3. A round strut of diameter 1.25-in is made from 7075-T6 aluminum, whose fatigu

Question

3. A round strut of diameter 1.25-in is made from 7075-T6 aluminum, whose fatigue behavior is showin in the Goodman diagram below. If the rod is subjected to an alternating force Pa 35,000 lb, what is the maximum mean force Pm that will not cause failure in 100,000 cycles? At this loading condition, what will be the values of Omax and Omin? 4.0 -0.6 2.33 -0.4 1.5 0.2 0.67 0.2 0.43 0.4 0.25 0.6 0.11 0,8 0 1.0 R-0 60 50 40 30 ' 20 10 0 Unnotched Notched 60-50-40 30 20 10 0 10 20 30 40 50 60 70 80 Minimum stress, ksi ) notched FIGURE 5.13 Constant-life fatigue diagram for (-) unnotched and ( 7075-T6 aluminum alloy specimens [17). Su- 82 ksi 2000 cpm; K3.:4

Explanation / Answer

alternating stress = Pa / pi * 1.25^2 / 4

                           = 35 * 4 / pi * 1.25^2     = 28.52 ksi

from the diagram provided at a alternating stress of 28.52 ksi and 10^5 life cycles

we have mean stress = 21 ksi   (approx.)

Pm = pi * 1.25^2 * 21 / 4   = 25770.87 lb

Maximum stress = mean stress + alternating stress

                          = 21 + 28.52    = 49.52 ksi

Minimum stress = mean stress - alternating stress

                         = 21 - 28.52 ksi     = -7.52 ksi

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