Finite element modelling of rectangular concrete-filled steel tube stub columns incorporating high strength and ultra-high strength materials under concentric axial compression

Tóm tắt Finite element modelling of rectangular concrete-filled steel tube stub columns incorporating high strength and ultra-high strength materials under concentric axial compression: ... the steel tube [21] by using the *Imperfection keyword in Abaqus. The shape of the local imperfection is assumed to be the first buckling mode shape, which is obtained by conducting an eigenvalue buckling analysis. Illustrations for the initial imperfection of steel tubes are presented in F...1 (fully damage). In this study, the CFST columns are subjected to monotonic axial compressive load only, therefore the damage parameters of concrete are not considered and only plasticity response is investigated. The damage parameters should indeed be considered to carefully investigate the res...1914.53 0.98 Yu et al. [11] S30-2 52.63 0.29 29.19 0.24 1220 1297.35 0.94 Aslani et al. [42] HSSC7 36.00 1.56 31.62 0.58 3882 3955.25 0.98 Khan et al. [15] CB20-SH(B) 22.12 1.59 36.62 0.37 2632 2684.51 0.98 Xiong et al. [13] S4 18.75 1.25 64.56 0.39 7276 7243.28 1.00 Xiong et al. [13] S9 12.50 ...

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han et al. [15] CB20-SH(B) 22.12 1.59 36.62 0.37 2632 2684.51 0.98
Xiong et al. [13] S4 18.75 1.25 64.56 0.39 7276 7243.28 1.00
Xiong et al. [13] S9 12.50 2.00 44.59 0.27 8730 8693.49 1.00
Yan et al. [43] S8-7-120 14.71 1.76 57.22 0.46 2368.9 2482.66 0.95
Yan et al. [43] S9-7-140 14.71 1.55 59.57 0.42 2492.1 2595.64 0.96
Nguyen et al. [19] C35-150 37.00 0.57 87.36 0.58 2437 2465.57 0.99
Nguyen et al. [19] C45-150 47.00 0.44 75.42 0.50 3131 3829.56 0.82
Nguyen et al. [19] C40-130 42.00 0.57 82.16 0.63 2739 2885.93 0.95
Varma [44] SC-32-80 34.27 0.65 96.85 0.88 14 116 15 318.6 0.92
Varma [44] SC-48-80 50.00 0.51 88.27 0.80 12 307 14 076.4 0.87
Xiong et al. [13] S12 12.00 1.30 73.08 0.46 5911 5819.85 1.02
Chen et al. [17] SS2-3 26.49 0.40 91.90 0.70 1676 1681.41 1.00
Chen et al. [17] SS3-3 13.20 1.11 87.37 0.67 2051 2056.53 1.00
Ibanez et al. [45] S125×125×4_90 31.25 0.51 54.50 0.58 1882.5 1961.59 0.96
Cai et al. [20] 80×80×4-C120-B 20.19 2.06 64.51 0.56 1898 1853.81 1.02
Cai et al. [20] 120×120×4-C80-B 31.15 1.64 66.20 0.77 2853 2920.5 0.98
Cai et al. [20] 100×50×4-C80-A 19.87 2.43 70.14 0.82 1211 1183.1 1.02
Cai et al. [20] 160×160×4-C120-A 40.00 0.59 57.82 0.50 4062 4272.42 0.95
µ = 0.97
CoV = 0.05
Journal of Science and Technology in Civil Engineering NUCE 2021 ISSN 1859-2996 
12 
the confining stress on the concrete core is also investigated. Herein, the maximum 
contact pressures (CPRSS variables) in the corner regions of the columns are reported to 
represent the confining pressure and these values are obtained when the column reaches 
its ultimate strength. This technique is employed because the concrete core is passively 
confined by the steel jacket and the significant lateral deformation of the steel tubes are 
normally occurs in the post-peak stage. In general, it is seen in Table 2 that the ratio of 
contact pressure to the compressive strength of concrete (σcont/fc’) is greater than 1/5 for 
all cases. 
