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Beam Strength in Inelastic LTB Zone

Hardlateral-torsional bucklingflexure
For a specified compact beam use Mn = Cb[Mp − (Mp − Mr)(Lb − Lp)/(Lr − Lp)] ≤ Mp, valid for Lp < Lb < Lr. Given Mp = 300 kN·m, Mr = 180 kN·m, Lp = 1.5 m, Lb = 4.0 m, Lr = 5.0 m, Cb = 1.0 and φb = 0.90, find the design flexural strength φbMn.
  1. A192.86 kN·m
  2. B270.00 kN·m
  3. C214.29 kN·m
  4. D216.00 kN·m
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Answer: A. 192.86 kN·m

Check 1.5 < 4.0 < 5.0, so the interpolation applies. Fraction = (4.0 − 1.5)/(5.0 − 1.5) = 0.7143. Mn = 1.0[300 − 120(0.7143)] = 214.29 kN·m (below Mp). φbMn = 0.90(214.29) = 192.86 kN·m. Wrong: 270 kN·m is φbMp, ignoring the reduction for unbraced length; 214.29 kN·m omits φb; 216 kN·m divides by Lr instead of (Lr − Lp), using fraction 0.5.
kN·m
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