Stress Concentration Factors of Concrete-Filled Double-Skin Tubular K-Joints
Abstract
:1. Introduction
2. Materials and Methods
2.1. Specimens
2.2. Test Setup
2.3. Measuring and Loading the System
3. Test Results
3.1. General
3.2. Extrapolation Method
3.3. SCF Values
4. Numerical Modelling of CFDST K-Joints
4.1. General
4.2. Material Properties
4.3. Validations
5. Parametric Study
5.1. General
5.2. Effect of Hollow Section Ratio ζ
5.3. Effect of the Ratio of Diameter of the Brace to That of Chord β
5.4. Effect of the Ratio of Radius to Thickness of Chord γ
5.5. Effect of the Ratio of Thickness of the Brace to That of Chord τ
5.6. Effect of Brace Angle θ
6. Proposed SCF Calculation Equations
6.1. Calculation Equations in Design Guidelines or Codes
6.2. Proposed Equations
6.3. Verifications
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Dong, F.; Shi, L.; Ding, X.; Li, Y.; Shi, Y. Study on China’s renewable energy policy reform and improved design of renewable portfolio standard. Energies 2019, 12, 2147. [Google Scholar] [CrossRef]
- Oh, K.-Y.; Nam, W.; Ryu, M.S.; Kim, J.-Y.; Epureanu, B.I. A review of foundations of offshore wind energy convertors: Current status and future perspectives. Renew. Sustain. Energy Rev. 2018, 88, 16–36. [Google Scholar] [CrossRef]
- Akadiri, P.O.; Chinyio, E.A.; Olomolaiye, P.O. Design of a sustainable building: A conceptual framework for implementing sustainability in the building sector. Buildings 2012, 2, 126–152. [Google Scholar] [CrossRef]
- Tetiranont, S.; Sadakorn, W.; Rugkhapan, N.T.; Prasittisopin, L. Enhancing sustainable railway station design in tropical climates: Insights from Thailand’s architectural theses and case studies. Buildings 2024, 14, 829. [Google Scholar] [CrossRef]
- Danatzko, J.M.; Sezen, H. Sustainable structural design methodologies. Pract. Period. Struct. Des. Constr. 2011, 16, 186–190. [Google Scholar] [CrossRef]
- Zain, M.; Ngamkhanong, C.; Kang, T.H.K.; Usman, M.; Prasittisopin, L. Modal-based fragility analysis of high-rise tubular structures: A methodology for vulnerability assessment. Structures 2024, 63, 106289. [Google Scholar] [CrossRef]
- Shi, W.; Park, H.; Chung, C.; Baek, J.; Kim, Y.; Kim, C. Load analysis and comparison of different jacket foundations. Renew. Energy 2013, 54, 201–210. [Google Scholar] [CrossRef]
- Tian, W.; Wang, Y.; Shi, W.; Michailides, C.; Wan, L.; Chen, M. Numerical study of hydrodynamic responses for a combined concept of semisubmersible wind turbine and different layouts of a wave energy converter. Ocean. Eng. 2023, 272. [Google Scholar] [CrossRef]
- Ricciardelli, F.; Maienza, C.; Vardaroglu, M.; Avossa, A.M. Wind energy into the future: The challenge of deep-water wind farms. Wind. Struct. 2021, 32, 321–340. [Google Scholar]
- Li, J.; Guo, Y.; Lian, J.; Wang, H. Mechanisms, assessments, countermeasures, and prospects for offshore wind turbine foundation scour research. Ocean. Eng. 2023, 281, 114893. [Google Scholar] [CrossRef]
- Ouyang, C.; Luo, J.; Wang, T.; Zhang, P. Research on the effect of burial depth on the bearing characteristics of three helical piles jacket foundation for offshore wind turbines. J. Mar. Sci. Eng. 2023, 11, 1703. [Google Scholar] [CrossRef]
- Song, S.-S.; Chen, J.; Xu, F. Mechanical behaviour and design of concrete-filled K and KK CHS connections. J. Constr. Steel Res. 2022, 188, 107000. [Google Scholar] [CrossRef]
