Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639

Wang, Yixun; Luo, Yuxiao; Tsutsumi, Seiichiro

doi:10.3390/ma14092433

Open AccessCorrection

Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639

by

Yixun Wang

¹

,

Yuxiao Luo

² and

Seiichiro Tsutsumi

^1,*

¹

Joining and Welding Research Institute, Osaka University, Osaka 567-0047, Japan

²

Department of Structural Engineering, Tongji University, Shanghai 200092, China

^*

Author to whom correspondence should be addressed.

Materials 2021, 14(9), 2433; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14092433

Submission received: 30 March 2021 / Accepted: 28 April 2021 / Published: 7 May 2021

(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)

Download Versions Notes

The authors wish to revise the following from pages 16–18 in the text of Appendix B [1] due to the presence of incorrect information.

The correct text is shown below:

Appendix B

Formulas for calculating SCFs for T-shape welded joint and cruciform welded joint under tensile and bending stress.

(1): T-shape welded joint under tensile stress:

$K_{t} = 1 + 1.39418 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1}))$

(A5)

where:

$\begin{array}{l} f (r_{1} / t) = & 1.824174 \cdot {(r_{1} / t)}^{- 0.145045} + 6.400210 \cdot {(r_{1} / t)}^{3} - 6.802011 \cdot {(r_{1} / t)}^{2} + 3.277059 \cdot (r_{1} / t) \\ - 2.692331 \end{array}$

$f (θ_{1}) = - 2.778232 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} + 1.531999 \cdot {(π - θ_{1})}^{2} - 3.394907 \cdot (π - θ_{1}) + 4.967130$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & - 1.001612 \times 10^{1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + 1.279269 \times 10^{1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} \\ + 5.761117 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.181649 \end{array}$
(2): T-shape welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 - 1.129553 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \\ \cdot f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A6)

where:

$f (T / t) = - 9.622916 \times 10^{- 3} \cdot {(T / t)}^{3} - 3.157009 \times 10^{- 2} \cdot {(T / t)}^{2} + 1.848086 \times 10^{- 1} \cdot (T / t) + 2.433139$

$\begin{array}{l} f (r_{1} / t) = & 6.477191 \times 10^{- 1} \cdot {(r_{1} / t)}^{- 0.258620} + 2.860640 \cdot {(r_{1} / t)}^{3} - 3.689862 \cdot {(r_{1} / t)}^{2} \\ + 2.089786 \cdot (r_{1} / t) - 1.238719 \end{array}$

$\begin{array}{l} f (θ_{1}) = & 3.450624 \times 10^{- 3} \cdot {(π - θ_{1})}^{3} - 3.531382 \times 10^{- 2} \cdot {(π - θ_{1})}^{2} + 6.008736 \times 10^{- 2} \cdot (π - θ_{1}) \\ + 8.576512 \times 10^{- 2} \end{array}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 3.532021 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{5.127981} - 8.442514 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ + 8.645182 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 1.481668 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 3.814145 \times 10^{- 1} \end{array}$

$\begin{array}{l} f (L_{1} / t) = & - 1 . 140609 \times 10^{1} \cdot {(L_{1} / t)}^{3.036113} + 7.436459 \times 10^{- 2} \cdot {(L_{1} / t)}^{4} + 1.188223 \times 10^{1} \cdot {(L_{1} / t)}^{3} \\ - 8 . 150334 \times 10^{- 1} \cdot {(L_{1} / t)}^{2} + 2 . 933742 \times 10^{- 1} \cdot (L_{1} / t) + 2 . 718308 \times 10^{- 2} \end{array}$

$\begin{array}{l} f (L_{2} / t) = & 1.919634 \times 10^{1} \cdot {(L_{2} / t)}^{- 0.1508265} - 7.315526 \times 10^{- 1} \cdot {(L_{2} / t)}^{4} + 4.967357 \cdot {(L_{2} / t)}^{3} \\ - 8.382442 \cdot {(L_{2} / t)}^{2} - 5.482638 \cdot (L_{2} / t) + 4.359819 \times 10^{1} \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 1.823407 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 1.469586 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ - 5.862377 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 8.301064 \end{array}$

$f (H / t) = - 1.913752 \times 10^{1} \cdot {(H / t)}^{3} + 7.690410 \cdot {(H / t)}^{2} - 5.994878 \times 10^{- 1} \cdot (H / t) + 1.201826$
(3): Cruciform welded joint under tensile stress:

$\begin{array}{l} K_{t} = & 1 + 9.355385 \times 10^{- 1} \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A7)

where:

$f (T / t) = - 4.241098 \times 10^{- 1} \cdot {(T / t)}^{3} + 1.392836 \cdot {(T / t)}^{2} - 1.072866 \cdot (T / t) + 5.223873$

$\begin{array}{l} f (r_{1} / t) = & - 2.214616 \cdot {(r_{1} / t)}^{0.5081972} + 3.365455 \cdot {(r_{1} / t)}^{3} - 4.439046 \cdot {(r_{1} / t)}^{2} + 3.726006 \cdot (r_{1} / t) \\ + 4.033244 \times 10^{- 1} \end{array}$

