To calculate the safe tensile load for the fillet weld joining the two round shafts, we need to follow these steps:
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Calculate the effective throat of the weld: The effective throat of a fillet weld is given by the formula: \[ t = \frac{a \cdot \sqrt{2}}{2} \] where \( a \) is the size of the weld. In this case, \( a = 5 , \text{mm} \).
Plugging in the values: \[ t = \frac{5 \cdot \sqrt{2}}{2} = \frac{5 \cdot 1.4142}{2} \approx 3.54 , \text{mm} \]
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Calculate the perimeter of the weld: Since the weld is applied around the complete circumference of the shaft, we first need to calculate the circumference of the shafts. The diameter of each shaft is \( 80 , \text{mm} \), so the circumference \( C \) is given by: \[ C = \pi \cdot d = \pi \cdot 80 , \text{mm} \approx 251.33 , \text{mm} \]
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Calculate the weld cross-sectional area: The cross-sectional area \( A_w \) of the weld can be calculated as: \[ A_w = \text{Effective Throat} \times \text{Length of weld} \] The length of the weld is equal to the circumference, thus: \[ A_w = t \cdot C = 3.54 , \text{mm} \cdot 251.33 , \text{mm} \approx 891.63 , \text{mm}^2 \]
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Calculate the safe tensile load: The safe tensile load \( P \) can now be calculated using the permissible tensile stress \( \sigma \) in the weld: \[ P = \sigma \cdot A_w \] Given that \( \sigma = 60 , \text{MPa} = 60 , \text{N/mm}^2 \), we can calculate: \[ P = 60 , \text{N/mm}^2 \cdot 891.63 , \text{mm}^2 \approx 53497.8 , \text{N} \]
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Convert to more practical units: To convert this to kilonewtons (kN): \[ P \approx 53.5 , \text{kN} \]
Final Result: The safe tensile load for the weld is approximately \( 53.5 , \text{kN} \).
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