To calculate the required weld size for the given hollow shafts connected by a fillet weld, we can use the following steps:
Given Data:
- Diameter of the hollow shaft (D) = 120 mm
- Force (F) = 600 kN = \( 600 \times 10^3 \) N
- Permissible shear stress in the weld (\( \tau \)) = 68 MPa = \( 68 \times 10^6 \) Pa
Step 1: Calculate the required shear area
The shear area of the weld can be calculated using the formula:
\[ A_s = \frac{F}{\tau} \]
where:
- \( A_s \) is the shear area of the weld,
- \( F \) is the applied force,
- \( \tau \) is the permissible shear stress.
Step 2: Substitute in the values
Substitute the known values into the formula:
\[ A_s = \frac{600 \times 10^3}{68 \times 10^6} \]
Calculating \( A_s \):
\[ A_s = \frac{600000}{68000000} = 0.008823529 , \text{m}^2 = 8823.53 , \text{mm}^2 \]
Step 3: Relate shear area to weld size
For a fillet weld, the shear area (A_s) can be calculated as:
\[ A_s = L \cdot t \]
where:
- \( L \) is the length of the weld,
- \( t \) is the size of the weld.
Assuming that the weld is applied all around the perimeter of the shaft, the length \( L \) can be approximated as the circumference of the shaft:
\[ L = \pi \cdot D \]
Substituting the diameter \( D \):
\[ L = \pi \cdot 120 , \text{mm} \approx 376.99 , \text{mm} \]
Step 4: Substitute and solve for weld size \( t \)
Substituting \( L \) back into the shear area equation:
\[ A_s = \pi \cdot D \cdot t \]
\[ 8823.53 = \pi \cdot 120 \cdot t \]
Now we can solve for \( t \):
\[ t = \frac{8823.53}{\pi \cdot 120} \]
Calculating \( t \):
\[ t = \frac{8823.53}{376.99} \approx 23.36 , \text{mm} \]
Conclusion
The required size of the fillet weld should be approximately 23.36 mm.
For practical applications, typically, we round it to the nearest standard weld size or consider any other design factors, so you might choose a weld size based on standard sizes available (e.g. 25 mm).
Thus, the calculated need is about 23.36 mm for non-standard, and 25 mm for practical applications.
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