$f (θ_{1}) = - 7.886656 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} + 2.966534 \cdot {(π - θ_{1})}^{2} - 5.878541 \cdot (π - θ_{1}) + 1.772818 \times 10^{1}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 1.557408 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{- 0.1158765} + 3.821716 {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ - 5.354226 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 7.153383 \cdot ((r_{1} / t) \cdot (π - θ_{1})) - 1.529427 \end{array}$

$\begin{array}{l} f (L_{1} / t) = & 8.158610 \cdot {(L_{1} / t)}^{1.944849} - 1.90075 \times 10^{- 2} \cdot {(L_{1} / t)}^{4} + 2.021235 \times 10^{- 1} \cdot {(L_{1} / t)}^{3} - 7.977936 \cdot {(L_{1} / t)}^{2} \\ - 4.569099 \times 10^{- 1} \cdot (L_{1} / t) + 1.108427 \times 10^{- 1} \end{array}$

$\begin{array}{l} f (L_{2} / t) = & 1.020926 \times 10^{1} \cdot {(L_{2} / t)}^{0.09585178} + 3.856400 \times 10^{- 1} \cdot {(L_{2} / t)}^{4} - 2.432551 \cdot {(L_{2} / t)}^{3} \\ + 6.069561 \cdot {(L_{2} / t)}^{2} - 8.045796 \cdot (L_{2} / t) - 5.364472 \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 2.421137 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 5.706142 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ - 2.159502 \times 10^{1} \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 2.240262 \end{array}$

$f (H / t) = 4.996101 \cdot {(H / t)}^{3} - 1.461031 \cdot {(H / t)}^{2} - 1.874919 \times 10^{- 1} \cdot (H / t) - 1.083093$
(4): Cruciform welded joint under bending stress:

$K_{t} = 1 + 1.20077 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot f ((L_{1} / t) \cdot (L_{2} / t))$

(A8)

where:

$f (r_{1} / t) = 1.245919 \cdot {(r_{1} / t)}^{- 0.1788861} + 5.187295 \cdot {(r_{1} / t)}^{3} - 5.888376 \cdot {(r_{1} / t)}^{2} + 2.948041 \cdot (r_{1} / t) - 2.024161$

$f (θ_{1}) = 4.518553 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} - 4.169720 \cdot {(π - θ_{1})}^{2} + 6.471859 \cdot (π - θ_{1}) + 1.232356 \times 10^{1}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 6.195167 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{1.958767} + 2.102936 \times 10^{- 1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ - 6.258362 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 4.307112 \times 10^{- 2} \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.578839 \times 10^{- 2} \end{array}$

$f (L_{1} / t) = 1.069048 \times 10^{- 1} \cdot {(L_{1} / t)}^{3} + 4.896665 \times 10^{- 1} \cdot {(L_{1} / t)}^{2} - 3.181390 \cdot (L_{1} / t) + 1.187674 \times 10^{1}$

$\begin{array}{l} f (L_{2} / t) = & 6.217977 \cdot {(L_{2} / t)}^{2.938345} + 8.220848 \times 10^{- 2} \cdot {(L_{2} / t)}^{4} - 5.872895 \cdot {(L_{2} / t)}^{3} - 5.835022 \times 10^{- 1} \cdot {(L_{2} / t)}^{2} \\ + 1.809699 \times 10^{- 1} \cdot (L_{2} / t) + 2.220297 \times 10^{- 2} \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 9.639892 \times 10^{- 2} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} - 2.213564 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ + 5.660853 \cdot ((L_{1} / t) \cdot (L_{2} / t)) + 3.300823 \times 10^{1} \end{array}$

The previously given text is shown below:

Appendix B

Formulas for calculating SCFs for T-shape welded joint and cruciform welded joint under tensile and bending stress.

(1): T-shape welded joint under tensile stress:

$K_{t} = 1 + 1.394 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1}))$

(A5)

where:

$f (r_{1} / t) = 1.824 \cdot {(r_{1} / t)}^{- 0.145} + 6.400 \cdot {(r_{1} / t)}^{3} - 6.802 \cdot {(r_{1} / t)}^{2} + 3.277 \cdot (r_{1} / t) - 2.692$

$f (θ_{1}) = - 0.278 \cdot {(π - θ_{1})}^{3} + 1.532 \cdot {(π - θ_{1})}^{2} - 3.395 \cdot (π - θ_{1}) + 4.967$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & - 10.016 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + 12.793 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 5.761 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.182 \end{array}$
(2): T-shape welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 - 1.130 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A6)

where:

$f (T / t) = - 0.010 \cdot {(T / t)}^{3} - 0.032 \cdot {(T / t)}^{2} + 0.185 \cdot (T / t) + 2.433$

$f (r_{1} / t) = 0.648 \cdot {(r_{1} / t)}^{- 0.259} + 2.861 \cdot {(r_{1} / t)}^{3} - 3.690 \cdot {(r_{1} / t)}^{2} + 2.090 \cdot (r_{1} / t) - 1.239$

