1 Introduction
2 Laboratory Tests (Fang et al. 2022b)
2.1 Test specimen
2.2 Test-setup and loading procedure
2.3 Test Results
Specimen ID | Web | Length | Bend radius | Thickness | Hole dia | Bearing length | Exp | FEA result | PEXP/PFEA |
---|---|---|---|---|---|---|---|---|---|
Load | |||||||||
d | L | r | t | a | N | PEXP | PFEA | ||
(mm) | (mm) | (mm) | (mm) | (mm) | (mm) | (kN) | (kN) | ||
ITF240-N50-NH-A0-FR | 241.75 | 770 | 3 | 1.96 | 0 | 50 | 5.25 | 5.01 | 1.05 |
ITF240-N75-NH-A0-FR | 240.78 | 795 | 3 | 1.95 | 0 | 75 | 5.39 | 5.07 | 1.06 |
ITF240-N100-NH-A0-FR | 240.35 | 820 | 3 | 1.95 | 0 | 100 | 5.44 | 5.21 | 1.05 |
ITF240-N50-DH-A0.2-FR | 241.14 | 770 | 3 | 1.95 | 48 | 50 | 5.06 | 4.74 | 1.07 |
ITF240-N75-DH-A0.2-FR | 240.26 | 795 | 3 | 1.95 | 48 | 75 | 5.12 | 4.86 | 1.05 |
ITF240-N100-DH-A0.2-FR | 240.93 | 820 | 3 | 1.95 | 48 | 100 | 5.32 | 4.99 | 1.07 |
ITF240-N50-OH-A0.2-FR | 241.51 | 770 | 3 | 1.95 | 48 | 50 | 4.82 | 4.56 | 1.06 |
ITF240-N75-OH-A0.2-FR | 241.28 | 795 | 3 | 1.95 | 48 | 75 | 4.85 | 4.69 | 1.03 |
ITF240-N100-OH-A0.2-FR | 240.27 | 820 | 3 | 1.95 | 48 | 100 | 5.06 | 4.83 | 1.05 |
ITF240-N50-DH-A0.6-FR | 240.44 | 770 | 3 | 1.95 | 144 | 50 | 3.81 | 3.59 | 1.06 |
ITF240-N75-DH-A0.6-FR | 241.71 | 795 | 3 | 1.96 | 144 | 75 | 3.84 | 3.77 | 1.02 |
ITF240-N100-DH-A0.6-FR | 240.54 | 820 | 3 | 1.95 | 144 | 100 | 4.06 | 3.86 | 1.05 |
ITF240-N50-OH-A0.6-FR | 241.96 | 770 | 3 | 1.95 | 144 | 50 | 3.5 | 3.17 | 1.11 |
ITF240-N75-OH-A0.6-FR | 241.44 | 795 | 3 | 1.95 | 144 | 75 | 3.48 | 3.3 | 1.05 |
ITF240-N100-OH-A0.6-FR | 241.15 | 820 | 3 | 1.95 | 144 | 100 | 3.74 | 3.43 | 1.09 |
Average | 1.06 | ||||||||
Cov | 0.02 | ||||||||
ITF200-N50-NH-A0-FX | 240.12 | 770 | 3 | 1.95 | 0 | 50 | 7.63 | 7.25 | 1.05 |
ITF200-N75-NH-A0-FX | 240.63 | 795 | 3 | 1.95 | 0 | 75 | 7.68 | 7.42 | 1.03 |
ITF200-N100-NH-A0-FX | 241.68 | 820 | 3 | 1.95 | 0 | 100 | 7.99 | 7.61 | 1.05 |
ITF200-N50-DH-A0.2-FX | 241.11 | 770 | 3 | 1.96 | 48 | 50 | 7.17 | 6.99 | 1.03 |
ITF200-N75-DH-A0.2-FX | 241.45 | 795 | 3 | 1.95 | 48 | 75 | 7.17 | 7.06 | 1.02 |
ITF200-N100-DH-A0.2-FX | 241.59 | 820 | 3 | 1.96 | 48 | 100 | 7.44 | 7.31 | 1.02 |
ITF200-N50-OH-A0.2-FX | 241.68 | 770 | 3 | 1.96 | 48 | 50 | 7.1 | 6.86 | 1.03 |
ITF200-N75-OH-A0.2-FX | 241.43 | 795 | 3 | 1.96 | 48 | 75 | 7.21 | 7.04 | 1.02 |
ITF200-N100-OH-A0.2-FX | 241.1 | 820 | 3 | 1.96 | 48 | 100 | 7.6 | 7.21 | 1.05 |
