Question

A beam with a square cross-section of linch x 1inch is cantilevered at one end, and subjected to a force that fluctuates from F = 1201bf (downward) to F= -600lbf (upward) at its tip. The length of beam is L = 25 inches. The selected steel material has mechanical properties as shown in the following S-N fatigue diagram. Hint: neglect any stress concentration at the support end. (a) (4 points) Calculate the midrange stress om and alternating stress og at point A and point B of the beam. (b) (6 points) Estimate the fatigue life of material at point A and point B of the beam using the modified Goodman criterion, and find which point will fail earlier. 25" А B Sur (N = 1) = 125 S; (N = 10%) = 90 . Fatigue strength, s, kpsi S.(N = 106) = 50 50 10 100 10 10 10 10' 10 10 Number of stress cycles, N

Answer 1

0 I may a boolff 25" Fruin = -120 lbf maximum beneling moment Max = 600x25= 15000 elf in - Iskpe Monin - - 120x25= - 3000 est in = -3 Apr Mm tc Mmayt Monon) voon (5-3) = 6 kg alternating Ma - 20 Mmax-wanden ) = 4( 15+3) = gkpe tenos Ma Man % = 15 10 = 56.310 Se z 50 from SN Diagram Sut = 125, + Sut Ta Mm Ja a 1.55m put in equation 1.50m Tm + 195 50 - 50x125 om [ Ls + 1125] =1 i 194.5+50) m= 26.32 kpgi Ta = 39.48 kpse

2.051 A - 1.954. 1.ggg to с. org Sut = oug (125) = 112151px; log (11215) = 2,051 log Se = log(50)=1.699 log sf = log (90)= 1.954 log (103) = 3 logo= 6 ++ 3 fig from Aruse - EF AB) (AR) (6-3) X(2.051 - 11954) 2.051 1.699) IEF 0.8267 Therepre logo 3 + EF 380.8267 - 3.8267 M 2 (0) 3.8267 =6709.7 Cyeles. 2