure may experience the effects of the peak overpressure of the air blast wave. The air blast wave is a pressure wave generated by the flow of gas caused by sudden events such as explosions or storms, and its power can have a serious impact on building structures. When considering the blast resistance of steel frame structures, it is necessary to pay attention to the peak overpressure of the air blast wave to evaluate the structural load capacity and stability [19]. Based on FEMA’s [20] guideline on the impact of shock wave overpressure leading to global collapse, it is considered that the collapse range is half the height of the building.

The determination of the air blast wave pressure generated by an explosion primarily depends on the total energy released during the explosion and the distance of the explosion source from the target. Therefore, it is possible to convert various types of explosives into standard TNT equivalents (related to air density and atmospheric pressure P₀) and use a unified standard to measure the energy generated by different explosive materials after detonation. This allows for the description of the blast wave pressure produced by different types of explosives in an infinite air medium using a unified equation. The expression of the peak overpressure of the air blast wave is as follows:

$$\Delta q_n=0.084\frac{C^{1/3}}{r}+0.27(\frac{C^{1/3}}{r}{)}^2+0.7(\frac{C^{1/3}}{r}{)}^3$$

(3)

$\Delta q_n$ is the peak overpressure of the shock wave generated by an explosion in air, measured in MPa; $C$ represents the mass of TNT equivalents, measured in kilograms; and $r$ denotes the distance between the explosion source and the target, measured in meters.

When dealing with the peak overpressure of air blast waves, the design and evaluation of steel frame structures involve critical considerations. These include the calculation of overpressure loads using appropriate mathematical models and engineering methods to determine specific overpressure values, taking into account various factors such as distance from the explosion source, explosion energy, and environmental conditions. Furthermore, structural response analysis is essential, as steel frame structures undergo dynamic responses when subjected to the effects of air blast waves, including structural vibration and deformation [21].

3. Reference Model and Influencing Factors

3.1. Reference Model

According to the GB50017-2017 [22] “Code for Design of Steel Structures”, the analysis model in this paper is a two-story steel frame structure with a lateral span of 3.9 m with a column spacing of 3.9 m, a longitudinal span of 6 m with a column spacing of 6 m, and a floor height of 3.9 m. The components are all made of Q345 steel. The rectangular column section size is 0.4 m × 0.4 m, and the I-beam section size is 0.15 m × 0.4 m × 0.01 m × 0.01 m (as shown in Figure 1). Common steel materials are isotropic, and their ductility ratio is the ratio of the maximum deflection to the yield deflection at the reference point. In this paper, the ductility ratio limit was 20 for beams and tension columns and 1 for compression columns. The effects of dead loads were calculated to be 4.5 kN/${\mathrm{m}}^2$, and those of live loads were calculated to be 2.5 kN/${\mathrm{m}}^2$ without considering wind and snow loads. These loads were converted into line loads arranged on the beam components at each level. The PKPM software was used to calculate the internal forces and reinforcement of the steel frame structure, and the data were imported into the model after meeting the code requirements. Hillerborg proposed the fracture energy assumption and suggested a fracture strain of 0.6 for flexible damage and the fracture energy of 0.1 kN/m² for damage evolution. The steel structure material parameters are shown in

Table 1. Values of the steel material parameters.

Density (kg·m−3)	Modulus of Elasticity (GPa)	Poisson’s Ratio	Yield Strength (MPa)	Maximum Strength (MPa)
7850	210	0.3	345	490

, and its intrinsic model is shown in Figure 2.

Based on explosion theory [23] and dynamic similitude relationships [24], the explosion load was set at TNT 80 kg under conditions that satisfied both the shock wave overpressure and the specific impulse similarity. The explosion reference point was chosen at a height of 1.5 m above the ground, with a horizontal distance of 0.2 m from column A1, and the explosion face of the structure was the side facing the steel structure source of the explosion, $q_n$ is the post-blast impact load(as shown in Figure 3), without considering the reflection of the explosive shockwave. A two-story steel structure was taken as the research object, and the COWNEP loading was used to simulate the explosive load. Two analysis stages were set up using an explicit dynamic analysis method to handle the structural response. Firstly, a static analysis was executed to simulate the initial static state of the structure. Secondly, the target columns were quickly modeled as failing, and the explicit dynamic method was used to calculate the dynamic response of the rest of the structure after demolition. The beam–column joints were handled by selecting the tie method to complete the definition of the constraints between the beams and columns, the bottom of the columns were constrained to translate and rotate in all three directions, and the approximate global size in the layout seed was set at 0.05. The finite element model of the structure is shown in Figure 4, and the structure plan is depicted in Figure 5.

