Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads
Abstract
:1. Introduction
2. Hot Spot Stress
2.1. Geometrical Details of T-Joints
2.2. Load Cases
2.3. Hot Spot Locations
2.4. Brief Introduction about SCFs in SHS-CFSHS Joints Subjected to Axial Force in the Brace
3. Finite Element Model and Validation
3.1. Establishment of Finite Element Models
3.2. Validation of Finite Element Models
4. Parametric Study and Proposed Design Equations
4.1. Parameter Selection
4.2. General Parametric Formulae for SCFs
4.3. SCF Formulae and Graphs for In-Plane Bending in the Brace
- (1)
- While keeping 2γ and τ constant, the parabola-like curves of SCFs can be found with the increase of β. The maximum SCFs are found for the medium β values.
- (2)
- While keeping β and τ constant, the higher the 2γ value, the higher the SCF, due to the higher bending deformation. For the higher 2γ value (2γ = 25.0), the maximum SCFs generally occur in the chord at lines B and C. For the lower 2γ value (2γ ≤ 16.0), comparable SCFs can be found in the chord and brace, thereby the SCFs at all the lines need to be checked.
- (3)
- While keeping β and 2γ constant, different influences of τ on the SCFs can be found. The higher the τ value, the lower the SCF in the brace, whereas it has opposite trend in the chord. Moreover, τ has less influence on the brace.
4.4. SCF Formulae and Graphs for Axial Force in the Chord
- (1)
- While keeping 2γ and τ constant, the SCFs increase with the increase of β values, which approximately keeps a linear relationship.
- (2)
- While keeping β constant, the higher the 2γ value and τ value, the higher the SCF at lines C and D.
- (3)
- All the non-dimensional parameters have less influence on the SCFs in the chord.
4.5. SCF Formulae and Graphs for In-Plane Bending in the Chord
- (1)
- The SCFs increase as the values of β and 2γ increase separately, similar to the conclusions of axial force in the chord. However, the SCFs are negatively correlated with τ, contrary to the axial force in the chord.
- (2)
- All the non-dimensional parameters have a much larger influence at line C compared with line D.
5. Comparisons of SCFs Derived from Formulae and FE Analysis
6. Comparisons of SCF Formulae between SHS-CFSHS T-Joints and Empty SHS T-Joints
7. Conclusions
- (1)
- A good agreement with the experimental results indicated that three-dimensional FE models developed by ABAQUS were accurate to capture the SCFs at all hot spot locations.
- (2)
- For in-plane bending in the brace, the maximum SCFs were found to occur at lines B and C for the tick-walled chord (2γ = 25.0). Meanwhile, for the thin-walled (2γ ≤ 16.0) chord, the SCFs at all the lines needed to be checked.
- (3)
- Under axial force in the chord and in-plane bending in the chord, only SCFs at lines C and D needed to be considered. There was a similar trend for SCFs which were positive which correlated with β and 2γ for both load cases. However, for in-plane bending in the chord, the SCFs were negatively correlated with τ, contrary to the axial force in the chord.
- (4)
- The comparisons of the SCFs derived from proposed formulae and the FE analysis indicated a good accuracy of multiple regression analysis. The proposed equations are applicable to the following range of parameters: 0.35 ≤ β ≤ 1.0; 12.5 ≤ 2γ ≤ 25.0 and 0.25 ≤ τ ≤ 1.0.
- (5)
- The comparisons of SCFs between SHS-CFSHS joints based on proposed formulae and empty SHS joints using CIDECT formulae were carried out. There were reductions of 10~26% and 14~31% in the SCFs in SHS-CFSHS joints compared to empty SHS joints for axial force in the brace and in-plane bending in the brace, respectively. In addition, a general increase was found for the loads in the chord. It should be noted that the SCFs caused by loads in the chord were much lower than those caused by loads in the brace.
- (6)
- This investigation focused on the SCF of SHS-CFSHS joints under the in-plane bending moment in the brace, axial force in the chord and the in-plane bending moment in the chord, and proposed corresponding design equations. The debonding between the concrete infill and steel tube should be considered in future work.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Types | Application Conditions | ω0 | ω1 |
---|---|---|---|
Butt weld | t1 > 8 mm | t1/2 | t1 |
Fillet weld | t1 ≤ 8 mm | ||
Weld for full width joints | full width joints | ≥3 mm | t1 |
Specimen No. | Chord Dimensions (mm) | Brace Dimensions (mm) | SCFEXP | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b0 | h0 | t0 | L0 | b1 | h1 | t1 | L1 | A | B | C | D | E | |
1 | 350 | 350 | 16 | 4130 | 250 | 250 | 16 | 2165 | 12.48 | 15.25 | 17.52 | 15.26 | 6.26 |
2 | 350 | 350 | 16 | 4130 | 200 | 200 | 16 | 2165 | 9.39 | 21.84 | 21.74 | 12.06 | 2.00 |
3 | 350 | 350 | 16 | 4130 | 200 | 200 | 12 | 2165 | 10.48 | 13.06 | 15.40 | 10.52 | 2.94 |
4 | 350 | 350 | 16 | 4130 | 200 | 200 | 10 | 2165 | 11.85 | 14.06 | 13.31 | 11.64 | 5.36 |
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Gao, L.; Jiang, L.; Wang, X.; Gao, S.; Cui, H.; Liu, J.; Zhou, H. Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads. Symmetry 2024, 16, 1082. https://doi.org/10.3390/sym16081082
Gao L, Jiang L, Wang X, Gao S, Cui H, Liu J, Zhou H. Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads. Symmetry. 2024; 16(8):1082. https://doi.org/10.3390/sym16081082
Chicago/Turabian StyleGao, Liyong, Lei Jiang, Xingzheng Wang, Sheng Gao, Hongxu Cui, Jun Liu, and Hekuan Zhou. 2024. "Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads" Symmetry 16, no. 8: 1082. https://doi.org/10.3390/sym16081082