To further verify th accuracy of the proposed simulation model, the load-
shortening curves obtained from FEM and experimental results are compared in Figure 7 
and Figure 8. In general, the predicted response obtained from FEM models is in 
reasonable agreement with experimental results, especially in terms of initial stiffness, 
ultimate strength, and the trend of softening branches. In Figure 7, the influence of initial 
imperfection and residual stress on the simulation results are illustrated. It can be seen 
that the residual stress has significant influence on the simulation results, while the 
inclusion of initial imperfection slightly affects the predicted ultimate strength. 
Therefore, the consideration of those effects is essential and should be accounted for in 
the simulation models to h ve a reasonable prediction. Additionally, it is seen that the 
simulation result obtained from the current model agrees well with one presented in Thai 
et al. [21], however, a better prediction for post-peak behavior is obtained with the 
proposed model in this study. 
Figure 6. Comparison between predicted ultimate strength and experimental results 
As illustrated in Figure 8, the load-deformation curves of CFST columns can be 
divided into two stages. In the first stage, the compressive load is linearly proportional to 
the axial deformation up until the limit point, where the column reaches its ultimate 
strength. In the second stage, the strength of the columns drops with different trends 
Figure 6. Comparison between predicted ultimate
strength and experimental results
Journal of Science and T chnology in Civil Engineering NUCE 2021 ISSN 1859-2996 
14 
Figure 7. Influences of imperfection and residual stress on simulation results 
Figure 7. Influences of imperfection and residual
stress on simulation results
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Thai, S., et al. / Journal of Science and Technology in Civil Engineering
To further verify the accuracy of the proposed simulation model, the load-shortening curves ob-
tained from FEM and experimental results are compared in Figs. 7 and 8. In general, the predicted
response obtained from FEMmodels is in reasonable agreement with experimental results, especially
in terms of initial stiffness, ultimate strength, and the trend of softening branches. In Fig. 7, the in-
fluence of initial imperfection and residual stress on the simulation results are illustrated. It can be
seen that the residual stress has a significant influence on the simulation results, while the inclusion
of initial imperfection slightly affects the predicted ultimate strength. Therefore, the consideration of
those effects is essential and should be accounted for in the simulation models to have a reasonable
Journal of Science and Technology in Civil Engineering NUCE 2021 ISSN 1859-2996 
14 
Figure 7. Influences of imperfection and residual stress on simulation results 
Journal of Science and Technology in Civil Engineering NUCE 2021 ISSN 1859-2996 
15 
Figure 8. Comparison of the load-deformation curve 
 Finally, the failure mode shapes of columns obtained from simulations and 
experimental results are compared in Figure 9. It is seen that the simulation results match 
well with the failure mode captured in the experimental programs. As expected, the 
failure mode of CFST stub columns under axial compression consists of a lateral 
expansion of columns’ section and outer buckling of steel jackets in the mid-height of the 
specimens. 
a. b. 
Figure 9. Comparison failure mode shapes: a. Specimen S9-7-140, b. Specimen S30-2 
4. Conclusions 
In this study, a Finite Element Model is developed based on Abaqus to analyze the 
behavior of rectangular CFST stub columns using high strength and ultra-high strength 
materials. A novel stress-strain relation confined concrete is proposed in this study to 
account for the composite effect, which might increase the strength and ductility of 
concrete. The present simulation model also considers the influences of residual stress 
for the welded-box section and initial imperfection. Verifications are conducted and the 
simulation results show that the proposed model can predict the ultimate strength, load-
Figure 8. Comparison of the load-deformation curve
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Thai, S., et al. / Journal of Science and Technology in Civil Engineering
prediction. Additionally, it is seen that the simulation result obtained from the current model agrees
well with one presented in Thai et al. [21], however, a better prediction for post-peak behavior is
obtained with the proposed model in this study.
As illustrated in Fig. 8, the load-deformation curves of CFST columns can be divided into two
stages. In the first stage, the compressive load is linearly proportional to the axial deformation up until
the limit point, where the column reaches its ultimate strength. In the second stage, the strength of
the columns drops with different trends depending on the confinement degree and slenderness ratio
of the steel section. For specimens SS2-3 and SS3-3, the load-deflection curves in the elastic region
obtained from FE simulations are slightly different from those presented by experimental programs.
