Question

Can you please show me a detailed solution to this problem.?

A beam with a square cross-section of linch x linch is cantilevered at one end, and subjected to a 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) Calculate the midrange stress om and alternating stress og at point A and point B of the beam. 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. (b) 25" А B Sut (N = 1) = 125 S; (N = 10%) = 90 Fatigue strength, Sykpsi S.(N = 106) = 50 50 10 10 10 10 109 10 104 10 10 Number of stress cycles, N

Answer 1

0 he B given, Beam cross section 1*1! =120lbf (pebonumopat (pebuth ) -Goodbf 25' L sut = 125, se =go, se se = es xou + amin 2 club a max 2

at point A, 120 x 12 = .691 ksi 25X1 480 x 122 2.764 k 31 a max 2.764 + = 1.728 ksi am 9764 .691 1.0365 at Point B, 2 600 X 12 - 3.456 ksi a max 25xi 2 450 X 12 2.764 Ksi amin 25'XI' a 3.456 +2.764 = 3.11 KST 2 Ksi 0.346 3.456 - 2-764 2 Nou 6 fatigue life for 'A' 1.01 ng 1.0365 1.728 + 125 fatigue life for 'B' 32.25 bu ng 0.346 --+ 3.1 125 so. A point fail earlier.