The allowable stress amplitude for a low-carbon steel is ±225 N/mm² and its ultimate tensile stress is 750 N/mm² . The steel is subjected to a repeated cycle of stress in which the minimum stress is zero.

Calculate the safe range of stress based on the Goodman and Gerber predictions.

Question

The allowable stress amplitude for a low-carbon steel is ±225 N/mm² and its ultimate tensile stress is 750 N/mm² . The steel is subjected to a repeated cycle of stress in which the minimum stress is zero.

Calculate the safe range of stress based on the Goodman and Gerber predictions.

Accepted Answer

For the Goodman prediction Eq. (8.3) applies in which [latex] S_{ a , 0}=450 N / mm ^{2} ext { and } S_{ m }=S_{ a } / 2 [/latex]. Then

[latex]\left(S_{ a } / S_{ a , 0} ight)=\left[1-\left(S_{ m } / S_{ u } ight) ight][/latex] (8.3)

[latex] S_{ a }=450\left[1-\left(S_{ a } / 2 imes 750 ight) ight][/latex]

from which

[latex] S_{ a }=346 N / mm ^{2} [/latex]

For the Gerber prediction m = 2 in Eq. (8.4). Then

[latex] \left(S_{ a } / S_{ a , 0} ight)=\left[1-\left(S_{ m } / S_{ u } ight)^{m} ight] [/latex] (8.4)

[latex] S_{a}=450\left[1-\left(S_{a} / 2 imes 750 ight)^{2} ight] [/latex]

which simplifies to

[latex] S_{a}^{2}+5000 S_{a}-2.25 imes 10^{6}=0 [/latex]

Solving gives

[latex] S_{ a }=415 N / mm ^{2} [/latex]

Question 8.1: The allowable stress amplitude for a low-carbon steel is ±22...

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