- Xu, G.; Tong, L.; Zhao, X.-L.; Zhou, H.; Xu, F. Numerical analysis and formulae for SCF reduction coefficients of CFRP-strengthened CHS gap K-joints. Eng. Struct. 2020, 210, 110369. [Google Scholar] [CrossRef]
- Ferrotto, M.F.; Fenu, L.; Xue, J.-Q.; Briseghella, B.; Chen, B.-C.; Cavaleri, L. Simplified equivalent finite element modelling of concrete-filled steel tubular K-joints with and without studs. Eng. Struct. 2022, 266, 114634. [Google Scholar] [CrossRef]
- Wang, K.; Tong, L.-W.; Zhu, J.; Zhao, X.-L.; Mashiri, F.R. Fatigue behavior of welded T-joints with a CHS brace and CFCHS chord under axial loading in the brace. J. Bridge Eng. 2013, 18, 142–152. [Google Scholar] [CrossRef]
- Xu, F.; Chen, J.; Jin, W.-L. Experimental investigation of SCF distribution for thin-walled concrete-filled CHS joints under axial tension loading. Thin-Walled Struct. 2015, 93, 149–157. [Google Scholar] [CrossRef]
- Zhao, X.-L. Fatigue Design Procedure for Welded Hollow Section Joints; Abington Publishing: Lisbon, TN, USA, 1999. [Google Scholar]
- Zhao, X.-L.; Herion, S.; Ja, P. Design Guide for Circular and Rectangular Hollow Section Joints under Fatigue Loading; CIDECT Publication: TUV-Verlag, Germany, 2000. [Google Scholar]
- DNV-RP-C203 2011; Det Norske Veritas. Fatigue Design of Offshore Steel Structures. p. 176. Available online: https://www.dnv.com/oilgas/download/dnv-rp-c203-fatigue-design-of-offshore-steel-structures/ (accessed on 6 May 2024).
- Xiao, L.; Wei, X.; Zhao, J.; Wu, C. Hot spot stress concentration factor of CFST T/Y joints based on modified equivalent thickness. Structure 2023, 51, 910–925. [Google Scholar] [CrossRef]
- Zheng, J.; Nakamura, S.; Ge, Y.; Chen, K.; Wu, Q. Formulation of stress concentration factors for concrete-filled steel tubular (CFST) T-joints under axial force in the brace. Eng. Struct. 2018, 170, 103–117. [Google Scholar] [CrossRef]
- Zheng, J.; Nakamura, S.; Okumatsu, T.; Nishikawa, T. Formulation of stress concentration factors for concrete-filled steel tubular (CFST) K-joints under three loading conditions without shear forces. Eng. Struct. 2019, 190, 90–100. [Google Scholar] [CrossRef]
- Tong, L.; Xu, G.; Zhao, X.-L.; Zhou, H.; Xu, F. Experimental and theoretical studies on reducing hot spot stress on CHS gap K-joints with CFRP strengthening. Eng. Struct. 2019, 201, 109827. [Google Scholar] [CrossRef]
- JGJ 81-2002, J; Technical Specification for Welding of Steel Structure of Building. China Standards Press: Beijing, China, 2002.
- ISO-6892-1; Metallic Materials—Tensile Testing—Part 1: Method of Test at Room Temperature. ISO: Geneva, Switzerland, 2019.
- Huang, Y.; Young, B. The art of coupon tests. J. Constr. Steel Res. 2014, 96, 159–175. [Google Scholar] [CrossRef]
- GB/T50081; Standard for Test Methods of Concrete Physical and Mechanical Properties. China Architecture & Building Press: Beijing, China, 2019.
- Shao, Y.B. Geometrical effect on the stress distribution along weld toe for tubular T- and K-joints under axial loading. J. Constr. Steel Res. 2007, 63, 1351–1360. [Google Scholar] [CrossRef]
- Shao, Y.B.; Lie, S.-T. Experimental and numerical studies of the stress concentration factor (SCF) of tubular K-joints. Eng. Mech. 2006, 23, 79–85. [Google Scholar]
- Van Wingerde, A.M.; Packer, J.A.; Wardenier, J. Criteria for the fatigue assessment of hollow structural section connections. J. Constr. Steel Res. 1995, 35, 71–115. [Google Scholar] [CrossRef]
- D1.1—Structural Welding Code-Steel; American Welding Society: Miami, FL, USA, 2004; p. 634.
