Kern Limit for a Rectangular Section
Mediumkerneccentricity
A solid rectangular uncracked section has height h = 0.60 m and any positive width b. It carries only a compressive prestress force P at eccentricity e from the centroid about the horizontal axis. No external bending moment acts. Using elastic stresses, what is the maximum |e| that avoids tension at either extreme face?
- A0.30 m
- B0.20 m
- C0.05 m
- D0.10 m
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Answer: D. 0.10 m
No tension requires P/A − P|e|/S ≥ 0, so |e| ≤ S/A. For a rectangle A = bh and S = bh²/6, so S/A = h/6 = 0.60/6 = 0.10 m (the kern limit). At the limit one face has zero stress and the other 2P/A. 0.30 m is h/2, the section edge. 0.20 m is h/3, the full middle-third width rather than its half-width. 0.05 m is h/12, half the kern distance.
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