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Special cases of fluctuating stresses
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There are two special cases of the fluctuating stresses:-

  1. Completely reversed stress

  2. Repeated stress

1. Completely Reversed stress :-

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  • It has zero mean stress.

  • In this case half portion of the cycle consists of tensile stress and remaining half of compressive stress. therefore, mean stress is zero.

  • For a completely reversed stress, $\sigma_{min}$ = -$\sigma_{max}$

  • $\sigma_{m}$ = $\frac{\sigma_{max} + \sigma_{min}}{2}$ = $\frac{\sigma_{max} + - (\sigma_{max})}{2}$ = 0

  • $\sigma_a$ = $\frac{\sigma_{max} - (\sigma_{min})}{2}$ = $\frac{\sigma_{max} - - (\sigma_{max})}{2}$ = $\sigma_{max}$

$\therefore \sigma_m = 0\ \text{and} \ \sigma_a = \sigma_{max}$

2. Repeated stress:

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  • The stresses which vary from zero to a certain maximum value are called repeated stresses.
  • The maximum stress is zero in this case and therefore, amplitude stress and mean stress are equal.

  • $\sigma_{m}$ = $\frac{\sigma_{max} + \sigma_{min}}{2}$ = $\frac{\sigma_{max} + 0}{2}$ = $\frac{\sigma_{max}}{2}$

  • $\sigma_a$ = $\frac{\sigma_{max} - \sigma_{min}}{2}$ = $\frac{\sigma_{max} - 0}{2}$ = $\frac{\sigma_{max}}{2}$

$\therefore \sigma_m = \frac{\sigma_{max}}{2}\ \text{and} \ \sigma_a = \frac{\sigma_{max}}{2}$

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