The main objective of this study is the numerical simulation of the behaviour and failure patterns of steel columns under blast loads using the dynamic finite element package ABAQUS/Explicit. A numerical model is suggested and validated against published experimental tests on fullscale wideflange steel columns subjected to dynamic blast loads under constant axial compressive force. Afterwards, the validated model is used to investigate the effect of important parameters on the behaviour and failure patterns of steel columns under blast pressure through an extensive parametric study. The parameters include the blast impulse, the blast energy, the blast load, the blast duration, the column boundary condition, the column slenderness ratio, and the blast direction. The conclusions extracted from this parametric study may be used to develop a thorough understanding of the behaviour and failure of steel columns subjected to blast load which, in turn, could lead to a more accurate practical design procedure. The study also presents derivations and validations of a proposed analytical approach to calculate the critical blast impulse at which a steel column losses its global stability. Comparison between the critical impulseaxial force curves obtained from the proposed equation and that extracted from numerical simulations indicates the validity and feasibility of the proposed equation.
Over the past few decades, many civil engineering structures have been subjected to explosions from terrorist attacks. The blast load and blast impulse generated from these explosions have caused failure to the structural members near to the detonation locations such as ground floor slabs, walls, and ground floor columns. Failure of such members can result in catastrophic consequences and progressive failure and collapse of the whole structure. Recent building standards and codes deal with such problems using approximate and conservative approaches. However, for accidental dynamic loads, a more accurate method needs to be developed and used in practical design.
For instance, Section
It is obvious that all the abovementioned methods neglect the dynamic characteristics of the blast load and its effects on the behaviour and failure of the structure (such as the blast duration, the blast impulse, the blast energy, the strain rate effect, etc). Moreover, for structural column under axial compressive load, the work generated by the axial load is not included in any of the above methods.
The need for more thorough understanding of the behaviour of civil engineering structures subjected to blast load has been well recognized by the engineering community, and a considerable amount of research has been published in this field of study. Within this research, the experimental study of Meknes and Opat [
Chen and Liew [
The effect of axial compression on the behaviour of structural steel columns under blast loads was also investigated by Shope [
Lee et al. [
Nassr et al. [
AlThairy [
The research aims to extend the abovementioned studies to gain a comprehensive understanding of steel column behaviour under dynamic blast. To achieve this aim, a numerical model for simulating the global and local behaviour and failure modes of steel columns subjected to blast load using the finite element package ABAQUS/Explicit will be presented and validated using the experimental tests of Nassr et al. [
This section presents a description and validation of the ABAQUS/Explicit model used for simulating the behaviour and failure of isolated steel columns under blast load. The validation is necessary to ensure the correct implementation of the simulation procedure so that the suggested model can be used to generate extensive numerical results through parametric studies for the development of a design method.
Nassr et al. [
Geometrical properties, loading conditions, and test results of the steel columns used in the validations [
Test symbol  Section  Blast direction 




Impulse ( 
Δ_{max} (mm) 

4C1  W150 × 24 

38  270000  4.283  2.1  0.003174  60.4 
5C1  W200 × 71 

27  640000  2.098  8.4  0.003144  32.8 
Numerical models used to simulate steel columns’ behaviour.
C3D8R element provided by ABAQUS [
Comparison of the permanent deflected shape of the steel column 4C1 between the experimental test of Nassr et al. [
To detect the possible local shear damage of the column, the progressive damage and failure model available in ABAQUS/Explicit were utilized in the present numerical model. According to this model, the onset of shear damage is characterized by the value equivalent to plastic strain at the initiation of shear damage
Failure parameters used in the present model.
Fracture strain  Maximum shear stress ratio  Maximum strain rate (sec^{−1}) 

