Tension Member Capacity with Bolt Holes

Hardsteeltension membersnet sectionrupture
An A36 steel plate 8 in wide 1/2 in thick ksi, ksi) is a tension member. It is connected with three 3/4-in diameter bolts arranged in a single line across the width, with no stagger, and all of the cross-section is connected so Per AISC LRFD, the design tensile strength is most nearly:
  1. A117 kips
  2. B130 kips
  3. C144 kips
  4. D156 kips
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Answer: A. 117 kips

Two limit states apply and the smaller governs. Yielding on the gross section: Ag = 8 × 0.5 = 4.0 in², φPn = 0.90 × 36 × 4.0 = 129.6 kips. Rupture on the net section: each hole is taken as the bolt diameter plus 1/8 in for the standard hole and damage, so 3/4 + 1/8 = 7/8 in. An = (8 − 3 × 0.875) × 0.5 = 2.69 in², Ae = U An = 2.69 in², and φPn = 0.75 × 58 × 2.69 = 116.9 kips. Rupture governs at about 117 kips. Stopping at 130 kips ignores the holes; 144 and 156 kips are the unfactored Fy Ag and Fu An.
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