Topic: Strength of Materials
A short column of external diameter D and internal diameter d, is subjected to a load W, with an eccentricity e, causing zero stress at an extreme fiber. Then the value of 'e' must be
- A. (D² + d²) / (8*pi*D)
- B. (D² + d²) / (8D)
- C. (D² - d²) / (8D)
- D. (D³ - d³) / (8D^2)
Answer: B. (D² + d²) / (8D)
Explanation: For zero stress at an extreme fiber, direct compressive stress + bending stress = 0. So, -W/A + M/Z = 0, where A = (pi/4)*(D² - d²) and Z = I/y = (pi/64)*(D^4 - d^4) / (D/2). Solving -W/A + (W*e)/Z = 0 gives e = (D² + d²) / 8D.