$f (θ_{1}) = 0.003 \cdot {(π - θ_{1})}^{3} - 0.035 \cdot {(π - θ_{1})}^{2} + 0.060 \cdot (π - θ_{1}) + 0.086$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 3.532 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{5.128} - 8.443 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + \\ 8.645 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 1.482 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 0.381 \end{array}$

$f (L_{1} / t) = - 11.406 \cdot {(L_{1} / t)}^{3.036} + 0.074 \cdot {(L_{1} / t)}^{4} + 11.882 \cdot {(L_{1} / t)}^{3} - 0.815 \cdot {(L_{1} / t)}^{2} + 0.293 \cdot (L_{1} / t) + 0.027$

$f (L_{2} / t) = 19.196 \cdot {(L_{2} / t)}^{- 0.151} - 0.732 \cdot {(L_{2} / t)}^{4} + 4.967 \cdot {(L_{2} / t)}^{3} - 8.382 \cdot {(L_{2} / t)}^{2} - 5.483 \cdot (L_{2} / t) + 43.598$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.182 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 1.470 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} - 5.862 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 8.301$

$f (H / t) = - 19.138 \cdot {(H / t)}^{3} + 7.690 \cdot {(H / t)}^{2} - 0.599 \cdot (H / t) + 1.202$
(3): Cruciform welded joint under tensile stress:

$\begin{array}{l} K_{t} = & 1 + 0.936 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A7)

where:

$f (T / t) = - 0.424 \cdot {(T / t)}^{3} + 1.393 \cdot {(T / t)}^{2} - 1.073 \cdot (T / t) + 5.224$

$f (r_{1} / t) = - 2.215 \cdot {(r_{1} / t)}^{0.508} + 3.365 \cdot {(r_{1} / t)}^{3} - 4.439 \cdot {(r_{1} / t)}^{2} + 3.726 \cdot (r_{1} / t) + 0.403$

$f (θ_{1}) = - 0.789 \cdot {(π - θ_{1})}^{3} + 2.967 \cdot {(π - θ_{1})}^{2} - 5.879 \cdot (π - θ_{1}) + 17.728$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 1.557 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{- 0.116} + 3.822 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} - 5.354 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 7.153 \cdot ((r_{1} / t) \cdot (π - θ_{1})) - 1.529 \end{array}$

$f (L_{1} / t) = 8.159 \cdot {(L_{1} / t)}^{1.945} - 0.019 \cdot {(L_{1} / t)}^{4} + 0.202 \cdot {(L_{1} / t)}^{3} - 7.978 \cdot {(L_{1} / t)}^{2} - 0.457 \cdot (L_{1} / t) + 0.111$

$f (L_{2} / t) = 10.209 \cdot {(L_{2} / t)}^{0.096} + 0.386 \cdot {(L_{2} / t)}^{4} - 2.433 \cdot {(L_{2} / t)}^{3} + 6.070 \cdot {(L_{2} / t)}^{2} - 8.046 \cdot (L_{2} / t) - 5.364$

$f (H / t) = 4.996 \cdot {(H / t)}^{3} - 1.461 \cdot {(H / t)}^{2} - 0.187 \cdot (H / t) - 1.083$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.242 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 0.571 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} - 21.595 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 2.240$
(4): Cruciform welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 + 1.201 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \end{array}$

(A8)

where:

$f (r_{1} / t) = 1.246 \cdot {(r_{1} / t)}^{- 0.179} + 5.187 \cdot {(r_{1} / t)}^{3} - 5.888 \cdot {(r_{1} / t)}^{2} + 2.948 \cdot (r_{1} / t) - 2.024$

$f (θ_{1}) = 0.452 \cdot {(π - θ_{1})}^{3} - 4.170 \cdot {(π - θ_{1})}^{2} + 6.472 \cdot (π - θ_{1}) + 12.324$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 6.195 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{1.959} + 0.210 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} - 6.258 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 0.043 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 0.016 \end{array}$

$f (L_{1} / t) = 0.107 \cdot {(L_{1} / t)}^{3} + 0.490 \cdot {(L_{1} / t)}^{2} - 3.181 \cdot (L_{1} / t) + 11.877$

$f (L_{2} / t) = 6.218 \cdot {(L_{2} / t)}^{2.938} + 0.082 \cdot {(L_{2} / t)}^{4} - 5.873 \cdot {(L_{2} / t)}^{3} - 0.584 \cdot {(L_{2} / t)}^{2} + 0.181 \cdot (L_{2} / t) + 0.022$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.096 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} - 0.221 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} + 5.661 \cdot ((L_{1} / t) \cdot (L_{2} / t)) + 33.008$

The authors would like to apologize for any inconvenience caused to the readers by these changes.

Reference

Wang, Y.; Luo, Y.; Tsutsumi, S. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Wang, Y.; Luo, Y.; Tsutsumi, S. Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639. Materials 2021, 14, 2433. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14092433

AMA Style

Wang Y, Luo Y, Tsutsumi S. Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639. Materials. 2021; 14(9):2433. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14092433

Chicago/Turabian Style

Wang, Yixun, Yuxiao Luo, and Seiichiro Tsutsumi. 2021. "Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639" Materials 14, no. 9: 2433. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14092433

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639

Appendix B

Appendix B

Reference

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI