Question

For a bolted assembly with eight bolts, the stiffness of cach bolt is k 1.0 MN/mm and the stiffness of the members is k26 MN/mm per bolt. The bolts are preloaded to 75 peroner of proof strength. Assume the external load is equally distrihuted to all the bolts. The bolts am M6 x1 class 5.8 with rolled threads. A fluctuating external load is applied to the cntire with P 60 kN and P - 20 kN. (a) Determine the yielding factor of safety. (b) Determine the overload factor of safety. (e) Determine the factor of safety based on joint separation. (d) Deternine the fatigue factor of safety using the Goodman criterion. Pmux Sp At CP+Fi Phmux Pmin Penin= nects nelts At = 20, L mut Sp At-Fi Fi = 6,75 At Sp Sp = 380 Mp %3D c(Pux-Ptnin) 2 At > no = %3D P(1-c) CP C(PEmx +Pt.min). Fi At - a Sut b ;a = 4,5 5 Sut = 520 MPea m estu 2 At Fij Si = 0,5 Suti At --0, 265 Ka = 0,85 ; K = 2,2 ; k = 1 ; ke %3D 1.se Ka ke ke ka ke KF Se = Ka Ke Ke Ka ke Kf %3D Se ( Sut -6i) Sat Gu + Se ( 6m-6i) nf A shaft is loaded in bending and torsion such that M, 70 N m, T, -45 N. m. M,- 55 N. m, and T.= 35 N m. For the shaft, 5, 700 MPa and 5,- 560 MPa and a fully corrected endurance limit of S, = 210 MIPa is assumed. Let K,- 22 and K 18. Wish a design factor of 2.0 determine the minimum acceptable diameter of the shaft using the Q.2 DE-Goodman criterion. 2. 16 n Se 4( kg Ma)+ 3( Kfs Tm) Sut %3D

Answer 1

Calculate the joint constant. 1.0 kg + 10+26=0.278 Calculate the preload value. F} = 0.75S, 4 = 0.75x(380) (20.1) = 5728.5 N Calculate the average external load acting on each bolt. Pea + Pain_160+20 28 2 Calculate the yielding factor of safety. S4 (380) (20.1) =1.073 yteid CP+F (0.278)(5x109)+(5728.5) Calculate the overload factor of safety. S,4-F (380) (20.1)-(5728.5), noverad = 9=1.374 CP (0.278)(5x103) Calculate the factor of safety based on joint separation. F (5728.5) "overicend (1-C)P (1-0.278)(5x10-) -- -1.587

Calculate the mean stress value on each bolt. F, CP+F (0.278) (5x109 )+(5728.5) -= 354.15 MPa (20.1) Calculate the preload stress value. F_(5728.5) -285 MPa 0,=(20.1) Calculate the stress amplitude value on each bolt. 60 20 C Paar (eachdair) - Pain(each boty) 0,=- 220.1) X10 8 8 -= 34.58 MPa - 24 Calculate the theoretical endurance limit. S, = 0.55 = 0.5(520) = 260 MPa Calculate surface finish factor. kn = a.. =(4.5) (520) 2 = 0.858 Calculate the modified endurance limit. S.' = k/A, KAK,S. =(0.858)(1)(0.85)(1)(1 =189.6 MPa

Calculate the fatigue factor of safety. S. (S-0) (189.6) (520-285) S40,+S,'(0-0) (520)(34.85)+(189.6) (354.15-285) = 1.427