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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2021, Vol. 15 Issue (1) : 194-212    https://doi.org/10.1007/s11709-020-0688-2
RESEARCH ARTICLE
An innovative model for predicting the displacement and rotation of column-tree moment connection under fire
Mohammad Ali NAGHSH1, Aydin SHISHEGARAN2, Behnam KARAMI3, Timon RABCZUK4,5(), Arshia SHISHEGARAN6, Hamed TAGHAVIZADEH3, Mehdi MORADI7
1. Department of Civil Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
2. School of Civil Engineering, School of Civil Engineering, Iran University of Science and Technology, Tehran 13114-16846, Iran
3. Department of Civil Engineering,International Institute of Earthquake Engineering and Seismology, Tehran 19539-14453, Iran
4. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
5. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
6. Department of Civil Engineering, Islamic Azad University, Tehran 16511-53311, Iran
7. Department of Civil Engineering, Isfahan University, Isfahan 81746-73441, Iran
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Abstract

In this study, we carried out nonlinear finite element simulations to predict the performance of a column-tree moment connection (CTMC) under fire and static loads. We also conducted a detailed parameter study based on five input variables, including the applied temperature, number of flange bolts, number of web bolts, length of the beam, and applied static loads. The first variable is changed among seven levels, whereas the other variables are changed among three levels. Employing the Taguchi method for variables 2–5 and their levels, 9 samples were designed for the parameter study, where each sample was exposed to 7 different temperatures yielding 63 outputs. The related variables for each output are imported for the training and testing of different surrogate models. These surrogate models include a multiple linear regression (MLR), multiple Ln equation regression (MLnER), an adaptive network-based fuzzy inference system (ANFIS), and gene expression programming (GEP). 44 samples were used for training randomly while the remaining samples were employed for testing. We show that GEP outperforms MLR, MLnER, and ANFIS. The results indicate that the rotation and deflection of the CTMC depend on the temperature. In addition, the fire resistance increases with a decrease in the beam length; thus, a shorter beam can increase the fire resistance of the building. The numbers of flanges and web bolts slightly affect the rotation and displacement of the CTMCs at temperatures of above 400°C.
Keywords column-tree moment connection      Finite element model      parametric study      fire      regression models      gene expression programming     
Corresponding Author(s): Timon RABCZUK   
Just Accepted Date: 20 January 2021   Online First Date: 10 March 2021    Issue Date: 12 April 2021
 Cite this article:   
Mohammad Ali NAGHSH,Aydin SHISHEGARAN,Behnam KARAMI, et al. An innovative model for predicting the displacement and rotation of column-tree moment connection under fire[J]. Front. Struct. Civ. Eng., 2021, 15(1): 194-212.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0688-2
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I1/194
Fig.1  A flowchart showing the process of the present study.
sample 1 sample 2 sample 3 sample 4 sample 5 sample 6 sample 7 sample 8 sample 9
80 92 116 72 84 108 64 76 100
Tab.1  Number of interactions of FE samples
Fig.2  The mechanical behavior of steel under fire: (a) the considered behavior of steel at temperatures of below 400°C; (b) the considered behavior of steel at temperatures of over 400°C; (c) reduction factors for the stress-strain curve of steel at elevated temperatures [34].
properties property symbol unit ST-37 bolts
mechanical properties elastic modulus E GPa 210 210
yield strength Fy MPa 240 640
ultimate strength Fu? MPa 300 800
Poisson’s ratio ν – 0.3 0.3
yield strain εy – 0.02 0.02
strain hardening strain εs – 0.04 0.04
limiting strain for yield/ultimate strength εt – 0.15 0.15
ultimate strain εu – 0.2 0.2
density ρ kg/m3 7850 7850
thermal properties thermal elongation α °C−1 1.2× 10 −5 1.2× 10 −5
specific heat capacity CT? J· g−1 ·°C−1 600 600
thermal conductivity λ W· m−1 ·°C−1 45 45
Tab.2  Mechanical and thermal properties of steel at ambient temperature
section/bolt coupon location steel type Fy (MPa) εy (%) Fu (MPa) εu (%)
beam
(488 × 300 × 11 × 18)		 flange SN490B 396.6 0.190 524.6 20
web SN490B 476.0 0.229 575.4 20
column
(600 × 600 × 25 × 25)		 flange SN490B 398.0 0.191 534.0 20
web SN490B 398.0 0.191 534.0 20
bolts shank S10T 981.2 0.472 1042.5? 20
Tab.3  Mechanical properties of the steel considered at room temperature [3]
Fig.3  The geometry and dimensions (unit: mm) of CTMC, location of the LVDT, and thermocouple in the study by Chung et al. [3].
Fig.4  The temperature-time of the validated CTMC: (a) the temperature–time curves for the beam sections; (b) the temperature–time curves for the column sections; (c) the considered temperature–time curves for applying the validated models, and the proposed temperature-time curve based on ISO-834 [3,33,34].
Fig.5  Comparison of the FE and experimental displacement-temperature results [3].
Fig.6  Comparison of rotation-temperature results in FE models and experimental test [3].