0.15  1.8  16.7 
The suggested numerical model is mainly intended to simulate the behaviour of a steel column subjected to blast load with a considerable value of static axial compressive load. Hence, the model must be able to maintain a static axial load on the column while it is subjected to the blast event. This means that both the static and dynamic loads should be exerted simultaneously during the entire dynamic analysis duration. In ABAQUS/Explicit, only dynamic analysis is allowed. Therefore, the static axial load must be applied as a quasistatic load using the quasistatic analysis in ABAQUS/Explicit. To perform a quasistatic analysis in the present study, the load was applied as a timedependent variable using the SMOOTH AMPLITUDE suboption [
The blast load was generated in the experimental test by a direct real explosion using different explosive charges [
Comparison between the recorded [
The results obtained from numerical simulations were compared with the corresponding recorded experimental test results in terms of permanent deflection shape and normal strain history for the two test cases considered in the validation, namely, 4C1 and 5C1, as shown in Figures
Comparison of the permanent deflected shape of the steel column 5C1 between the experimental test of Nassr et al. [
Comparison of the strain time histories of the steel columns 4C1 (a) and 5C1 (b) between the experimental tests of Nassr et al. [
To investigate the sensitivity of the simulation results to the mesh size selected to model the steel columns, simulations were carried out using five different sizes of mesh used at zones where high stress concentrations were excepted to develop (i.e., at the column midspan and at the column ends) as shown in Figure
Figures
Finally, Figure
Numerical prediction of the damage initiation criterion along the tension flange and the web of steel columns 4C1 and 5C1 used in Nassr et al.’s tests [
The above validation results indicate that the present numerical model is capable of predicting the response and failure of steel columns under blast loads.
This section investigates the effects of important parameters on the behaviour and failure modes of axially and statically preloaded steel column subjected to blast load through an extensive parametric study. The conclusions extracted from this parametric study may be used to suggest assumptions that could enable simple and practical methods of analysis to be developed. These parameters have been identified to be blast impulse, blast energy, axial compressive load, column slenderness ratio, column boundary condition, and the blast direction.
The parametric study used the same steel columns’ sections selected in the validation exercises with same material properties. However, the columns’ lengths were increased to 3 m since this length is more common in practical application. The direction of blast pressure was to cause bending about both the major (
The parameters used in the parametric study.
Section  Axial load ratio  Boundary conditions  Blast direction  Slenderness ratio 

W150 
0.25, 0.5, 0.75,  Rolledpinned 


Rolledfixed 



W200 
0.25, 0.5, 0.75,  Rolledpinned 


Rolledfixed 


Numerical simulations were first carried out on a simply supported W150 × 24 section column subjected to increasing levels of the blast impulse to cause column failure under 50% of the column design axial static load. The direction of blast pressure was selected to cause bending about the column strong axis. Column failure was detected either by column global buckling which is identified by large deformation or by local damage and failure which is identified by the value of the damage initiation criterion. Figure
Midspan lateral displacement time histories of the steel column W150 × 24 subjected to different values of blast impulse.
Damage initiation criterion profile along the steel column W150 × 24 subjected to different values of the blast impulse: (a) at the middle of the tension flange; (b) at the middle of the web.
Now, numerical simulations were carried out using the same column but considering a constant level of the blast impulse with different combinations of blast pressure (
Midspan lateral displacement time histories of the steel column W150 × 24 subjected to constant values of blast impulses with different combinations of blast parameters.
The kinetic energy of the steel column imparted from the blast can be related to the total blast impulse as expressed by the equations in Table
Equations for the kinetic energy of the column induced by the blast [
Boundary condition  Kinetic energy  Equation no. 

