A solid circular rod of diameter d undergoes a bending moment M = 1000lbf in inducing

A solid circular rod of diameter d undergoes a bending moment M = 1000lbf ∙ in inducing a stress σ = 16M/(πd3). Using a material strength of 25kpsi and a design factor of 2.5, determine the minimum diameter of the rod. Using Table A–17 select a preferred fractional diameter and determine the resulting factor of safety.

TableA–17

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Fraction of Inches 1 1 1 3 1 5 31 5 371 9 5 1 3 7 64, 32 , 16, 32 , 8, 32, 16, 4, į6, 8, 16, 2, 16, 8, 16, 4, 8, '' ·4"·° , 4,~, ~4,-2,-4° , 31,34,3.4,44.4,45,51.54, 54.6,647, 7 8, 84.9,94 10, 104, 11, 114. 12, 123. 13, 13, 14, 143. 15, 151, 16, 163. 17, 17 18, 18, 19, 19, 20 4 24 Decimal Inches 0.010, 0.012, 0.016, 0.020, 0.025, 0.032, 0.040, 0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.24. 0.30, 0.40, 0.50, 0.60, 0.80,.00 1.20, 140, 1.60, 1.80, 2.0, 2.4, 2.6, 2.8, 3.0, 3.2,3.4.3.6, 3.8, 4.0, 4.2. 4.4, 4.6,4.8, 5.0, 5.2. 5.4, 5.6, 5.8, 6.0,7.0, 7.5, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0,.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5, 20 Millimeters 0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 090, 1.0,. 1.2., 1.4, 1.5, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0.9.0, 10, 12, 14, 16, 18, 20, 22, 25, 28, 30, 32, 35, 40, 45, 50, 60, 80, 100, 120, 140, 160, 180, 200, 250, 300 Renard Numbers Ist choice, R5: 1.6, 2.5, 4, 6.3, 10 2d choice, R10:.25, 2, 3.15, 5, 8 3d choice, R20:12, .4, 1.8, 2.24, 2.8, 3.55, 4.5, 5.6. 7.1.9 4th choice, R40: 1.06, 118, 1.32. 1.5, 1.7, 1.9, 2.12,2.36, 2.65, 3, 3.35, 3.75, 4.25, 4.75, 5.3, 6, 6.7, 7.5, 8.5, 9.5