- Shen, J.C. Fatigue Performance of CFDST Members under Bending. Master’s Thesis, Tsinghua University, Beijing, China, 2022. [Google Scholar]
- Hai, H.L. Concrete-Filled Steel Tubular Structures: Theory and Practice, 3rd ed.; Science Press: Beijing, China, 2016. [Google Scholar]
- Xu, F. Mechanical Behaviour of Concrete-Filled Thin-Walled Steel Tube Members and Connections. Ph.D. Thesis, Zhejiang University, Hangzhou, China, 2016. [Google Scholar]
- Mohamed, H.; Zhang, L.; Shao, Y.; Yang, X.; Shaheen, M.; Suleiman, M. Stress concentration factors of CFRP-reinforced tubular K-joints via zero point structural stress approach. Mar. Struct. 2022, 84, 103239. [Google Scholar] [CrossRef]
- Tong, L.W.; Xu, G.W.; Yang, D.L.; Mashiri, F.R.; Zhao, X.L. Fatigue behavior and design of welded tubular T-joints with CHS brace and concrete-filled chord. Thin-Walled Struct. 2017, 120, 180–190. [Google Scholar] [CrossRef]
- Li, W.; Cheng, Y.-F.; Wang, D.; Han, L.-H.; Zhao, X.-L. Behaviour of high-strength CFDST chord to CHS brace T-joint: Experiment. Eng. Struct. 2020 219, 110780. [CrossRef]
- Tong, L.; Xu, G.; Zhao, X.-L.; Yan, Y. Fatigue tests and design of CFRP-strengthened CHS gap K-joints. Thin-Walled Struct. 2021, 163, 107694. [Google Scholar] [CrossRef]
- Recommended Practice for Planning, Desigining and Constructing Fixed Offshore Plaforms; American Petroleum Institute: Washington, DC, USA, 1993; p. 274.
- Smedley, P.; Fisher, P. Stress concentration factors for simple tubular joints. In Proceedings of the ISOPE International Ocean and Polar Engineering Conference, Edinburgh, UK, 11–16 August 1991. [Google Scholar]
- Background Notes to the Fatigue Guidance of Offshore Tubular Joints; United Kingdom Department of Energy: London, UK, 1983; p. 123.
- Bomel Consulting Engineers. Assessment of SCF Equations Using Shell/KSEPL Finite Element Data. C5970R0201 REV C. 1994. Available online: http://refhub.elsevier.com/S0951-8339(22)00078-8/sref52 (accessed on 6 May 2024).
- Qiu, C.F. Study on Hot Spot Stress of Concrete-Filled Tubular T-Joints and Y-Joints. Master’s Thesis, Xihua University, Chengdu, China, 2021. [Google Scholar]
Number | L | l | D | D1 | d | T | T1 | t | α | β | γ | τ | ζ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm | mm | mm | mm | mm | mm | mm | mm | ||||||
OC300-6-IC0-0-BR168-8-1 | 1800 | 485 | 300 | - | 168 | 6 | - | 8 | 12 | 0.56 | 25.00 | 1.33 | - |
OC300-6-IC0-0-BR168-8-2 | 1800 | 485 | 300 | - | 168 | 6 | - | 8 | 12 | 0.56 | 25.00 | 1.33 | - |
OC300-6-IC203-8-BR121-8 | 1800 | 485 | 300 | 203 | 121 | 6 | 8 | 8 | 12 | 0.40 | 25.00 | 1.33 | 0.715 |
OC300-10-IC203-8-BR102-14 | 1800 | 485 | 300 | 203 | 102 | 10 | 8 | 14 | 12 | 0.34 | 15.00 | 1.40 | 0.725 |
OC300-5-IC180-5-BR121-8 | 1800 | 485 | 300 | 180 | 121 | 5 | 5 | 8 | 12 | 0.40 | 30.00 | 1.60 | 0.621 |
