Parametric equations for notch stress concentration factors of rib–deck welds under bending loading

doi:10.1007/s11709-021-0720-1

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (3) : 595-608 https://doi.org/10.1007/s11709-021-0720-1

RESEARCH ARTICLE

Parametric equations for notch stress concentration factors of rib–deck welds under bending loading

Qiudong WANG, Bohai JI(

), Zhongqiu FU, Yue YAO

College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China

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Abstract

The effective notch stress approach for evaluating the fatigue strength of rib–deck welds requires notch stress concentration factors obtained from complex finite element analysis. To improve the efficiency of the approach, the notch stress concentration factors for three typical fatigue-cracking modes (i.e., root–toe, root–deck, and toe–deck cracking modes) were thoroughly investigated in this study. First, we developed a model for investigating the effective notch stress in rib–deck welds. Then, we performed a parametric analysis to investigate the effects of multiple geometric parameters of a rib–deck weld on the notch stress concentration factors. On this basis, the multiple linear stepwise regression analysis was performed to obtain the optimal regression functions for predicting the notch stress concentration factors. Finally, we employed the proposed formulas in a case study. The notch stress concentration factors estimated from the developed formulas show agree well with the finite element analysis results. The results of the case study demonstrate the feasibility and reliability of the proposed formulas. It also shows that the fatigue design curve of FAT225 seems to be conservative for evaluating the fatigue strength of rib–deck welds.

Keywords notch stress concentration factor rib–deck weld parametric analysis regression analysis parametric equation

Corresponding Author(s): Bohai JI

Just Accepted Date: 12 May 2021 Online First Date: 13 July 2021 Issue Date: 14 July 2021

Cite this article:

Qiudong WANG,Bohai JI,Zhongqiu FU, et al. Parametric equations for notch stress concentration factors of rib–deck welds under bending loading[J]. Front. Struct. Civ. Eng., 2021, 15(3): 595-608.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0720-1
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I3/595

Fig.1 Fatigue stress at a weld.

Fig.2 Schematic of the model.

Fig.3 Finite element models with weld root or toe notch under bending loading. (a) Weld root notch; (b) weld toe notch.

Fig.4 Effect of meshing size on the effective notch stress.

Fig.5 Determination of the nominal stress points.

Fig.6 K_f based on different stresses.

Tab.1 Coefficients of the regression formula for K_f of full penetrated cruciform joints

Fig.7 Geometry of a full penetrated cruciform joint. Herein, t₁ = t₂ = 20 mm, L₁ = L₂ = 40 mm, l₁ = l₂ = 10 mm, α = 45°.

Fig.8 Nephogram of the first principle stress, including the boundary conditions.

Fig.9 Comparison of the FEA and estimated results. L₁ = L₂ = 40 mm, l₁ = l₂ = 10 mm, α = 45°.

Fig.10 Notch stress concentration positions obtained in this study. (a) Concentration position related to root–toe crack (CP1); (b) concentration position related to root–deck crack (CP2); (c) concentration position related to toe–deck crack (CP3).

Fig.11 Variation of effective notch stress concentration factor (K_f) at CP1 of weld root. (a) Effect of the weld penetration rate (1 − t_p/t_r) and rib thickness (t_r); (b) effect of the weld penetration rate (1 − t_p/t_r) and relative weld leg length in the deck (l_w,d/t_r); (c) effect of the weld penetration rate (1 − t_p/t_r) and relative weld leg length in the rib (l_w,r/t_r); (d) effect of the weld penetration rate (1 − t_p/t_r) and the angle between the deck and the rib (θ); (e) effect of the weld penetration rate (1 − t_p/t_r) and relative deck thickness (t_d/t_r).

Fig.12 Variation of K_f at CP2 of weld root. (a)Effect of the weld penetration rate (1 − t_p/t_r) and t_r; (b) effect of the weld penetration rate (1 − t_p/t_r) and l_w,d/t_r; (c) effect of the weld penetration rate (1 − t_p/t_r) and l_w,r/t_r; (d) effect of the weld penetration rate (1 − t_p/t_r) and θ; (e) effect of the weld penetration rate (1 − t_p/t_r) and t_d/t_r.

Fig.13 Variation of K_f at CP3 of weld toe. (a) Effect of the weld penetration rate (1 − t_p/t_r) and t_r; (b) Effect of the weld penetration rate (1 − t_p/t_r) and l_w,d/t_r; (c) Effect of the weld penetration rate (1 − t_p/t_r) and l_w,r/t_r; (d) Effect of the weld penetration rate (1 − t_p/t_r) and θ; (e) Effect of the weld penetration rate (1 − t_p/t_r) and t_d/t_r.

k	f_k	$c k CP1$	$c k CP2$	$c k CP3$	k	f_k	$c k CP1$	$c k CP2$	$c k CP3$
1	1	11.167	3.824	2.367	15	X₁X₃	2.159	−0.216	0.077
2	X₁	−12.861	0.000	0.000	16	X₁X₄	2.960	0.000	0.000
3	X₂	0.000	0.000	0.000	17	X₁X₅	0.000	0.000	0.000
4	X₃	0.000	0.000	0.000	18	X₁X₆	1.543	0.182	0.000
5	X₄	0.000	0.000	0.000	19	X₂X₃	0.000	0.000	0.000
6	X₅	0.000	0.000	0.000	20	X₂X₄	0.000	−0.320	0.873
7	X₆	0.000	−0.801	0.000	21	X₂X₅	0.000	0.000	0.000
8	X₁²	1.363	−0.085	0.114	22	X₂X₆	0.177	0.000	0.000
9	X₂²	0.000	0.000	0.000	23	X₃X₄	0.000	0.791	−0.259
10	X₃²	0.000	−0.229	0.000	24	X₃X₅	0.000	0.000	0.000
11	X₄²	1.989	−0.334	0.000	25	X₃X₆	−0.919	0.000	0.024
12	X₅²	−2.245	0.353	0.000	26	X₄X₅	0.000	0.000	0.000
13	X₆²	0.526	0.117	0.000	27	X₄X₆	−3.785	0.000	0.000
14	X₁X₂	0.792	0.578	−0.295	28	X₅X₆	0.000	0.000	0.000

Tab.2 Coefficients for the regression formula of

K f CP1

K f CP2

, and

K f CP3

Fig.14 Comparison of FEA and estimated results. (a) K_f at CP1; (b) K_f at CP2; (c) K_f at CP3.

Fig.15 Validation of the proposed formula using additional data. (a) K_f at CP1; (b) K_f at CP2;(c) K_f at CP3.

Fig.16 Illustration of the fatigue test. (a) Geometry of full and 80% penetrated specimens; (b) bending loading mode.

Tab.3 Comparison of FEA and estimated values of K_f

Fig.17 Notch stress concentration and fatigue cracking of OSD series.

Fig.18 Fatigue data in the notch stress system.

Table A1 Stepwise regression analysis results of

K f CP1

Table A2 Stepwise regression analysis results of

K f CP2

Table A3 Stepwise regression analysis results of

K f CP3

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