Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression
Abstract
:1. Introduction
2. Materials and Methods
2.1. Selection of Specimen
2.2. Properties of the Specimen
2.3. Validation of the Selected Specimen with GBTUL
2.4. Testing of Specimen
2.5. DSM (Direct Strength Method) Approach
2.6. Modeling of Specimen Using FEM
2.6.1. Finite Element Modeling
2.6.2. Incorporation of Material Parameter
2.6.3. Selecting the End Condition and Loading
3. Results and Discussion
3.1. Validation of Experimentally Tested Specimen with FEM and DSM
3.2. Load Bearing Capacity vs. Axial Shortening Performance
3.3. Comparison of DSM vs. FEM
3.4. Parametric Study
Buckling Mode
3.5. Results of Parametric Study
3.6. Discussion
- The experimental method shows that the load-carrying capacity is governed by residual stress, slenderness ratio, and battened width.
- The buckling mode started with local buckling and ended up with a combination of local and distortional with respect to slenderness ratio. The buckling mode started with local buckling and ended up with the combination of local and distortional for slenderness ratio.
- Increasing the slenderness ratio from 20 to 30 and 30 to 40, the resistance against loading decreased by the nominal verge of 10 percent for the experimental specimen. The failure of the column is predicted for a lower slenderness ratio (≤30) may be local or a combination of local and flexural buckling. For the higher-order slenderness ratio (>30), the buckling will combine local, distortional, and flexural buckling modes.
- The experimental specimen subjected to buckling mode was matched with the FEA specimen from the validation study. Therefore, for the tedious situation, such as for the CFS back-to-back stiffened column, the observed value for a larger slenderness ratio can be predicted by finding out the product of 1.072 with PFEM (analytical value).
- From the theoretical study, it can be inferred that the DSM analysis is found to be conservative with the inclusion of service load and predicted the column’s strengthen equation, which calculates the failure load irrespective of the thickness and slenderness ratio.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Lipped c-Section with Web Stiffener | One or Two Intermediate Stiffeners: |
---|---|
| h/t < 489 |
b/t < 160 | |
6 < D/t < 33 | |
1.3 < h/b < 2.7 | |
0.05 < D/b < 0.41 | |
E/fy > 340 (fy < 593 MPa or 6050 kg/cm2) |
No. | Specimen ID BBSC-BW×Bf×D-t | Young’s Modulus E (GPa) | Tension Stress fy (MPa) | Failure Stress fu (MPa) | Elongation (%) | Loading Condition |
---|---|---|---|---|---|---|
1 | BBSC-130×78.5×17.25×2 | 200 | 316 | 350 | 28 | Pinned end condition |
2 | BBSC-132.5×78.75×16.75×2 | |||||
