A tie member consists of ISA 100 × 75 × 8 longer leg is connected to a gusset plate. The gross cross sectional area of connected and unconnected leg are _______ mm2respectively.a)768 and 568b)344 and 288c)976 and 654d)1206 and 743Correct answer is option 'A'. Can you explain this answer?

Question

A tie member consists of ISA 100 &times; 75 &times; 8 longer leg is connected to a gusset plate. The gross cross sectional area of connected and unconnected leg are _______ mm2respectively.a)768 and 568b)344 and 288c)976 and 654d)1206 and 743Correct answer is option 'A'. Can you explain this answer?

Answer

Answer

Understanding the Tie Member
A tie member, specifically an ISA (Indian Standard Angle) with dimensions 100 × 75 × 8, has specific properties that need to be analyzed for its cross-sectional area.
Dimensions Breakdown
- Long leg: 100 mm
- Short leg: 75 mm
- Thickness: 8 mm
Gross Cross-Sectional Area Calculation
To calculate the gross cross-sectional areas of the connected and unconnected legs, we use the following formulas:
- Area of the long leg (connected):
- Area = Length × Thickness
- Area = 100 mm × 8 mm = 800 mm²
- Area of the short leg (unconnected):
- Area = Length × Thickness
- Area = 75 mm × 8 mm = 600 mm²
However, the gross area also accounts for the reduction due to the corner cut-out, which is approximately 32 mm² for each leg.
Final Areas Adjustment
- Connected leg (long leg):
- Gross Area = 800 mm² - 32 mm² = 768 mm²
- Unconnected leg (short leg):
- Gross Area = 600 mm² - 32 mm² = 568 mm²
Conclusion
Thus, the gross cross-sectional area of the connected and unconnected leg are 768 mm² and 568 mm², respectively. This aligns with option 'A', confirming it as the correct answer.

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