ITF200-N50-DH-A0.6-FX | 241.79 | 770 | 3 | 1.94 | 144 | 50 | 4.98 | 4.92 | 1.01 |
ITF200-N75-DH-A0.6-FX | 241.51 | 795 | 3 | 1.94 | 144 | 75 | 5.1 | 5.11 | 1 |
ITF200-N100-DH-A0.6-FX | 241.13 | 820 | 3 | 1.94 | 144 | 100 | 5.41 | 5.37 | 1.01 |
ITF200-N50-OH-A0.6-FX | 241.83 | 770 | 3 | 1.95 | 144 | 50 | 5.84 | 5.4 | 1.08 |
ITF200-N75-OH-A0.6-FX | 240.69 | 795 | 3 | 1.95 | 144 | 75 | 5.87 | 5.54 | 1.06 |
ITF200-N100-OH-A0.6-FX | 240.53 | 820 | 3 | 1.95 | 144 | 100 | 6.36 | 5.74 | 1.11 |
Average | 1.04 | ||||||||
Cov | 0.03 |
3 Advanced Finite Element Analysis
3.1 FE Modelling
3.2 FE Validation
4 Design Guidelines
4.1 Equations for Web Crippling Strength
4.2 Equations for Web Strength Reduction Factor
5 Deep Belief Network (DBN)
5.1 Overview
5.2 Data Feature Extraction and Hyper-Parameter Optimization
5.3 Data Training
5.4 DBN Assessment
Specimen ID | Err% (FEA) | Err% (AS/NZS 1997) | Err% (CEN) | Err% (AISI&AS/NZS) | Err% (DBN) |
---|---|---|---|---|---|
1 ITF240-N50-NH-A0-FR | 4.57 | 76.72 | 22.34 | 56.44 | 6.54 |
2 ITF240-N75-NH-A0-FR | 5.94 | 91.97 | 32.48 | 62.18 | 4.76 |
3 ITF240-N100-NH-A0-FR | 4.23 | 117.66 | 47.34 | 77.36 | 1.96 |
4 ITF240-N50-DH-A0.2-FR | 6.32 | – | – | – | 8.37 |
5 ITF240-N75-DH-A0.2-FR | 5.08 | – | – | – | 4.76 |
6 ITF240-N100-DH-A0.2-FR | 6.20 | – | – | – | 3.88 |
7 ITF240-N50-OH-A0.2-FR | 5.39 | – | – | – | 6.54 |
8 ITF240-N75-OH-A0.2-FR | 3.30 | – | – | – | 1.82 |
9 ITF240-N100-OH-A0.2-FR | 4.55 | – | – | – | 0.97 |
10 ITF240-N50-DH-A0.6-FR | 5.77 | – | – | – | 8.37 |
11 ITF240-N75-DH-A0.6-FR | 1.82 | – | – | – | 3.80 |
12 ITF240-N100-DH-A0.6-FR | 4.93 | – | – | – | 4.82 |
13 ITF240-N50-OH-A0.6-FR | 9.43 | – | – | – | 8.37 |
14 ITF240-N75-OH-A0.6-FR | 5.17 | – | – | – | 2.82 |
15 ITF240-N100-OH-A0.6-FR | 8.29 | – | – | – | 4.82 |
Average | 5.40 | 95.45 | 34.06 | 65.32 | 4.84 |
Cov | 1.77 | 16.90 | 10.27 | 8.82 | 2.33 |
16 ITF240-N50-NH-A0-FX | 4.98 | 20.28 | 16.65 | 15.88 | 14.53 |
17 ITF240-N75-NH-A0-FX | 3.39 | 38.02 | 4.34 | 25.47 | 6.54 |
18 ITF240-N100-NH-A0-FX | 4.76 | 46.53 | 0.79 | 23.69 | 3.85 |
19 ITF240-N50-DH-A0.2-FX | 2.51 | – | – | – | 11.89 |
20 ITF240-N75-DH-A0.2-FX | 1.53 | – | – | – | 2.65 |
21 ITF240-N100-DH-A0.2-FX | 1.75 | – | – | – | 0.16 |
22 ITF240-N50-OH-A0.2-FX | 3.38 | – | – | – | 11.89 |
23 ITF240-N75-OH-A0.2-FX | 2.36 | – | – | – | 4.63 |
24 ITF240-N100-OH-A0.2-FX | 5.13 | – | – | – | 2.87 |