3 | BBSC-131.15×78.75×16.75×2 | |||||
4 | BBSC-131.6×78.175×16.75×2 | |||||
5 | BBSC-131.6×78×16.95×2 | |||||
6 | BBSC-132.65×78.375×17.5×2 |
S.I.NO. | Specimen ID Boundary Condition-Specimen ID | Slenderness Ratio | Thickness t (mm) | Battened Width b (mm) | Web bW (mm) | Flange bf (mm) | Lip d1 & d2 (mm) | Length (mm) | Spacing between Chords S (mm) |
---|---|---|---|---|---|---|---|---|---|
1 | BC-1-1 | 20 | 2 | 105 | 78.5 | 130 | 17.25 | 995 | 26 |
2 | BC-2-1 | 30 | 2 | 105 | 78.5 | 130 | 17.25 | 1492.5 | 26.5 |
3 | BC-1-2 | 20 | 2 | 104.5 | 79 | 130.5 | 17.10 | 995 | 25.2 |
4 | BC-2-2 | 30 | 2 | 104.5 | 79 | 130.5 | 17.10 | 1492.5 | 25.7 |
5 | BC-1-3 | 20 | 2 | 104.5 | 78.6 | 129.5 | 17.12 | 998 | 27 |
6 | BC-2-3 | 30 | 2 | 104.5 | 78.8 | 129.3 | 17.15 | 1492 | 26.7 |
7 | BC-3-1 | 20 | 2 | 149 | 78.75 | 132.5 | 16.75 | 990 | 27 |
8 | BC-4-1 | 30 | 2 | 149 | 78.76 | 132.5 | 16.75 | 1485 | 26.5 |
9 | BC-3-2 | 20 | 2 | 149 | 78.78 | 132.7 | 16.8 | 995 | 26 |
10 | BC-4-2 | 30 | 2 | 149 | 78.32 | 132.6 | 16.65 | 1492 | 26.2 |
11 | BC-3-3 | 20 | 2 | 149 | 77.75 | 132.52 | 16.76 | 1485 | 25 |
12 | BC-4-3 | 30 | 2 | 149 | 78.72 | 132.51 | 16.81 | 1485 | 26.5 |
13 | BC-5-1 | 30 | 2 | 105 | 78.75 | 131.15 | 16.75 | 1470 | 25 |
14 | BC- 6-1 | 40 | 2 | 105 | 78.75 | 131.23 | 16.754 | 1960 | 25.6 |
15 | BC-5-2 | 30 | 2 | 105 | 78.753 | 131.15 | 16.751 | 1468 | 24 |
16 | BC-6-2 | 40 | 2 | 105 | 78.75 | 131.14 | 16.746 | 1956 | 23.5 |
17 | BC-5-3 | 30 | 2 | 105 | 78.745 | 131.15 | 16.752 | 1469 | 24.2 |
18 | BC-6-3 | 40 | 2 | 105 | 78.746 | 131.15 | 16.656 | 1964 | 24.7 |
19 | BC-7-1 | 30 | 2 | 150 | 78.175 | 131.56 | 16.75 | 1472 | 27 |
20 | BC-8-1 | 40 | 2 | 150 | 78.174 | 131.55 | 16.746 | 1964 | 26.25 |
21 | BC-7-2 | 30 | 2 | 150 | 78.25 | 132 | 16.752 | 1462 | 26 |
22 | BC-8-2 | 40 | 2 | 150 | 78.175 | 131.62 | 16.748 | 1949 | 26.5 |
23 | BC-7-3 | 30 | 2 | 150 | 78.173 | 131.62 | 16.762 | 1468 | 25 |
24 | BC-8-3 | 40 | 2 | 150 | 78.175 | 131.63 | 16.752 | 1957 | 25.2 |
25 | BC-9-1 | 30 | 2 | 105 | 78 | 133.25 | 16.95 | 1472 | 27 |
26 | BC-10-1 | 40 | 2 | 105 | 78.23 | 133.25 | 16.95 | 1964 | 26.5 |
27 | BC-9-2 | 30 | 2 | 105 | 78.2 | 133.25 | 17 | 1472 | 26 |
28 | BC-10-2 | 40 | 2 | 105 | 78.3 | 133.25 | 16.95 | 1964 | 26.46 |
29 | BC-9-3 | 30 | 2 | 105 | 78.15 | 133.25 | 16.95 | 1472 | 25 |
30 | BC-10-3 | 40 | 2 | 105 | 78 | 133.25 | 16.95 | 1964 | 27 |
31 | BC-11-1 | 30 | 2 | 150 | 78.38 | 132.65 | 17.5 | 1965 | 29.5 |
32 | BC-12-1 | 40 | 2 | 150 | 78.375 | 132.65 | 17.46 | 2620 | 29.62 |
33 | BC-11-2 | 30 | 2 | 150 | 78.42 | 132.65 | 17.45 | 1965 | 28.5 |
34 | BC-12-2 | 40 | 2 | 150 | 78.4 | 132.65 | 17.53 | 2620 | 29.25 |
