Question 2 Figure Q2 shows (1) a straight bar and (2) a bar with a hole, all dim

Question

Question 2 Figure Q2 shows (1) a straight bar and (2) a bar with a hole, all dimensions are given. Both bars were machined from steel having S-1000 MPa, and S 800 MPa. Repeated axial load P of 0 to 600 KN is applied. a). Estimate the endurance limit, Sa, and low cycle fatigue strength, Sio', then draw the S-N curve applicable for both bars (use CG-0.8). b). Calculate the fatigue life for the straight bar c). Calculate the fatigue life for the bar with a hole (use extrapolation of Figure 8.24 to get q itf necessary). Will local yielding occur at the hole? To A° Figure Q2

Explanation / Answer

a)

Theoretical endurance strength is Se' = 0.5Su = 500 MPa

Actual endurance strength, Se = CloadCsizeCsurfCtempCreliabSe'

Here the loading is axial so, Cload = 0.7

Csize , A95 = 0.05bh = 0.05 x 50 x 50 = 125 mm2

dequiv=sqrt of A95/0.0766

=sqrt of 125/0.0766

=40.39mm

Csize = 1.189d-0.097 = 0.83

Csurf = 4.51 x (1000)-0.265 = 0.723

Ctemp = 1

Creliab = 1

Se = 0.7 x 0.83 x 0.723 x 500 = 210.05 MPa

Endurance strength at 103 cycles = 0.9Sut = 0.9 x 1000 = 900 MPa

Endurance strength at 106 cycles = Se = 210.05 MPa

Let the S-N curve equation be, S = aNb

Taking log on both sides, log S = log a + b log N

At N = 103 , log 900 = log a + 3b

N = 106 , log 210.05 = log a + 6b

Subtracting above two equations, 3b = log 210.05 - log 900 = -0.6319

b = -0.2106

Using the above value in equation, log 900 = log a - 0.6319

log a = 3.586

a = 3856.04

The equation will be, S = 3856.04 N-0.2106

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