Member | Parameter | lt/mm | lr/mm | lg/mm | lc/mm | R/mm | t/mm | wg/mm | wc/mm | Rh/mm | lh/mm | Number |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Brace | 168 × 8 | 214 | 15.0 | 64 | 60 | 15 | 8 | 10 | 35 | 6 | 30 | 2 |
121 × 8 | 214 | 15.0 | 64 | 60 | 15 | 8 | 10 | 35 | 6 | 30 | 2 | |
102 × 14 | 213.6 | 14.8 | 64 | 60 | 15 | 14 | 6 | 30 | 6 | 30 | 2 | |
203 × 8 | 214 | 15.0 | 64 | 60 | 15 | 8 | 10 | 35 | 6 | 30 | 2 | |
180 × 5 | 214 | 15.0 | 64 | 60 | 15 | 5 | 16 | 45 | 6 | 30 | 2 | |
Chord | 300 × 5 | 214 | 15.0 | 64 | 60 | 15 | 5 | 16 | 45 | 6 | 30 | 2 |
300 × 6 | 214 | 15.0 | 64 | 60 | 15 | 6 | 13 | 40 | 6 | 30 | 2 | |
300 × 10 | 213 | 14.5 | 64 | 60 | 15 | 10 | 8 | 30 | 6 | 30 | 2 |
Stage | Strain Rate/s−1 |
---|---|
Elastic stage | 0.000017 |
Yield plateau stage | 0.00005 |
Strain hardening stage | 0.0002 |
Necking stage | 0.00033 |
Member | Specimen | Elastic Modulus/GPa | Yield Strength/MPa | Ultimate Strength/MPa |
---|---|---|---|---|
Chord | 300 × 5-1 | 220.72 | 435.79 | 582.86 |
300 × 5-2 | 223.37 | 435.71 | 571.33 | |
300 × 6-1 | 200.76 | 405.37 | 559.31 | |
300 × 6-2 | 197.37 | 394.75 | 556.34 | |
300 × 10-1 | 217.14 | 451.91 | 583.88 | |
300 × 10-2 | 213.15 | 449.59 | 586.35 | |
Brace | 121 × 8-1 | 215.64 | 371.00 | 563.29 |
121 × 8-2 | 191.20 | 366.50 | 555.17 | |
203 × 8-1 | 199.53 | 427.83 | 591.27 | |
203 × 8-2 | 192.77 | 418.07 | 588.33 | |
102 × 14-1 | 230.66 | 347.06 | 546.45 | |
102 × 14-2 | 228.12 | 349.93 | 538.35 | |
180 × 5-1 | 231.44 | 361.26 | 576.74 | |
180 × 5-2 | 228.11 | 364.41 | 581.39 | |
168 × 8-1 | 226.83 | 389.49 | 553.76 | |
168 × 8-2 | 238.97 | 392.26 | 560.36 |
Cement | Water | Fine Aggregate | Coarse Aggregate | Fly Ash | Water Reducer |
---|---|---|---|---|---|
392 | 145.6 | 681.5 | 1036.2 | 168 | 5.6 |
Specimen No. | Tensile Side | Compressive Side | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0° | 45° | 90° | 135° | 180° | 0° | 45° | 90° | 135° | 180° | ||
OC300−6−IC0−0−BR168−8−1 | Chord | 1.19 | 3.80 | 5.53 | 5.67 | 3.12 | 2.36 | 5.75 | 8.47 | 6.95 | 6.23 |
Brace | 0.46 | 0.97 | 2.13 | 2.30 | 1.72 | 0.34 | 2.02 | 2.47 | 1.87 | 1.80 | |
OC300−6−IC0−0−BR168−8−2 | Chord | 1.23 | 4.12 | 6.16 | 5.73 | 3.08 | 2.39 | 4.80 | 9.00 | 8.08 | 5.82 |
Brace | 0.51 | 1.15 | 2.46 | 2.33 | 1.59 | 0.29 | 1.65 | 2.85 | 2.25 | 1.50 | |
OC300−6−IC203−8−BR121−8 | Chord | −1.16 | −0.52 | 3.68 | 8.70 | 10.47 | −2.26 | −0.78 | 4.27 | 8.40 | 10.77 |
Brace | 0.32 | 0.47 | 0.63 | 0.94 | 3.26 | 0.58 | 1.81 | 2.26 | 2.09 | 3.54 | |
OC300−10−IC203−8−BR102−14 | Chord | −1.05 | 1.66 | 4.00 | 4.96 | 5.62 | 0.42 | 2.65 | 5.32 | 5.71 | 6.66 |
Brace | 0.45 | 0.59 | 0.69 | 1.75 | 2.80 | 0.33 | 1.26 | 1.66 | 2.41 | 2.65 | |
OC300−5−IC180−5−BR121−8 | Chord | 0.82 | 1.76 | 5.33 | 13.39 | 10.70 | 2.33 | 4.48 | 13.53 | 14.10 | 13.71 |
