Question

a A beam with a square cross-section of linch x 1inch is cantilevered at one end, and subjected to force that fluctuates from F = 120lbf (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 Oa 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" A B Sut (N = 1) = 125 S. S; (N = 103) = 90 100 Fatigue strength, Sg ,kpsi Se (N = 106) = 50 10 100 102 10 10 10 109 10 10 Number of stress cycles, N

Answer 1

Answer:

1 25" B a) =) Maximum force a А 2 120 1x1 = 120 lbflin? >) Minimum force -600 1x1 2 =-600 lbf lin2 >) Midrange stress (m) max t min 2 20-600 2 -200 lbflin? Alternating stress, Tás max - 1 min 2 120 + 600 2 Ta= 360/dbflin b) Good yonan's criteria, K+ ( at ) +*+ ( )= ☆ Negleeting stress concentration Kf and kf im Tale to Jut + = N 240 360 125x106 50X106 N = 1893. 93 cycles - Fatique life. u. At point t will be failwe earlier.