3.2. Factors Influencing a Steel Structure’s Resistance to Continuous Collapse

This paper investigates the dynamic response of steel frame structures under explosive loading and measures to improve the resistance of steel structures to progressive collapse. Based on theoretical knowledge, adding storeys and diagonal bracing can increase the load reserve paths of steel frame structures [25], enhancing the steel structure’s resistance to progressive collapse. Considering the reaction mechanism of steel structures under explosive loading with an equivalent TNT of 80 kg, the maximum vertical displacement of the steel structure is 33.28 mm.

(1)

Height

This study selected a four-story steel frame structure for comparative analysis with the original model to investigate the factors influencing the stability of steel structures based on the number of stories, as shown in Figure 6. The displacement–time curve of the corner column A1 after the explosion is shown in Figure 7.

In the displacement–time curves in Figure 7, it can be seen that with the equivalent TNT of 80 kg, the structure did not collapse, the maximum vertical displacement of the column top was 1.82 mm, and increasing the number of floors could significantly reduce the vertical displacement of the column top. By increasing the number of storeys, the load backup path of the structure increased, the gravity distribution of internal forces in the remaining structure was better achieved, and the stability of the structure was improved by 94.53% compared with that of the original structural model. The maximum vertical displacement of the top of the column was 1.82 mm, not reaching one-fifth of the height of the building structure, and the whole structure did not undergo continuous collapse.

(2)

Adding support

For the establishment of a diagonally braced steel frame structure model, the structure was designed using the method of pulling structural elements, each spanning between diagonal supports, employing an I-beam for the design of the tie with a length of 7.2 m. We studied how the addition of the support influenced the factors affecting the resistance of the steel structure to the successive collapse of the pairs of columns, as shown in Figure 8. The A1 corner column displacement–time curve after the explosion is shown in Figure 9.

Bracing is a method used to enhance the stability of structures, which can reduce the lateral displacement of a structure and increase its bearing capacity. After the steel structure of this model was supported, it can be seen from the displacement–time curve that the structure did not collapse, and the maximum vertical displacement of the column top was 1.45 mm, which increased the structural stability by 95.64% compared with that of the original structure model; in addition, the spatial acceleration was reduced by 92.39% compared to that of the original model. The vertical displacement of the top of the column was 1.45 mm, not reaching one-fifth of the height of the building structure, and the whole structure did not undergo continuous collapse.

The analysis results indicated (as shown in

Table 2. Influencing factors of steel frame structures.

Target Model	Equivalent TNT (kg)	Vertical Displacement of Column Top (mm)	Spatial Acceleration (m/s2)	Total Energy (J)
Original model	80	33.28	−11,218	33,366.3
Addition of floors model		1.82	−1314.34	135.54
Addition of diagonal support model		1.45	−854.2	131.5

), both increasing the number of stories or adding supports could significantly improve the stability of the structure, greatly reducing the vertical displacement at the column top, the total energy, and the spatial acceleration, achieving the distribution of internal forces in the remaining structure under gravity, and enhancing the structure’s resistance to progressive collapse.

3.3. Continuous Collapse of Different Target Columns under Explosion Load

3.3.1. Column Explosion Condition

(1)

Corner column explosion condition

When the target column was the corner column A1, as shown in Figure 10, models were established for TNT equivalents of 60 kg, 80 kg, and 100 kg to compare the dynamic responses and damage rates of the corner column under explosive loading at these three TNT equivalent levels.

In analyzing the dynamic response of the structure during progressive collapse, the magnitude of the structure’s dynamic response can be reflected by the vertical displacement of the target column under the explosive load, its change over time, and the spatial acceleration of the target column in collapse conditions. It can be observed from the displacement–time curve of the corner column in Figure 11 that the vertical displacement of the corner column varied with different TNT equivalents, with a larger equivalent resulting in a greater vertical displacement. When the TNT equivalent increased from 60 kg to 80 kg, the vertical displacement of the column top increased by 0.33%, and when the TNT equivalent increased from 80 kg to 100 kg, vertical displacement of the column top increased by 0.9%. According to

Table 3. Different target columns under different TNT equivalents.

