Using the rope diameter D (in inches), which expression gives a quick estimate of the safe working load?

Using the rope diameter D (in inches), which expression gives a quick estimate of the safe working load?

• A. D² × 8 × 2000
• B. D × 10 × 1000
• C. D³ × 5 × 1000
• D. D² × 6 × 1500

Answer: (A)

Rope strength grows with cross-sectional area, which is proportional to the square of the diameter. So a quick rule of thumb for safe working load uses D² with a constant that converts that area into pounds. The expression D² × 8 × 2000 simplifies to D² × 16,000, giving SWL in pounds when D is in inches. This reflects the idea that doubling the diameter makes the load capability roughly four times larger. The other forms don’t match how strength scales with diameter (they’re linear or cubic), or use a smaller factor, making them less accurate as a quick estimate. Remember, this is a rough guideline and should be checked against the rope’s rated working load and safety factors from the manufacturer.

Rope strength grows with cross-sectional area, which is proportional to the square of the diameter. So a quick rule of thumb for safe working load uses D² with a constant that converts that area into pounds. The expression D² × 8 × 2000 simplifies to D² × 16,000, giving SWL in pounds when D is in inches. This reflects the idea that doubling the diameter makes the load capability roughly four times larger. The other forms don’t match how strength scales with diameter (they’re linear or cubic), or use a smaller factor, making them less accurate as a quick estimate. Remember, this is a rough guideline and should be checked against the rope’s rated working load and safety factors from the manufacturer.