Knowing that the allowable stress for the beam shown is 12ksi,determine the allo

Question

Knowing that the allowable stress for the beam shown is 12ksi,determine the allowable bending moment M when the radius r of thefillets is (a) 1/2 in. , (b)3/4 in.

Explanation / Answer

Moment of inertia, I = bh3/12 I = 0.5*2.53/12 I = 0.651 in4 c = 2.5/2 =1.25 in D/d = 5/2.5 =>D/d = 2 (a) r =0.5 in r/d = 0.5/2.5=>r/d =0.2 from the figure"stress concentration factor for flat bars withfillets under pure bending " in test book K = 1.5 so = KM.c/I 12*103=1.5*M*1.25/0.651 M = 4.164 kip.in (b) r =0.75 in r/d = 0.75/2.5=>r/d =0.3 from the figure"stress concentration factor for flat bars withfillets under pure bending " in test book K = 1.35 so = KM.c/I 12*103=1.35*M*1.25/0.651 M = 4.6293 kip.in

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