Brace | −0.05 | 0.49 | 0.93 | 1.58 | 4.30 | −0.45 | 1.34 | 2.59 | 2.69 | 4.16 |
No. | SCFFE | SCFTest | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Tensile Side | 0° | 45° | 90° | 135° | 180° | 0° | 45° | 90° | 135° | 180° | |
OC300−6−IC0−0−BR168−8−1 | Chord | 1.13 | 2.86 | 7.16 | 5.09 | 3.89 | 1.19 | 3.80 | 5.53 | 5.67 | 3.12 |
Brace | 0.09 | 1.01 | 2.44 | 2.14 | 1.19 | 0.46 | 0.97 | 2.13 | 2.30 | 1.72 | |
OC300−6−IC0−0−BR168−8−2 | Chord | 1.13 | 2.86 | 7.16 | 5.09 | 3.89 | 1.23 | 4.12 | 6.16 | 5.73 | 3.08 |
Brace | 0.09 | 1.01 | 2.44 | 2.14 | 1.19 | 0.51 | 1.15 | 2.46 | 2.33 | 1.59 | |
OC300−6−IC203−8−BR121−8 | Chord | −1.95 | −0.83 | 5.22 | 7.35 | 11.38 | −1.16 | −0.52 | 3.68 | 8.70 | 10.47 |
Brace | 0.19 | 0.42 | 0.52 | 1.17 | 3.40 | 0.32 | 0.47 | 0.63 | 0.94 | 3.26 | |
OC300−10−IC203−8−BR102−14 | Chord | −0.15 | 1.02 | 3.63 | 3.86 | 5.24 | −1.05 | 1.66 | 4.00 | 4.96 | 5.62 |
Brace | 0.55 | 0.71 | 0.84 | 1.68 | 2.95 | 0.45 | 0.59 | 0.69 | 1.75 | 2.80 | |
OC300−5−IC180−5−BR121−8 | Chord | 0.64 | 2.20 | 6.62 | 15.89 | 10.47 | 0.82 | 1.76 | 5.33 | 13.39 | 10.70 |
Brace | −0.06 | 0.50 | 0.81 | 1.44 | 3.82 | −0.05 | 0.49 | 0.93 | 1.58 | 4.30 | |
Compressive side | 0° | 45° | 90° | 135° | 180° | 0° | 45° | 90° | 135° | 180° | |
OC300−6−IC0−0−BR168−8−1 | Chord | 2.50 | 3.58 | 7.69 | 6.51 | 5.79 | 2.36 | 5.75 | 8.47 | 6.95 | 6.23 |
Brace | 0.15 | 1.47 | 2.79 | 2.39 | 1.13 | 0.34 | 2.02 | 2.47 | 1.87 | 1.80 | |
OC300−6−IC0−0−BR168−8−2 | Chord | 2.50 | 3.58 | 7.69 | 6.51 | 5.79 | 2.39 | 4.80 | 9.00 | 8.08 | 5.82 |
Brace | 0.15 | 1.47 | 2.79 | 2.39 | 1.13 | 0.29 | 1.65 | 2.85 | 2.25 | 1.50 | |
OC300−6−IC203−8−BR121−8 | Chord | −1.32 | −1.00 | 4.86 | 7.10 | 11.37 | −2.26 | −0.78 | 4.27 | 8.40 | 10.77 |
Brace | 0.21 | 1.31 | 1.82 | 2.12 | 3.47 | 0.58 | 1.81 | 2.26 | 2.09 | 3.54 | |
OC300−10−IC203−8−BR102−14 | Chord | 1.44 | 2.55 | 5.11 | 5.71 | 6.85 | 0.42 | 2.65 | 5.32 | 5.71 | 6.66 |
Brace | 0.37 | 1.47 | 1.64 | 2.24 | 3.14 | 0.33 | 1.26 | 1.66 | 2.41 | 2.65 | |
OC300−5−IC180−5−BR121−8 | Chord | 1.82 | 5.21 | 9.44 | 14.35 | 13.64 | 2.33 | 4.48 | 13.53 | 14.10 | 13.71 |
Brace | −0.35 | 1.36 | 2.06 | 2.13 | 3.29 | −0.45 | 1.34 | 2.59 | 2.69 | 4.16 |
No. | SCFFE/SCFTest | Average | CV | |||||
---|---|---|---|---|---|---|---|---|
Tensile Side | 0° | 45° | 90° | 135° | 180° | |||
OC300-6-IC0-0-BR168-8-1 | Chord | 0.95 | 0.75 | 1.29 | 0.90 | 1.25 | 1.05 | 0.22 |
Brace | 0.20 | 1.04 | 1.15 | 0.93 | 0.69 | 0.95 | 0.14 | |
OC300-6-IC0-0-BR168-8-2 | Chord | 0.92 | 0.69 | 1.16 | 0.89 | 1.26 | 1.00 | 0.21 |
Brace | 0.18 | 0.88 | 0.99 | 0.92 | 0.75 | 0.88 | 0.07 | |
OC300-6-IC203-8-BR121-8 | Chord | 1.68 | 1.60 | 1.42 | 0.84 | 1.09 | 1.24 | 0.27 |
Brace | 0.59 | 0.89 | 0.83 | 1.24 | 1.04 | 1.00 | 0.14 | |