Pinnedpinned column 

( 
Fixedfixed column 

( 
Fixedpinned column 

( 
KE = the kinetic energy;
Comparison of the kinetic energy time histories of steel column W150 × 24 subjected to different values of blast impulses under 50% of the design axial load: (a) without column failure; (b) with column failure.
In this section, the steel columns listed in Table
Midspan displacement time histories of steel column W150 × 24 with bending about the major
Midspan displacement time histories of the propped cantilever column W150 × 24 with bending about the minor
Midspan displacement time histories of steel column W200 × 71 with bending about the major
Damage initiation criterion profile of simply supported column W150 × 24 with bending about major
Damage initiation criterion profile of propped cantilever column W150 × 24 with bending about major
Damage initiation criterion profile of propped cantilever column W150 × 24 with bending about minor
Damage initiation criterion profile of simply supported column W200 × 71 with bending about major
Damage initiation criterion profile of propped cantilever column W200 × 71 with bending about major
(a) Deformation shape and damage initiation criterion distribution along the column length for the propped cantilever column W200 × 71 with bending about major
Figures
On the other hand, Figure
Figures
Deformation shape and plastic hinge locations of simply supported column W150 × 24 with bending about the major
Deformation shape and plastic hinge locations of propped cantilever column W150 × 24 with bending about the major
Deformation shape and plastic hinge locations of propped cantilever column W150 × 24 with bending about the minor
Deformation shape and plastic hinge locations of simply supported steel column W200 × 71 with bending about the major
According to AISC Specifications [
Dynamic stressplastic strain relationship of the steel at the locations of the plastic hinges. (a) Simply supported W150 × 24 with bending about the major
The parametric study conducted in this research has demonstrated that global instability is the major failure mode for steel columns under blast load and column global failure was mainly dependent on the value of blast impulse and/or blast energy imparted to the column. These two conclusions are crucial and will be used to suggest a simplified analytical method for this particular type of dynamic blast problem. The main goal of this analytical method is to obtain the column axial loadcritical blast impulse relationship. The critical blast impulse can be defined as the minimum impulse of the blast pressure that causes the column to lose its global bucking under axial compressive load. The suggested method can be implemented in the design of steel columns that are vulnerable to blast pressure since it can provide a reasonable prediction of the axial load and at the onset of column global failure.
The suggested analytical approach is based on the energy conservation principle with a quasistatic simplification of the column behaviour. The energy balance principle is more appropriate to handle the dynamic blast problem when the time period of the blast is very short compared to the natural period of the steel column [
The general energy conservation equation for the structural system under dynamic blast pressure can be described as
For the critical situation, the column is at rest; therefore,
Hence, for a column subjected to blast pressure, (
Total blast energy imparted to the column can be expressed by equations listed in Table
AlThairy and Wang [
Column deformation shape used in analytical model. (a) Elastic phase. (b) Plastic phase.
Based on the above assumptions, the strain energy (
The work done by the axial load can be expressed by [
Substituting the value of
Now, substituting the strain energy absorbed by the column (
The critical blast impulse
Table
Equations for the critical blast impulse.
Boundary condition  Critical blast impulse 

Pinnedpinned column 

Fixedfixed column 

Fixedpinned column 

The suggested analytical method has been validated by comparing the column axial forcecritical blast impulse curves calculated by the analytical method with that predicted from numerical simulations. The two steel columns used in the parametric study of this research were used in the validation examples with same loading ratios, geometrical parameters, and material properties. However, the steel stressstrain relationship was simulated to be elastic perfectly plastic with a modulus of elasticity 206000 N/mm^{2} and a yield strength 440 N/mm^{2} to match the assumption used in the derivations.
Figures
Comparison between analytical method and ABAQUS predictions of critical impulseaxial force curve for steel column section W150 × 24 with simply supported (S.S.) and propped cantilever (Prop.) boundary conditions and with blast pressure to cause bending about major and minor axes of the column.
Comparison between analytical method and ABAQUS predictions of critical impulseaxial force curve for simply supported steel column section W200 × 71 with blast pressure to cause bending about major axis of the column.
This study has presented numerical simulations of the behaviour and failure of wideflange steel columns subjected to dynamic blast loads. First, a numerical model has been put forward using the dynamic finite element package ABAQUS/Explicit. The suggested numerical model has been validated against the experimental tests conducted by Nassr et al. [
Global plastic instability is the main failure pattern of steel columns under dynamic blast load with a considerable value of static axial compressive load (i.e., >0.25 of the design axial load).
When the applied static axial load is low (i.e., ≤0.25 of the design axial load), shear failure can also occur at the column fixed supports.
The critical blast impulse and the blastinduced kinetic energy can be used to define the column failure conditions and set an upper limit of the column strength. For the same value of the critical blast impulse, different combinations of blast pressure and time duration had minor effects on column failure.
The plastic resistance of the steel columns increases when the columns are subjected to dynamic blast loads due to the strain rate sensitivity effect. However, local buckling of the compression flange may occur before the section reaches the full dynamic plastic resistance in the plastic mechanism collapse mode. Should the strain rate effect have to be considered in an analytical method, the reduction in dynamic plastic moment capacity of the column at failure must be considered.
The study has also presented a simplified method to predict the critical blast impulse at which a steel column losses its global stability when subjected to transverse blast pressure. The suggested method utilizes the energy conservation principle with quasistatic simplification of the column response. The column is assumed to fail under global buckling following the plastic hinge mechanism. Comparison between the critical impulseaxial force curves obtained from the proposed method and that extracted from numerical simulations indicates the validity and accuracy of the presented method.
The author declares that there are no conflicts of interest.