Question 15.12: Design of a Butt Welding for Fatigue Loading The tensile loa...
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 safety of 2.5.
By Table 15.8 for E6010, S_{u} = 427 MPa. The endurance limit of the weld metal, from Equation 7.6, is
S_e=C_f C_r C_s C_t\left(1 / K_f\right) S_e^{\prime}
Referring to Section 7.7, we have
C_{r} = 1 (based on 50% reliability)
C_{s} = 0.7 (lacking information)
C_{f} = AS^{b} = 272(427)^{–0.995} = 0.657 (by Equation [7.7])
C_{t} = 1 (normal room temperature)
K_{f} = 1.2 (from Table 15.9)
S_e^{\prime} = 0.5S_{u} = 0.5(427) = 213.5 MPa
C_f=A S_u^b (7.7)
Hence,
S_e=(1)(0.7)(0.657)(1)(1 / 1.2)(213.5)=81.82 MPaThe mean and alternating loads are given by
P_m=\frac{100+20}{2}=60 kN , \quad P_a \frac{100-20}{2}=40 kNCorresponding stresses are
\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}Through the use of Equation 7.16, we have
\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} \right\rgroupSolving,
L = 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 K_{f} for Welds |
|
| Type of Weld | K_{f} |
| 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. | |