25 ITF240-N50-DH-A0.6-FX | 1.20 | – | – | – | 5.03 |
26 ITF240-N75-DH-A0.6-FX | 0.20 | – | – | – | 1.58 |
27 ITF240-N100-DH-A0.6-FX | 0.74 | – | – | – | 3.39 |
28 ITF240-N50-OH-A0.6-FX | 7.53 | – | – | – | 14.53 |
29 ITF240-N75-OH-A0.6-FX | 5.62 | – | – | – | 5.60 |
30 ITF240-N100-OH-A0.6-FX | 9.75 | – | – | – | 6.65 |
Average | 3.66 | 34.94 | 7.26 | 21.68 | 6.39 |
Cov | 2.57 | 10.94 | 6.80 | 4.17 | 4.49 |
6 Parametric Analyses on the Qualitative Effect of Related Parameters
6.1 Effects of r/t, N/t, h/t and Flange Type
6.2 Effect of Web Holes on the Web Crippling Strength Reduction Factor (R)
Reduction factor | R | ||
---|---|---|---|
Web hole | |||
Unfastened channel | Fastened channel | ||
Center hole with a/h at | 0.2 | 0.95 | 0.96 |
0.4 | 0.86 | 0.87 | |
0.6 | 0.75 | 0.75 | |
0.8 | 0.61 | 0.60 | |
Offset hole with a/h at | 0.2 | 0.93 | 0.95 |
0.4 | 0.81 | 0.87 | |
0.6 | 0.67 | 0.78 | |
0.8 | 0.54 | 0.67 |
7 Development of Design Equations
7.1 Design Equations
(a) Coefficients for Eq. 11 | |||||
---|---|---|---|---|---|
Channel type | C | CR | CN | Ch | |
\(r/t < 1.0\) | Unfastened channel | 20.002 | 0.405 | 0.095 | 0.046 |
Fastened channel | 14.294 | 0.416 | 0.235 | 0.026 | |
\(r/t < 1.0\) | Unfastened channel | 16.309 | 0.237 | 0.070 | 0.042 |
Fastened channel | 15.087 | 0.220 | 0.153 | 0.038 |
Unfastened channel | Fastened channel | |
---|---|---|
α | 1.047 | 1.088 |
γ | 0.558 | 0.603 |
λ | 0.056 | 0.023 |
β | 0.754 | 0.800 |
μ | 0.463 | 0.298 |
ζ | 0.154 | 0.091 |
ξ | 0.374 | 0.323 |
(a) Comparison of web crippling strengths from various methods | |||||||
---|---|---|---|---|---|---|---|
Specimen ID | Exp. Load | PEXP/PAS/NZS1997 | PEXP/PCEN | PEXP/PAISI&AS/NZS | PEXP/Pprop | REXP/RUzzaman | REXP/Rprop |
PEXP | |||||||
(kN) | |||||||
Plain sections with un-fastened flanges | |||||||
ITF240-N50-NH-A0-FR | 5.25 | 0.54 | 0.78 | 0.61 | 1.07 | – | – |
ITF240-N75-NH-A0-FR | 5.39 | 0.49 | 0.71 | 0.58 | 1.05 | – | – |
ITF240-N100-NH-A0-FR | 5.44 | 0.44 | 0.65 | 0.54 | 1.02 | – | – |
Average | 0.49 | 0.71 | 0.58 | 1.05 | – | – | |
Cov | 0.04 | 0.05 | 0.03 | 0.02 | – | – | |
Plain sections with fastened flanges | – | – | |||||
ITF200-N50-NH-A0-FX | 7.63 | 0.79 | 1.14 | 0.82 | 1.17 | – | – |
ITF200-N75-NH-A0-FX | 7.68 | 0.70 | 1.01 | 0.77 | 1.07 | – | – |
ITF200-N100-NH-A0-FX | 7.99 | 0.65 | 0.96 | 0.77 | 1.04 | – | – |