Target Column	Equivalent TNT (kg)	Vertical Displacement of Column Top (mm)	Spatial Acceleration (m/s2)
Corner column	60	33.17	−3693.8
	80	33.28	−11218
	100	33.58	−15,285.1
Long middle column	60	19.31	−769.1
	80	22.14	−3103.21
	100	22.18	−5866.13
Short middle column	60	0.93	444.39
	80	1.47	582.11
	100	2.98	959.92
Inner column	60	0.33	921.52
	80	0.67	1146.07
	100	1.73	1329.371

, the spatial acceleration had a significant impact on the progressive collapse of the structure. An increase from 60 kg to 80 kg in TNT equivalent resulted in a 203.7% increase in spatial acceleration, and an increase from 80 kg to 100 kg, caused a 36.26% increase, indicating a more pronounced collapse of the steel frame structure. Based on an energy-based analysis method for the vulnerability assessment of steel structures [18], as the TNT equivalent increased from 60 kg to 80 kg, the strain energy of the damaged structure increased by 126.8%. It is evident that a higher TNT equivalent led to more significant structural damage.

Under the action of gravity, after the initial corner column failure in a steel frame structure, the load-bearing capacity that was originally dependent on the corner and side columns needs to be redistributed. Specifically, the beams on the second floor began to collectively bear the vertical loads that were previously provided by the corner column A1 and the side columns A2 and B1. This redistribution of internal forces resulted in bending moments being generated at the beam ends at the column nodes A3 and C1. Over time, the internal force redistribution caused by gravity prevents the cantilevered beams from effectively resisting the vertical loads from the upper part of the structure, leading to tensile stress cracking at the beam end nodes. Ultimately, this results in the formation of plastic hinges, indicating that the nodes have lost their original bending capacity, which can lead to further structural damage. In summary, after the structure is damaged, the internal force redistribution caused by gravity makes some beams bear more load, but these beams ultimately cannot withstand the increased load, causing node cracking.

When a detonation occurs in the bottom corner of a structure with different quantities of TNT explosives, the initial failure is primarily caused by the accumulation of shock waves and the lack of external constraints. The framework beams mainly fail due to bending along the weak axis direction and shear failure at the beam ends, while the framework columns fail due to detachment from the nodes. Once the corner columns and adjacent edge columns fail, the upper double cantilever beams span across two openings. Due to the lack of vertical and horizontal constraints, an effective tension tie state cannot be achieved, leading to the inability to obtain an effective catenary mechanism. In this case, the upper structure is highly likely to collapse continuously. The explosion in the bottom corner of the structure causes the premature failure of critical support points, resulting in the instability of the entire structure and the potential for continuous collapse. In this study, due to the different TNT equivalents, the vertical displacements of the corner column tops were 33.17 mm, 33.28 mm, and 33.58 mm, all of which did not reach one-fifth of the height of the building structure, and the whole structure did not undergo continuous collapse.

(2)

Long middle column explosion condition

Considering as the target column the A2 long middle column, we established models for TNT equivalents of 60 kg, 80 kg, and 100 kg, comparing the column’s displacement under explosion load and the damage rates.

As shown in Figure 12, the vertical displacement of the top of the long center column with different equivalents of TNT was different, and the larger the equivalents were, the larger the vertical displacement of the long center column was; in addition, the increase in the equivalent TNT from 60 kg to 80 kg increased the vertical displacement of the top of the column by 14.66%, and the increase in the equivalent TNT from 80 kg to 100 kg increased the vertical displacement of the top of the column by 0.18%. In Table 3, the effect of spatial acceleration on the continuous-collapse resistance of the structure can be seen; when the TNT equivalent of 60 kg was increased to 80 kg, the spatial acceleration increased by 303.49%, and when the TNT equivalent of 80 kg was increased to 100 kg, the spatial acceleration increased by 89.03%. The experimental data showed that the larger the TNT equivalent, the larger the spatial acceleration, the larger the vertical displacement, and the more obvious the degree of damage to the steel structure. The stiffness of the remaining steel structure was greatly reduced, the bearing capacity decreased sharply, and local structural damage occurred. The vertical displacements of the top of the collapsed columns were 19.31 mm, 22.14 mm, and 22.18 mm, not exceeding one-fifth of the height of the building structure, and the structure did not collapse.

(3)

Short middle column explosion condition

Considering as the target column the B1 short middle column, we established models for TNT equivalents of 60 kg, 80 kg, and 100 kg, comparing the column’s displacement under explosion load.