Fig.7  Comparison of failure mode in FE model and experimental test [3].
model element size (mm) number of elements
stub
beam		 link beam column splice
plate		 bolts stub
beam		 link beam column splice
plate		 bolts
MS#1 80 80 100 10??? 10??? ?344 ??817 1128 2 × 855? 10 × 115
MS#2 40 40 75 7.5 7.5 ?711 ?1692 4110 2 × 1358 10 × 138
MS#3 20 20 50 5?? 5?? 2227 ?5209 6472 2 × 6380 10 × 636
MS#4 10 10 25 2.5 2.5 13347? 27208 16976? ?2 × 48000 10 × 4728
Tab.4  The element sizes and number of elements in the validation process
Fig.8  The displacement-temperature of each type of mesh size [3].
model critical temperature (°C)
present study experimental [3] error (%) FE analysis [3] error (%)
MS#1 612.3 573.4 6.78 598.9 2.24
MS#2 606.3 573.4 5.74 598.9 1.24
MS#3 601.1 573.4 4.83 598.9 0.37
MS#4 601.1 573.4 4.83 598.9 0.37
Tab.5  The effect of the element sizes on the critical temperature
Fig.9  Schematic view and geography of samples: (a) dimensions of CTMC and its components; (b) a section of beam; (c) a section of column; (d) a flange plate and distance between its holes; (e) a web plate and distance between its holes.
model dw1 dw2 dw3 dw4 dw5 dw6 dw7
samples 1, 4, and 7 75 100 – 150 75 87.5 –
samples 2, 5, and 8 75 100 – 150 50 75 75
samples 3, 6, and 9 50 75 75 100 50 75 75
Tab.6  Arrangement of holes in splice the plate
variables name of variables unit number of levels levels
1 temperature °C 7 20, 100, 200, 300, 400, 500, and 600
2 number of flange bolts – 3 3, 4, and 5
3 number of web bolts – 3 12, 16, and 24
4 length of beam mm 3 1450, 1650, and 1800
5 the applied static load kN 3 50, 100, and 150
Tab.7  The variables and levels of the present study
sample sample ID number of flange bolts number of web bolts length of beam (mm) the static load (kN) the applied temperature (°C)
1 F5W12L1.45P90 5 12 1450 90 20, 100, 200, 300, 400, 500, 600
2 F5W16L1.65P120 5 16 1650 120
3 F5W24L1.8P150 5 24 1800 150
4 F4W12L1.65P150 4 12 1650 150
5 F4W16L1.8P90 4 16 1800 90
6 F4W24L1.45P120 4 24 1450 120
7 F3W12L1.8P120 3 12 1800 120
8 F3W16L1.45P150 3 16 1450 150
9 F3W24L1.65P90 3 24 1650 90
Tab.8  The considered levels for variables of models
component element number
sample 1 sample 2 sample 3 sample 4 sample 5 sample 6 sample 7 sample 8 sample 9
stub beam 2160 2242 2342 2065 2116 2228 1942 1963 2094
link beam 1653 1925 2314 1832 2045 1870 2180 1626 2050
column 2223 2223 2223 2223 2223 2223 2223 2223 2223
splice plate 788 1015 1505 788 1015 1505 788 1015 1505
bolts 1744 1912 2248 1496 1664 2000 1248 1416 1752
total 8568 9317 10632 8404 9063 9826 8381 8243 9624
Tab.9  Element numbers of connection components in FE samples
Fig.10  Rotation-temperature of samples.
Fig.11  Displacement-temperature of samples.
outputs variables
number of flange bolt number of web bolt length of beam the static load temperature
displacement 0.0261 −0.0008 0.1269 0.2093 0.6961
rotation 0.0360 0.0008 0.1138 0.2661 0.5212
Tab.10  The correlation coefficient between input variables and outputs
Fig.12  Architecture of typical ANFIS.
Fig.13  Gene expression program flowchart.
output of prediction model model calibration validation
coefficient of determination RMSE NMSE fractional bias coefficient of determination RMSE NMSE fractional bias
displacement MLR 0.8746 9.7188 0.174 1.13E–03 0.6786 27.3618 0.749 −1.02E–03
MLnER 0.8273 4.0189 0.1596 1.57E–03 0.5816 36.5098 1.7546 −7.73E–03
ANFIS 0.9581 1.1475 0.0547 −1.53E–04 0.9990 5.9677 0.0122 6.64E–05
GEP 0.9832 0.6657 0.039 2.93E–05 0.9926 2.9884 0.0247 −3.81E–05
rotation MLR 0.813 0.0017 0.2119 1.40E–03 0.5785 0.0053 0.9295 −1.30E–03
MLnER 0.7624 0.0006 0.21 1.60E–03 0.4186 0.0067 2.9339 −1.07E–02
ANFIS 0.9784 0.0005 0.0387 −3.60E–05 0.9921 0.0096 0.0325 −7.38E–04
GEP 0.9706 0.0001 0.0447 −1.00E–04 0.9967 0.0004 0.0164 −1.00E–04
Tab.11  Statistical parameters for predicting the displacement and rotation of CTMC under fire conditions and a static load
output of prediction model error terms MLR MLnER ANFIS GEP
displacement maximum positive error 818.16% 73.64% 99.33% 22.84%
maximum negative error −154.59% −96.51% −26.49% −37.36%
MAPE 12.69% 41.04% 7.71% 1.33%
rotation maximum positive error 472.44% 84.69% 89.54% 63.41%
maximum negative error −195.52% −76.31% −44.12% −8.88%
MAPE 10.29% 22.95% 6.77% 0.57%
Tab.12  Error terms of prediction models for forecasting the displacement and rotation of CTMC under fire conditions and a static load
Fig.14  Comparison of errors of MLnER and GEP: distribution of errors of MLnER and GEP for predicting (a) the displacement and (b) the rotation.
Fig.15  Comparison of displacement and rotation obtained from nonlinear FE model and the values predicted through GEP. (a) The predicted displacement through GEP and the obtained displacement from the nonlinear FE analysis; (b) the predicted displacement through GEP and the displacement obtained from a nonlinear FE analysis.
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