35 | BC-11-3 | 30 | 2 | 150 | 78.35 | 132.65 | 17.52 | 1965 | 31 |
36 | BC-12-3 | 40 | 2 | 150 | 78.37 | 132.65 | 17.5 | 2620 | 32.5 |
30 | BC-10-3 | 40 | 2 | 105 | 78 | 133.25 | 16.95 | 1964 | 27 |
31 | BC-11-1 | 30 | 2 | 150 | 78.38 | 132.65 | 17.5 | 1965 | 29.5 |
32 | BC-12-1 | 40 | 2 | 150 | 78.375 | 132.65 | 17.46 | 2620 | 29.62 |
33 | BC-11-2 | 30 | 2 | 150 | 78.42 | 132.65 | 17.45 | 1965 | 28.5 |
34 | BC-12-2 | 40 | 2 | 150 | 78.4 | 132.65 | 17.53 | 2620 | 29.25 |
35 | BC-11-3 | 30 | 2 | 150 | 78.35 | 132.65 | 17.52 | 1965 | 31 |
36 | BC-12-3 | 40 | 2 | 150 | 78.37 | 132.65 | 17.5 | 2620 | 32.5 |
No. | Specimen ID Boundary Condition-Specimen ID | Slenderness Ratio | PEXP (kN) | PFEM (kN) | PDSM (kN) | PFEM/PEXP | PFEM/PDSM |
---|---|---|---|---|---|---|---|
1 | BC-1-1 | 20 | 250 | 263 | 269 | 1.052 | 0.978 |
2 | BC-2-1 | 30 | 242 | 259 | 263 | 1.070 | 0.985 |
3 | BC-1-2 | 20 | 248 | 261 | 265.3 | 1.052 | 0.984 |
4 | BC-2-2 | 30 | 236 | 257.2 | 262.4 | 1.090 | 0.980 |
5 | BC-1-3 | 20 | 252 | 263 | 265.2 | 1.044 | 0.992 |
6 | BC-2-3 | 30 | 238 | 258 | 264.5 | 1.084 | 0.975 |
7 | BC-3-1 | 20 | 264 | 273 | 276 | 1.034 | 0.989 |
8 | BC-4-1 | 30 | 220 | 242 | 252 | 1.100 | 0.960 |
9 | BC-3-2 | 20 | 268 | 275 | 279 | 1.026 | 0.986 |
10 | BC-4-2 | 30 | 216 | 254 | 258 | 1.176 | 0.984 |
11 | BC-3-3 | 20 | 258 | 270 | 275 | 1.047 | 0.982 |
12 | BC-4-3 | 30 | 242 | 258 | 262 | 1.066 | 0.985 |
13 | BC-5-1 | 30 | 234 | 244 | 252 | 1.043 | 0.968 |
14 | BC-6-1 | 40 | 192 | 210 | 224 | 1.094 | 0.938 |
15 | BC-5-2 | 30 | 230 | 240 | 252 | 1.043 | 0.952 |
16 | BC-6-2 | 40 | 194 | 208 | 219 | 1.072 | 0.950 |
17 | BC-5-3 | 30 | 232 | 242 | 251 | 1.043 | 0.964 |
18 | BC-6-3 | 40 | 196 | 206 | 212.5 | 1.051 | 0.969 |
19 | BC-7-1 | 30 | 226 | 247 | 256 | 1.093 | 0.965 |
20 | BC-8-1 | 40 | 196 | 213.2 | 230 | 1.088 | 0.927 |
21 | BC-7-2 | 30 | 230 | 247 | 252 | 1.074 | 0.980 |
22 | BC-8-2 | 40 | 198 | 207 | 214 | 1.045 | 0.967 |
23 | BC-7-3 | 30 | 228 | 247 | 249.5 | 1.083 | 0.990 |
24 | BC-8-3 | 40 | 192 | 208.5 | 212.5 | 1.086 | 0.981 |
25 | BC-9-1 | 30 | 230 | 253 | 257 | 1.100 | 0.984 |
26 | BC-10-1 | 40 | 206 | 219.25 | 226.32 | 1.064 | 0.969 |
27 | BC-9-2 | 30 | 226 | 249 | 252 | 1.102 | 0.988 |
28 | BC-10-2 | 40 | 206 | 214.5 | 224 | 1.041 | 0.958 |
29 | BC-9-3 | 30 | 236 | 251 | 259 | 1.064 | 0.969 |
30 | BC-10-3 | 40 | 206 | 219.25 | 227.89 | 1.064 | 0.962 |
31 | BC-11-1 | 30 | 250 | 272.5 | 282 | 1.090 | 0.966 |
32 | BC-12-1 | 40 | 210 | 228.33 | 236 | 1.087 | 0.968 |
33 | BC-11-2 | 30 | 242 | 264.5 | 272.4 | 1.093 | 0.971 |
34 | BC-12-2 | 40 | 210 | 228.33 | 234.23 | 1.087 | 0.975 |
35 | BC-11-3 | 30 | 246 | 263.2 | 276 | 1.070 | 0.954 |
36 | BC-12-3 | 40 | 210 | 228.33 | 235 | 1.087 | 0.972 |