Various factors might be attributed to those differences, e.i. the errors during experimental programs
when the axial deformation is measured, the unreliable value of elastic modulus obtained from the
empirical equation proposed by ACI 318 for these cases. In general, the columns with a relatively
large confinement factor (ξc > 1.5) and small slenderness ratio (Beq/t < 30) have a flatter softening
response as indicated in Table 2 and Fig. 8.
Finally, the failure mode shapes of columns obtained from simulations and experimental results
are compared in Fig. 9. It is seen that the simulation results match well with the failure mode captured
in the experimental programs. As expected, the failure mode of CFST stub columns under axial com-
pression consists of a lateral expansion of columns’ section and outer buckling of steel jackets in the
mid-height of the specimens.
Journal of Science and Technology in Civil Engineering NUCE 2021 ISSN 1859-2996 
15 
Figure 8. Comparison of the load-deformation curve 
 Finally, the failure mode shapes of columns obtained from simulations and 
experimental results are compared in Figure 9. It is seen that the simulation results match 
well with the failure mode captured in the experimental programs. As expected, the 
failure mode of CFST stub columns under axial compression consists of a lateral 
expansion of columns’ section and outer buckling of steel jackets in the mid-height of the 
specimens. 
a. b. 
Figure 9. Comparison failure mode shapes: a. Specimen S9-7-140, b. Specimen S30-2 
4. Conclusions 
In this study, a Finite Element Model is developed based on Abaqus to analyze the 
behavior of rectangular CFST stub columns using high strength and ultra-high strength 
materials. A novel stress-strain relation confined concrete is proposed in this study to 
account for the composite effect, which might increase the strength and ductility of 
concrete. The present simulation model also considers the influences of residual stress 
for the welded-box section and initial imperfection. Verifications are conducted and the 
simulation results show that the proposed model can predict the ultimate strength, load-
(a) Specimen S9-7-140
Journal of Science and Technology in Civil Engineering NUCE 2021 ISSN 1859-2996 
15 
Figure 8. Comparison of the load-deformation curve 
 Finally, the failure mode shapes of columns obtained from simulations and 
experimental results are compared in Figure 9. It is seen that the simulation results atch 
well with the failure mode captured in the experimental programs. As expected, the 
failure mode of CFST stub columns under axial compression consists of a lateral 
expansion of columns’ section and outer buckling of steel jackets in the mid-height of the 
specimens. 
a. b. 
Figure 9. Com ar son failure mode shapes: a. Specimen S9-7-140, b. Specimen S30-2 
4. Conclusions 
In this study, a Finite Element Model is developed based on Abaqus to analyze the 
behavior of rectangular CFST stub columns using high strength and ultra-high strength 
materials. A novel stress-strain relation confined concrete is proposed in this study to 
account for the composite effect, which might increase the strength and ductility of 
concrete. The present simulation model also considers the influences of residual stress 
for the welded-box section and initial imperfection. Verifications are conducted and the 
simulation results show that the proposed model can predict the ultimate strength, load-
(b) Specimen S30-2
Figure 9. Comparison failure mode shapes
4. Conclusions
In this study, a Finite Element Model is developed based on Abaqus to analyze the behavior of
rectangular CFST stub columns using high strength and ultra-high strength materials. A novel stress-
strain relation confined concrete is proposed in this study to account for the composite effect, which
might increase the strength and ductility of concrete. The present simulation model also considers
the influences of residual stress for the welded-box section and initial imperfection. Verifications are
conducted and the simulation results show that the proposed model can predict the ultimate strength,
load-deformation relations, and failure modes of CFST columns for wide ranges of geometrical and
material parameters.
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Thai, S., et al. / Journal of Science and Technology in Civil Engineering
Acknowledgments
This research is funded by Ho Chi Minh City University of Technology (HCMUT), VNU-HCM
under grant number T-KTXD-2020-55. We acknowledge the support of time and facilities from Ho
Chi Minh City University of Technology (HCMUT), VNU-HCM for this study.
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