OC300-10-IC203-8-BR102-14 | Chord | 0.14 | 0.61 | 0.91 | 0.78 | 0.93 | 0.81 | 0.11 |
Brace | 1.22 | 1.20 | 1.22 | 0.96 | 1.05 | 1.11 | 0.10 | |
OC300-5-IC180-5-BR121-8 | Chord | 0.78 | 1.25 | 1.24 | 1.19 | 0.98 | 1.16 | 0.09 |
Brace | 1.20 | 1.02 | 0.87 | 0.91 | 0.89 | 0.92 | 0.05 | |
Compressive side | 0° | 45° | 90° | 135° | 180° | |||
OC300-6-IC0-0-BR168-8-1 | Chord | 1.06 | 0.62 | 0.91 | 0.94 | 0.93 | 0.85 | 0.11 |
Brace | 0.44 | 0.73 | 1.13 | 1.28 | 0.63 | 0.94 | 0.26 | |
OC300-6-IC0-0-BR168-8-2 | Chord | 1.05 | 0.75 | 0.85 | 0.81 | 0.99 | 0.85 | 0.07 |
Brace | 0.52 | 0.89 | 0.98 | 1.06 | 0.75 | 0.92 | 0.10 | |
OC300-6-IC203-8-BR121-8 | Chord | 0.58 | 1.28 | 1.14 | 0.85 | 1.06 | 1.08 | 0.13 |
Brace | 0.36 | 0.72 | 0.81 | 1.01 | 0.98 | 0.88 | 0.12 | |
OC300-10-IC203-8-BR102-14 | Chord | 3.43 | 0.96 | 0.96 | 1.00 | 1.03 | 0.99 | 0.03 |
Brace | 1.12 | 1.17 | 0.99 | 0.93 | 1.18 | 1.07 | 0.11 | |
OC300-5-IC180-5-BR121-8 | Chord | 0.78 | 1.16 | 0.70 | 1.02 | 0.99 | 0.97 | 0.14 |
Brace | 0.78 | 1.01 | 0.80 | 0.79 | 0.79 | 0.85 | 0.08 |
Joint | Number | Variable | D | D1 | d | T | T1 | t | d/D | D/2T | t/T | θ | ζ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CHS K-joints | K-FE-1 | β = d/D | 300 | - | 60 | 8 | - | 8 | 0.2 | 18.75 | 1 | 45 | - |
K-FE-2 | 300 | - | 90 | 8 | - | 8 | 0.3 | 18.75 | 1 | 45 | - | ||
K-FE-3 | 300 | - | 120 | 8 | - | 8 | 0.4 | 18.75 | 1 | 45 | - | ||
K-FE-4 | 300 | - | 150 | 8 | - | 8 | 0.5 | 18.75 | 1 | 45 | - | ||
K-FE-5 | 300 | - | 180 | 8 | - | 8 | 0.6 | 18.75 | 1 | 45 | - | ||
K-FE-6 | 300 | - | 210 | 8 | - | 8 | 0.7 | 18.75 | 1 | 45 | - | ||
K-FE-7 | 300 | - | 240 | 8 | - | 8 | 0.8 | 18.75 | 1 | 45 | - | ||
K-FE-8 | γ = D/2T | 300 | - | 120 | 4 | - | 4 | 0.4 | 37.5 | 1 | 45 | - | |
K-FE-9 | 300 | - | 120 | 5 | - | 5 | 0.4 | 30 | 1 | 45 | - | ||
K-FE-10 | 300 | - | 120 | 6 | - | 6 | 0.4 | 25 | 1 | 45 | - | ||
K-FE-11 | 300 | - | 120 | 10 | - | 10 | 0.4 | 15 | 1 | 45 | - | ||
K-FE-12 | 300 | - | 120 | 12 | - | 12 | 0.4 | 12.5 | 1 | 45 | - | ||
K-FE-13 | 300 | - | 120 | 14 | - | 14 | 0.4 | 10.71 | 1 | 45 | - | ||
K-FE-14 | 300 | - | 120 | 16 | - | 16 | 0.4 | 9.38 | 1 | 45 | - | ||
K-FE-15 | τ = t/T | 300 | - | 120 | 8 | - | 4 | 0.4 | 18.75 | 0.5 | 45 | - | |
K-FE-16 | 300 | - | 120 | 8 | - | 6 | 0.4 | 18.75 | 0.75 | 45 | - | ||
K-FE-17 | 300 | - | 120 | 8 | - | 10 | 0.4 | 18.75 | 1.25 | 45 | - | ||
K-FE-18 | 300 | - | 120 | 8 | - | 12 | 0.4 | 18.75 | 1.5 | 45 | - | ||
K-FE-19 | θ | 300 | - | 120 | 8 | - | 8 | 0.4 | 18.75 | 1 | 30 | - | |
K-FE-20 | 300 | - | 120 | 8 | - | 8 | 0.4 | 18.75 | 1 | 40 | - | ||
K-FE-21 | 300 | - | 120 | 8 | - | 8 | 0.4 | 18.75 | 1 | 50 | - | ||
K-FE-22 | 300 | - | 120 | 8 | - | 8 | 0.4 | 18.75 | 1 | 60 | - | ||
CFDST K-joints | K-FE-23 | β = d/D | 300 | 260 | 60 | 8 | 4 | 8 | 0.2 | 18.75 | 1 | 45 | 0.915 |