Mean | 1.072 | 0.971 | |||||
Standard Deviation | 0.030 | 0.027 | |||||
Coefficient of Variation | 0.028 | 0.025 |
No. | Specimen ID BC 1-BW×Bf× D-t-bw | Batten Width (mm) | Thickness (mm) | Spacing between Chords (mm) | Ultimate Strength fu (N/mm2) and Poisson’s Ratio | Slenderness Ratio | Young’s Modulus (N/mm2) |
---|---|---|---|---|---|---|---|
1 | BC 1-90×60×15-2-60.27 | 60.27 | 2 | 25 | 305 and 0.3 | 20-120 | 2 × 105 |
2 | BC 2-90×60×15-2-120 | 120 | 2 | 25 | 20-120 | ||
3 | BC 3-150×75×15-2-150 | 150 | 2 | 73 | 20-100 | ||
4 | BC 4-150×75×15-2-105 | 105 | 2 | 73 | 20-100 |
No. | Specimen ID | Slenderness Ratio | PFEM (KN) | PDSM (kN) | PCorrected (kN) | PCorrected /PFEM | PDSM /PFEM | Failure Mode |
---|---|---|---|---|---|---|---|---|
1 | BC 1-90×60×15×2-60.27-20-4 | 20 | 208.250 | 224.000 | 202.830 | 0.974 | 1.076 | NL + ND + NE |
2 | BC 1-90×60×15×2-60.27-30-5 | 30 | 207.719 | 223.000 | 201.870 | 0.972 | 1.074 | NL + ND + NE |
3 | BC 1-90×60×15×2-60.27-40-5 | 40 | 202.221 | 214.000 | 193.230 | 0.956 | 1.058 | NL + ND + NE |
4 | BC 1-90×60×15×2-60.27-50-5 | 50 | 190.381 | 207.000 | 186.510 | 0.980 | 1.087 | NL + ND + NE |
5 | BC 1-90×60×15×2-60.27-60-6 | 60 | 180.738 | 201.000 | 180.750 | 1.000 | 1.112 | NL + ND + NE |
6 | BC 1-90×60×15×2-60.27-70-6 | 70 | 175.848 | 195.000 | 174.990 | 0.995 | 1.109 | ND + NE |
7 | BC 1-90×60×15×2-60.27-80-7 | 80 | 167.495 | 185.000 | 165.390 | 0.987 | 1.105 | ND + NE |
8 | BC 1-90×60×15×2-60.27-90-8 | 90 | 141.358 | 169.000 | 150.030 | 1.061 | 1.196 | ND + NE |
9 | BC 1-90×60×15×2-60.27-100-9 | 100 | 126.266 | 142.000 | 124.110 | 0.983 | 1.125 | ND + NE |
10 | BC 1-90×60×15×2-60.27-110-10 | 110 | 111.572 | 134.000 | 116.430 | 1.044 | 1.201 | ND + NE |
11 | BC 1-90×60×15×2-60.27-120-10 | 120 | 105.377 | 126.000 | 108.750 | 1.032 | 1.196 | ND + NE |
12 | BC 2-90×60×15×2-120-20-4 | 20 | 213.432 | 236.000 | 214.350 | 1.004 | 1.106 | NL + ND + NE |
13 | BC 2-90×60×15×2-120-30-5 | 30 | 211.901 | 227.200 | 205.902 | 0.972 | 1.072 | NL + ND + NE |
14 | BC 2-90×60×15×2-120-40-5 | 40 | 201.476 | 213.000 | 192.270 | 0.954 | 1.057 | NL + ND + NE |
15 | BC 2-90×60×15×2-120-50-5 | 50 | 195.485 | 211.000 | 190.350 | 0.974 | 1.079 | NL + ND + NE |
16 | BC 2-90×60×15×2-120-60-6 | 60 | 190.488 | 206.500 | 186.030 | 0.977 | 1.084 | NL + ND + NE |
17 | BC 2-90×60×15×2-120-70-6 | 70 | 184.242 | 203.000 | 182.670 | 0.991 | 1.102 | ND + NE |
18 | BC 2-90×60×15×2-120-80-7 | 80 | 172.343 | 196.000 | 175.950 | 1.021 | 1.137 | ND + NE |
19 | BC 2-90×60×15×2-120-90-8 | 90 | 159.321 | 178.000 | 158.670 | 0.996 | 1.117 | ND + NE |
20 | BC 2-90×60×15×2-120-100-9 | 100 | 142.187 | 159.000 | 140.430 | 0.988 | 1.118 | ND + NE |