According to the results obtained for the short central column top displacement in time, shown in Figure 13, there were differences in the vertical displacement of the short central column caused by different equivalents of TNT. When the TNT equivalent increased, the vertical displacement of the short central column also increased. Taking the equivalent TNT of 60 kg as a base, the vertical displacement of the column top increased by 6.04% when the TNT equivalent was increased to 80 kg, and the vertical displacement of the column top increased by 15.96% when the TNT equivalent was further increased to 100 kg. In addition, from the data in Table 3, it can be seen that the spatial acceleration played an important role in the continuous collapse resistance of the structure. When increasing the equivalent TNT from 60 kg to 80 kg, the spatial acceleration increased by 30.99%, while when increasing the equivalent TNT from 80 kg to 100 kg, the spatial acceleration increased by 64.9%.

The combined data led to the conclusion that the greater the TNT equivalent, the greater the spatial acceleration, which in turn led to an increase in vertical displacement. This indicated that the degree of damage to the steel structure was more significant, the stiffness of the remaining steel structure was substantially reduced, and the load-carrying capacity was drastically reduced but did not reach one-fifth of the height of the building, and no localized collapse damage to the structure occurred.

(4)

Inner column explosion condition

Considering as the target column the B2 inner column, we established models for TNT equivalents of 60 kg, 80 kg, and 100 kg, comparing the column’s displacement under explosion load.

The time –displacement curve for the top of the inner column is shown in Figure 14, which shows that the vertical displacement of the inner column increased when the TNT equivalent increased. When the benchmark TNT equivalent of 60 kg was increased to 80 kg, the vertical displacement of the inner column increased by 4.08%; when the TNT equivalent was further increased to 100 kg, the vertical displacement of the inner column increased by 12.22%. From Table 3, it can be seen that the spatial acceleration also affected the continuous collapse resistance of the structure. When increasing the TNT equivalent from 60 kg to 80 kg, the spatial acceleration increased by 24.37%, while, when increasing the TNT equivalent from 80 kg to 100 kg, the spatial acceleration increased by 16%. The experimental data showed that with the increase in the TNT equivalent, the spatial acceleration and the vertical displacement increased, and the steel structure underwent local damage; however, depending on the explosion load, the vertical displacement of the top of the inner column was 8.33 mm, 8.67 mm, 9.73 mm, i.e., less than one-fifth of the height of the structure of the building, and the structure as a whole did not undergo local collapse.

In summary, explosive loads led to initial damage to the steel structure, but the progressive collapse of the steel frame structure was primarily caused by the internal force redistribution and the displacement increase due to the self-weight loads. Comparing the four scenarios of corner column failure, long middle column failure, short middle column failure, and inner column failure under explosive loading, it is evident that the change in TNT equivalents had a relatively minor impact on the degree of structural damage compared to the explosion locations in the four scenarios. When the TNT equivalent was the same, the vertical displacement at the top of the corner column was the largest, i.e., three times greater than that of the inner column, the corner column fractured, and the side beam without support bent downward and deformed. The long side beam and the short side beam of the corner column are equivalent to a cantilever beam; the internal force is borne by the cantilever beam, and the vertical deflection of the frame beam increases. The beam mechanism or catenary mechanism can be used to balance the vertical load, so that the internal force of the beam increases, resulting in a large vertical displacement, and bending and torsional damage of the longitudinal and horizontal frame beams around the failure column along the weak axis direction occurs in different degrees, resulting in compressive stress in the beam axis direction. The axial compressive stress of the bottom side beam increases as the number of layers increases, and the axial compressive stress of the beam decreases rapidly with the increase in the number of layers. On the other hand, the vertical displacement of the top of the inner column is the smallest, and a small deformation occurs. The spare load transfer path of the remaining structure is good, the external load can be re-balanced, and the structure does not collapse continuously.

3.3.2. Explosion Targeting Coupled Columns

We considered an explosion load at multiple target columns and studied the dynamic response and failure mode of the models with a TNT equivalent of 80 kg (as shown in Figure 15), analyzing the collapse mechanism in the examined conditions.

We considered as the target columns the corner column A1, the corner column + the short column (A1 + B1), and the corner column + the long middle column (A1 + A2). When the explosion occurred at the corner column and long middle column at the same time, the column top vertical displacement was the largest (as shown in Figure 16); the corner column top vertical displacement was lower by 62.44%. Regarding the effect of spatial acceleration on the continuous-collapse resistance of the structure, as shown in

Table 4. Different target columns with different TNT equivalents.