K-FE-24 | 300 | 260 | 90 | 8 | 4 | 8 | 0.3 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-25 | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-26 | 300 | 260 | 150 | 8 | 4 | 8 | 0.5 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-27 | 300 | 260 | 180 | 8 | 4 | 8 | 0.6 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-28 | 300 | 260 | 210 | 8 | 4 | 8 | 0.7 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-29 | 300 | 260 | 240 | 8 | 4 | 8 | 0.8 | 18.75 | 1 | 45 | 0.915 | ||
K-FE-30 | γ = D/2T | 300 | 267.32 | 120 | 4 | 4 | 4 | 0.4 | 37.5 | 1 | 45 | 0.915 | |
K-FE-31 | 300 | 265.49 | 120 | 5 | 4 | 5 | 0.4 | 30 | 1 | 45 | 0.915 | ||
K-FE-32 | 300 | 263.66 | 120 | 6 | 4 | 6 | 0.4 | 25 | 1 | 45 | 0.915 | ||
K-FE-33 | 300 | 256.34 | 120 | 10 | 4 | 10 | 0.4 | 15 | 1 | 45 | 0.915 | ||
K-FE-34 | 300 | 252.68 | 120 | 12 | 4 | 12 | 0.4 | 12.5 | 1 | 45 | 0.915 | ||
K-FE-35 | 300 | 249.01 | 120 | 14 | 4 | 14 | 0.4 | 10.71 | 1 | 45 | 0.915 | ||
K-FE-36 | 300 | 245.35 | 120 | 16 | 4 | 16 | 0.4 | 9.38 | 1 | 45 | 0.915 | ||
K-FE-37 | τ = t/T | 300 | 260 | 120 | 8 | 4 | 4 | 0.4 | 18.75 | 0.5 | 45 | 0.915 | |
K-FE-38 | 300 | 260 | 120 | 8 | 4 | 6 | 0.4 | 18.75 | 0.75 | 45 | 0.915 | ||
K-FE-39 | 300 | 260 | 120 | 8 | 4 | 10 | 0.4 | 18.75 | 1.25 | 45 | 0.915 | ||
K-FE-40 | 300 | 260 | 120 | 8 | 4 | 12 | 0.4 | 18.75 | 1.5 | 45 | 0.915 | ||
K-FE-41 | θ | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 30 | 0.915 | |
K-FE-42 | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 40 | 0.915 | ||
K-FE-43 | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 50 | 0.915 | ||
K-FE-44 | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 60 | 0.915 | ||
K-FE-45 | ζ | 300 | 260 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.915 | |
K-FE-46 | 300 | 230 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.81 | ||
K-FE-47 | 300 | 200 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.704 | ||
K-FE-48 | 300 | 170 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.599 | ||
K-FE-49 | 300 | 140 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.493 | ||
K-FE-50 | 300 | 120 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.423 | ||
K-FE-51 | 300 | 90 | 120 | 8 | 4 | 8 | 0.4 | 18.75 | 1 | 45 | 0.317 |
No. | Evaluation Criteria | Conclusion | Correction Factor | ||||
---|---|---|---|---|---|---|---|
P/R < 0.8 | P/R > 1.5 | ||||||
Previous | Subsequent | Previous | Subsequent | Previous | Subsequent | ||
Equation (43) | 13.9% > 5% | 3.6% < 5% | 2.2% < 50% | 12.4% < 50% | Needs Correction | Satisfy | 1.216 |
Equation (44) | 16.5% > 5% | 4.8% < 5% | 9.6% < 50% | 23.2% < 50% | Needs Correction | Satisfy | 1.283 |
Specimen No. | Name of the Specimen in the Literature | Type | Literature | D | α | β | γ | τ | θ | ζ |