21 | BC 2-90×60×15×2-120-110-10 | 110 | 130.060 | 142.000 | 124.110 | 0.954 | 1.092 | ND + NE |
22 | BC 2-90×60×15×2-120-120-10 | 120 | 116.872 | 125.000 | 107.790 | 0.922 | 1.070 | ND + NE |
23 | BC 3-150×75×15-2-20-150-5 | 20 | 186.273 | 210.000 | 189.390 | 1.017 | 1.127 | NL + ND + NE |
24 | BC 3-150×75×15-2-20-150-5 | 30 | 181.683 | 204.000 | 183.630 | 1.011 | 1.123 | NL + ND + NE |
25 | BC 3-150×75×15-2-20-150-5 | 40 | 161.259 | 185.000 | 165.390 | 1.026 | 1.147 | NL + ND + NE |
26 | BC 3-150×75×15-2-20-150-6 | 50 | 152.433 | 178.000 | 158.670 | 1.041 | 1.168 | NL + ND + NE |
27 | BC 3-150×75×15-2-20-150-7 | 60 | 142.812 | 169.000 | 150.030 | 1.051 | 1.183 | NL + ND + NE |
28 | BC 3-150×75×15-2-20-150-8 | 70 | 132.662 | 156.000 | 137.550 | 1.037 | 1.176 | ND + NE |
29 | BC 3-150×75×15-2-20-150-10 | 80 | 124.053 | 146.000 | 127.950 | 1.031 | 1.177 | ND + NE |
30 | BC 3-150×75×15-2-20-150-11 | 90 | 113.355 | 133.000 | 115.470 | 1.019 | 1.173 | ND + NE |
31 | BC 3-150×75×15-2-20-150-12 | 100 | 105.377 | 126.000 | 108.750 | 1.032 | 1.196 | ND + NE |
32 | BC 4-150×75×15-2-20-105-5 | 20 | 185.596 | 208.000 | 187.470 | 1.010 | 1.121 | NL + ND + NE |
33 | BC 4-150×75×15-2-20-105-5 | 30 | 177.289 | 198.000 | 177.870 | 1.003 | 1.117 | NL + ND + NE |
34 | BC 4-150×75×15-2-20-105-5 | 40 | 163.444 | 189.000 | 169.230 | 1.035 | 1.156 | NL + ND + NE |
35 | BC 4-150×75×15-2-20-105-6 | 50 | 154.630 | 180.000 | 160.590 | 1.039 | 1.164 | NL + ND + NE |
36 | BC 4-150×75×15-2-20-105-7 | 60 | 146.100 | 172.000 | 152.910 | 1.047 | 1.177 | NL + ND + NE |
37 | BC 4-150×75×15-2-20-105-8 | 70 | 136.274 | 159.000 | 140.430 | 1.030 | 1.167 | ND + NE |
38 | BC 4-150×75×15-2-20-105-10 | 80 | 124.053 | 145.600 | 127.566 | 1.028 | 1.174 | ND + NE |
39 | BC 4-150×75×15-2-20-105-11 | 90 | 113.355 | 132.000 | 114.510 | 1.010 | 1.164 | ND + NE |
40 | BC 4-150×75×15-2-20-105-12 | 100 | 106.743 | 128.000 | 110.670 | 1.037 | 1.199 | ND + NE |
Mean | 0.978 | 1.101 | ||||||
Standard Deviation | 0.027 | 0.031 | ||||||
Coefficient of Variation | 0.028 | 0.028 |
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Mohan, M.; Ramachandran, A.; Amran, M.; Borovkov, A. Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression. Materials 2022, 15, 2968. https://doi.org/10.3390/ma15092968
Mohan M, Ramachandran A, Amran M, Borovkov A. Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression. Materials. 2022; 15(9):2968. https://doi.org/10.3390/ma15092968
Chicago/Turabian StyleMohan, Muthuraman, Anuradha Ramachandran, Mugahed Amran, and Aleksey Borovkov. 2022. "Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression" Materials 15, no. 9: 2968. https://doi.org/10.3390/ma15092968