You are on the right track, but there are a few mistakes in your calculations.
To determine the factor of safety, you should use the formula:
Factor of safety = Ultimate strength / Design load
Ultimate strength = 550,000 MPa = 550,000,000 Pa (since 1 MPa = 1,000,000 Pa)
Design load = 64,000 N
Now, let's calculate the factor of safety:
Factor of safety = 550,000,000 Pa / 64,000 N
Converting the units, we have:
Factor of safety = (550,000,000 / 1,000,000) Pa / 64,000 N
= 550 Pa / 64,000 N
= 8.594
So, the factor of safety is 8.594 (rounded to 3 decimal places).
To calculate the tension design, you need to multiply the ultimate strength (in Pa) by the cross-sectional area (in m²):
Tension design = Ultimate strength * Cross-sectional area
Here, cross-sectional area = 7.600 cm² = 7.600 × 10⁻⁴ m² (since 1 cm² = 0.0001 m²)
Now, let's calculate the tension design:
Tension design = 550,000,000 Pa * 7.600 × 10⁻⁴ m²
= 418,000 N
So, the tension design is 418,000 N.
Therefore, please make the necessary changes in your calculations.