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A 1-in-diameter solid round bar has a groove 0.1-i

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Find the tensile strength from table deterministic ASTM minimum tensile and yield strengths for some hot rolled and cold drawn steels for 1020 CD steel Tensile strenth S)68kpsi Calculate the depth of groove. groove =1-2×0.1 - 0.8in T Calculate the ratio T 0.1 d 0.8 - 0.125 Calculate the ratio D 1 d 0.8 Find the stress concentration factor using the charts of theoretical- concentration Factors From figure grooved round bar in torsion At0.125 and at1.25 The value of stress concentration factor isk. -1.4 Find the notch sensitivity from figure notch sensitivity curves for materials in reversed torsion for notch radius 0.1 in The value of notch sensitivity is, q0.81

Calculate the fatigue stress concentration factor using the following expression, = 1+0.81(14-1) - 1.32 Calculate the maximum shear stress using the following expression, max k Tx 2 32 kた167. 1.32 × 16 × 1 800 π × 0.8 23634.5 psi - 23.6 ksi Calculate the endurance limit Since the tensile strength is less than the 200 kpsi (St)<200ksi 68kpsi<200ksi Hence, use the following relation to find the endurance limit = 0.5(68) 34 ksi

From table parameters for Marin surface modification factor for machined surface finish a 2.7,b-0.265 Calculate the surface factor using the following expression, -(2.7)(68) (2.7) (68) 0 205 = 0.882 Calculate the size factor. Since, the value depth of groove is lies between 0.11 in to 2in 0.11s d<2in 0.11 0.8 2in Hence, the expression for finding the size factor is 0.879d-0.107 0.879 (0.8) 0.107 = 0.9 Loading factor for torsion is k0.59 Temperature factor is k-1 Reliability factor k, -1 Find the endurance strength using the Marin equation, (0.882)×0.9× 0.59 x1x1x(34) -15.9 ksi

For pure revering torsion, consider ultimate shear stress only and it is expressed as, S0.67S 0.67 × 68 Calculate the constants a and b using the following expressions, (0.9(45.6) 15.9 -105.9 SL 1. (0.9x 45.6 15.9 0.137 Calculate the number of cycles to failure using the following expression, max 23.6 (-0.137) 105.9 -57.4×103 cycles

From table effect of operating temperature on the tensile strength of steel for 750°F 0.927 +0.872 Temperature factor is, ki - -0.8995 Find the endurance strength using the Marin equation, 0.882 (0.90.59(0.8995)34 -14.32 ksi Calculate the constants a and b using the following expressions, S 2 (0.9(45.6)) 14.32 0.9×45.6 --og 14.32 0.1524 Calculate the number of cycles to failure using the following expression, T. max 23.6 01524) -37.7 x103 cycles

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