---|---|---|---|---|---|---|---|---|---|---|
S1 | OC300-6-IC0-0-BR168-8-1 | K | This study | 300 | 12 | 0.56 | 25.00 | 1.33 | 45 | |
S2 | OC300-6-IC0-0-BR168-8-2 | K | This study | 300 | 12 | 0.56 | 25.00 | 1.33 | 45 | |
S3 | OC300-6-IC203-8-BR121-8 | K | This study | 300 | 12 | 0.40 | 25.00 | 1.33 | 45 | 0.715 |
S4 | OC300-10-IC203-8-BR102-14 | K | This study | 300 | 12 | 0.34 | 15.00 | 1.40 | 45 | 0.725 |
S5 | OC300-5-IC180-5-BR121-8 | K | This study | 300 | 12 | 0.40 | 30.00 | 1.60 | 45 | 0.621 |
S6 | K1-13 | K | Tong et al. [36] | 219 | 16.27 | 0.58 | 13.32 | 0.76 | 45 | |
S7 | K2-23 | K | 219 | 16.27 | 0.58 | 18.25 | 0.75 | 45 | ||
S8 | K3-23 | K | 219 | 16.27 | 0.58 | 13.69 | 1.01 | 45 | ||
S9 | K4-23 | K | 219 | 16.27 | 0.41 | 18.25 | 0.75 | 45 | ||
S10 | K | Eq. Efthymiou [19,39] | 600 | 15.00 | 0.60 | 15.00 | 0.60 | 30 | ||
S11 | K | 600 | 15.00 | 0.40 | 20.00 | 0.60 | 45 | |||
S12 | K | 600 | 15.00 | 0.80 | 15.00 | 0.60 | 45 | |||
S13 | K | Eq. LR [40] | 600 | 15.00 | 0.60 | 25.00 | 0.40 | 45 | ||
S14 | K | 600 | 15.00 | 0.80 | 20.00 | 0.80 | 45 | |||
S15 | K | 600 | 15.00 | 0.60 | 15.00 | 0.60 | 60 | |||
S16 | K | API [39], DNV [19] | 300 | 15.00 | 0.40 | 18.75 | 1.00 | 45 | 1.000 | |
S17 | K | 300 | 15.00 | 0.60 | 18.75 | 1.00 | 45 | 1.000 | ||
S18 | K | 300 | 15.00 | 0.40 | 15.00 | 1.00 | 45 | 1.000 | ||
S19 | K | 300 | 15.00 | 0.40 | 10.71 | 1.00 | 45 | 1.000 |
Specimen No. | SCFeq | SCF Efthymiou | SCFLR | SCFAPI | SCFDNV | SCFTest |
---|---|---|---|---|---|---|
S1 | 7.23 | 6.83 | 10.49 | 8.47 | ||
S2 | 7.23 | 6.83 | 10.49 | 9.00 | ||
S3 | 6.65 | 2.43 | 5.17 | 10.47 | ||
S4 | 5.21 | 1.79 | 3.11 | 5.62 | ||
S5 | 8.48 | 2.64 | 7.62 | 13.39 | ||
S6 | 2.52 | 3.00 | 3.57 | 4.96 | ||
S7 | 3.49 | 3.47 | 4.39 | 4.14 | ||
S8 | 3.73 | 3.93 | 4.79 | 5.83 | ||
S9 | 3.59 | 3.48 | 4.63 | 4.57 | ||
S10 | 3.15 | 2.57 | 2.52 | |||
S11 | 3.26 | 2.97 | 4.07 | |||
S12 | 2.11 | 2.39 | 2.55 | |||
S13 | 3.16 | 2.30 | 3.10 | |||
S14 | 3.90 | 3.58 | 4.43 | |||
S15 | 3.63 | 2.57 | 3.75 | |||
S16 | 3.90 | 2.08 | ||||
S17 | 4.13 | 2.07 | ||||
S18 | 3.58 | 2.22 | ||||
S19 | 3.11 | 2.36 |
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Xia, Q.; Ma, L.; Li, G.; Hu, C.; Zhang, L.; Xu, F.; Liu, Z. Stress Concentration Factors of Concrete-Filled Double-Skin Tubular K-Joints. Buildings 2024, 14, 1363. https://doi.org/10.3390/buildings14051363
Xia Q, Ma L, Li G, Hu C, Zhang L, Xu F, Liu Z. Stress Concentration Factors of Concrete-Filled Double-Skin Tubular K-Joints. Buildings. 2024; 14(5):1363. https://doi.org/10.3390/buildings14051363
Chicago/Turabian StyleXia, Qian, Ling Ma, Gang Li, Chao Hu, Lei Zhang, Fei Xu, and Zhenhai Liu. 2024. "Stress Concentration Factors of Concrete-Filled Double-Skin Tubular K-Joints" Buildings 14, no. 5: 1363. https://doi.org/10.3390/buildings14051363