Question

A flat bar (thickness b = 10 mm) with a shoulder fillet is loaded by a cyclic force F-10-2013 shown below. The bar is made of alloy steel (S. = 900 MPa, S, - 700 MPa) and has dimensions of 35 mm, H = 50 mm, r = 4 mm and I = 80 mm. The actual fatigue strength of the component is estimated as S = 360 MPa for commercially polished surface conditions. The bar should be safe against yielding and be able to withstand an infinite number of load cycles. H---- --- (a) Calculate the mean and alternating bending stress components induced at the files including effects of stress concentrations. [4 points) (b) Construct a Goodman diagram for infinite life and include the yield line. (4 points) (c) Calculate the actual safety factor of the component if infinite fatigue life is required and no yielding is permitted. You may neglect the effects of the direct shear stresses induced in the bar. 12 points)

Answer 1

IF 900 MPa Sy - 700 MPa H = 35 mm 9 TH S = 360mpa Pag H=50mw 8= 4 mm l = 80 mm b = lomm F = 1.07 2.0 KN man = 1+2= 3 kH ; Emin = 1-2=-1 KN Emean = 1 KN. -- SOKN mm Iman Fimin = 3-(-1) = 2 kN Fmean = Mmean = Fineant & = 160klum Ma - Faxl= 2 x 80 Iman x t = 3480 = 240 kHMm/ Min = minx1 = -1880 - - 80 kHMm Iman Gmane : Mman y Ki = k 240 x103 x 4 bh? 2 Co 1 4 k = 1.9 Corresponding t = 1.428 7 5o = 1.428 7 = 1 / 2 = 0.1143 = 0.11 43 SOX10 mean Gmean : Mmean XY xky = 8 th x 1.9 меаи bh3 I 74.45 MPa 6 mean = comean 80x103 TOX33 X 3 X 19 = To X3r3 12 160 .x35x1.9 = 148.89 MPa 11 Ma x 48kg = 10x353 35 X1.9

Yield line 1 goodman line be = 66 = 360MPa bu = 700 MPa ou = goro MPa Alterheating stres » Mean strell - - 148.89 & 74.45 360 goo n = 2.015