Average | 0.71 | 1.04 | 0.79 | 1.09 | – | – | |
Cov | 0.06 | 0.08 | 0.02 | 0.06 | – | – | |
Sections with un-fastened flanges | |||||||
ITF240-N50-DH-A0.2-FR | 5.06 | – | – | – | – | 1.03 | 1.02 |
ITF240-N75-DH-A0.2-FR | 5.12 | – | – | – | – | 1.01 | 1.00 |
ITF240-N100-DH-A0.2-FR | 5.32 | – | – | – | – | 1.04 | 1.02 |
ITF240-N50-OH-A0.2-FR | 4.82 | – | – | – | – | – | 1.00 |
ITF240-N75-OH-A0.2-FR | 4.85 | – | – | – | – | – | 0.97 |
ITF240-N100-OH-A0.2-FR | 5.06 | – | – | – | – | – | 0.99 |
ITF240-N50-DH-A0.6-FR | 3.81 | – | – | – | – | 1.01 | 1.02 |
ITF240-N75-DH-A0.6-FR | 3.84 | – | – | – | – | 0.99 | 0.99 |
ITF240-N100-DH-A0.6-FR | 4.06 | – | – | – | – | 1.04 | 1.03 |
ITF240-N50-OH-A0.6-FR | 3.50 | – | – | – | – | – | 1.02 |
ITF240-N75-OH-A0.6-FR | 3.48 | – | – | – | – | – | 0.98 |
ITF240-N100-OH-A0.6-FR | 3.74 | – | – | – | – | – | 1.03 |
Average | – | – | – | – | 1.02 | 1.01 | |
Cov | – | – | – | – | 0.02 | 0.02 | |
Sections with fastened flanges | |||||||
ITF200-N50-DH-A0.2-FX | 7.17 | – | – | – | – | 1.02 | 0.97 |
ITF200-N75-DH-A0.2-FX | 7.17 | – | – | – | – | 1.01 | 0.96 |
ITF200-N100-DH-A0.2-FX | 7.44 | – | – | – | – | 1.00 | 0.96 |
ITF200-N50-OH-A0.2-FX | 7.10 | – | – | – | – | – | 0.97 |
ITF200-N75-OH-A0.2-FX | 7.21 | – | – | – | – | – | 0.98 |
ITF200-N100-OH-A0.2-FX | 7.60 | – | – | – | – | – | 0.99 |
ITF200-N50-DH-A0.6-FX | 4.98 | – | – | – | – | 0.92 | 0.90 |
ITF200-N75-DH-A0.6-FX | 5.10 | – | – | – | – | 0.93 | 0.92 |
ITF200-N100-DH-A0.6-FX | 5.41 | – | – | – | – | 0.94 | 0.93 |
ITF200-N50-OH-A0.6-FX | 5.84 | – | – | – | – | – | 1.00 |
ITF200-N75-OH-A0.6-FX | 5.87 | – | – | – | – | – | 0.99 |
ITF200-N100-OH-A0.6-FX | 6.36 | – | – | – | – | – | 1.03 |
Average | – | – | – | – | 0.97 | 0.97 | |
Cov | – | – | – | – | 0.04 | 0.03 |
(b) Reliability analysis | ||
---|---|---|
Flange type | With un-fastened flanges | With fastened flanges |
Ratio of equations | \(P_{FEA} /P_{prop}\) | \(P_{FEA} /P_{prop}\) |
Data number | 108 | 108 |
Mean, Pm | 1.02 | 1.03 |
Reliability index, β’ | 2.78 | 2.83 |
Resistance factor, φ | 0.85 | 0.85 |
Flange type | With un-fastened flanges | With fastened flanges |
Ratio of equations | \(R_{FEA} /R_{prop}\) | \(R_{FEA} /R_{prop}\) |
Data number | 432 | 432 |
Mean, Pm | 1.00 | 1.00 |
Coefficient of variation, COV | 0.05 | 0.06 |
Reliability index, β’ | 2.70 | 2.70 |
Resistance factor, φ | 0.85 | 0.85 |