Target Column	Equivalent TNT (kg)	Vertical Displacement of Column Top (mm)	Spatial Acceleration (m/s2)
Corner column	80	33.28	−11,218
Corner column + Short middle column		35.28	−12,149.7
Corner column + Long middle column		54.06	−15,450.54

, with the equivalent of 80 kg, the spatial acceleration increased by 37.73% when the explosion targeted the corner column and the long middle column at the same time compared to that measured when the explosion targeted the corner column only; therefore, the collapse of the steel structure was faster. From the structural dynamic response analysis, the angle column and the long middle column failed simultaneously under the explosion load, and the vertical displacement of the top of the column was the largest. The steel reinforcement yielded and fractured under the blast load, its transmission path was reduced, and the structural bearing capacity was reduced. The damage degree of the long middle column was larger than that of the short column, mainly because its span was larger; in fact, the larger the vertical displacement of the column top, the more unstable it is under the action of dynamic loading. Reducing the span can improve the overall stability of a steel structure. The vertical displacements of the column tops were 33.28 mm, 35.28 mm, and 54.06 mm, not exceeding one-fifth of the structural height of the building, and the structure as a whole did not collapse locally.

3.3.3. Results and Discussion

In the four conditions of damage to the corner column only, the long center column, the short center column damage, and the inner column, we examined the effects of TNT equivalent change and explosion location on the degree of structural damage. If the TNT equivalent was the same, the maximum vertical displacement was measured for the top of the corner column, which was three times the vertical displacement of the top of the inner column, and the maximum spatial acceleration was measured at the top of the corner column, which was nine times that measured for the inner column. With a TNT equivalent of 80 kg, the vertical downward displacement of the top of a single target column was smaller than the vertical displacement of the top of the column coupled with another target columns, which indicated that when multiple columns are targeted, they fail at the same time, and the steel structure damage is more destructive. In the comparison of the corner column + the short middle column (A1 + B1) and the corner column + the long middle column (A1 + A2), the vertical displacement of the column top during the simultaneous failure of the corner column and the short middle column under the explosion load was smaller, which indicated that there was a significant improvement in the performance of the small span ratio against the successive collapses.

4. Conclusions

This paper conducted a nonlinear dynamic analysis of a steel structure under explosion load, analyzed the stability of the corner column, long side column, short side column, inner column and conditions in which two target columns were simultaneously subjected to the explosion load, and compared and analyzed the displacement time–history curve indicating the failure point and the acceleration under six kinds of working conditions. The conclusions are as follows:

• Adding floors and diagonal bracing improved the resistance of the steel-framed structure to continuous collapse. The higher the number of floors added, the more alternate load transfer paths there were in the structure, which was conducive to the improvement of the structure’s load-carrying capacity and favorable to the stability of the structure. However, if the number of storeys is too high, the magnitude of displacement reduction at the top of the corner columns will be reduced, and the bearing capacity of the steel frame structure would be relatively weakened. Adding diagonal bracing could greatly reduce the vertical displacement of the top of the failed column, reducing the lateral displacement of the structure, increasing the load-carrying capacity of the structure, and also significantly improving the performance of the structure against continuous collapse.
• Vertical displacements at the top of columns and spatial accelerations were positively correlated with the vulnerability of the steel frame structure.
• The change in TNT equivalent had a small effect on the degree of structural damage compared to the location of the blast action.
• If the explosive load was instantaneous and had a large impact, the steel frame structure was destroyed in 0.03 s, and the vertical displacement of the top of the column stabilized.
• Degree of structural damage of single-target columns: corner column > middle long middle column > short middle column> inner column. The damage is related to the span, and the importance of the corner column in the structure is higher than that of the other target columns, which are more sensitive to the stability of the steel frame structure. Therefore, considering the influence of singl columns on a steel frame structure under explosion load, the corner columns should be strengthened.
• Degree of structural damage when multiple target columns were coupled: corner column and long middle column > corner column and short middle column > corner column. However, due to the high cost of the structure blast resistance test and the difficulty of data collection, it was not possible to experimentally study the resistance of steel frames to continuous collapse, and it is hoped that in the future, some scholars will be able to study the resistance of steel frames to continuous collapse experimentally.