Design of a Butt Welding for Fatigue Loading The tensile load P on a butt weld (Figure 15.25a) fluctuates continuously between 20 and 100 kN. Plates are 20 mm thick. Determine the required length L of the weld, applying the Goodman criterion. Assumptions: Use an E6010 welding rod with a factor of

Question

Design of a Butt Welding for Fatigue Loading

The tensile load [latex]P[/latex] on a butt weld (Figure 15.25a) fluctuates continuously between 20 and 100 kN. Plates are 20 mm thick. Determine the required length [latex]L[/latex] of the weld, applying the Goodman criterion.

Assumptions: Use an E6010 welding rod with a factor of safety of 2.5.

Accepted Answer

By Table 15.8 for E6010, [latex]S_{u}[/latex] = 427 MPa. The endurance limit of the weld metal, from Equation 7.6, is

[latex] S_e=C_f C_r C_s C_t\left(1 / K_f ight) S_e^{\prime} [/latex]

Referring to Section 7.7, we have

[latex]C_{r}[/latex] = 1 (based on 50% reliability)

[latex]C_{s}[/latex] = 0.7 (lacking information)

[latex]C_{f} = AS^{b} = 272(427)^{–0.995}[/latex] = 0.657 (by Equation [7.7])

[latex]C_{t}[/latex] = 1 (normal room temperature)

[latex]K_{f}[/latex] = 1.2 (from Table 15.9)

[latex]S_e^{\prime}[/latex] = 0.5[latex]S_{u}[/latex] = 0.5(427) = 213.5 MPa

[latex] C_f=A S_u^b [/latex] (7.7)

Hence,

[latex] S_e=(1)(0.7)(0.657)(1)(1 / 1.2)(213.5)=81.82 MPa [/latex]

The mean and alternating loads are given by

[latex] P_m=\frac{100+20}{2}=60 kN , \quad P_a \frac{100-20}{2}=40 kN [/latex]

Corresponding stresses are

[latex] \begin{array}{l} \sigma_m=\frac{60,000}{20 L}=\frac{3000}{L} \ \sigma_a=\frac{40,000}{20 L}=\frac{2000}{L} \end{array} [/latex]

Through the use of Equation 7.16, we have

[latex] \frac{S_u}{n}=\sigma_m+\frac{S_u}{S_e} \sigma_a ; \quad \frac{427}{2.5}=\frac{3000}{L}+\frac{427}{81.82}\left\lgroup \frac{2000}{L} ight group [/latex]

Solving,

[latex]L[/latex] = 78.67 mm

Comment: A 79 mm long weld should be used.

Table 15.8 Typical Weld-Metal Properties
	Ultimate Strength		Yield Strength
AWS Electrode Number	ksi	(MPa)	ksi	(MPa)	Percent Elongation
E6010	62	(427)	50	(345)	22
E6012	67	(462)	55	(379)	17
E6020	62	(427)	50	(345)	25
E7014	72	(496)	60	(414)	17
E7028	72	(496)	60	(414)	22
Source: American Welding Society Code AWSD.1.77, American Welding Society, Miami, FL.

Table 15.9 Fatigue Stress Concentration Factors [latex]K_{f}[/latex] for Welds
Type of Weld	[latex]K_{f}[/latex]
Reinforced butt weld	1.2
Toe of transverse fillet weld	1.5
End of parallel fillet weld	2.7
T-butt joint with sharp corners	2.0
Source: American Welding Society Code AWSD.1.77, American Welding Society, Miami, FL.

Question 15.12: Design of a Butt Welding for Fatigue Loading The tensile loa...

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