Page 304 - Marks Calculation for Machine Design

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mean stress is zero, then the loading is completely reversed as presented in the previous
section. January 4, 2005 15:4 STRENGTH OF MACHINES
Although fluctuating loading, like reversed loading, can be represented by a square wave,
saw tooth wave, sinusoidal wave, or some other wave form as long as it has a constant period,
the remainder of the discussion in this section assumes a sinusoidal wave form like that
shown in Fig. 7.6.

s max s
Stress (s) s m a s

s min a

0 Time
FIGURE 7.6 Fluctuating loading (positive stresses).

In Fig. 7.6, the mean stress (σ m ) has been shown positive and the alternating stress
(σ a ) has a magnitude such that the maximum stress (σ max ) and the minimum stress (σ min )
are also positive. However, a second possibility is for the mean stress (σ m ) to be pos-
itive and the alternating stress (σ a ) having a magnitude such that the maximum stress
(σ max ) is still positive; whereas the minimum stress (σ min ) becomes negative as shown in
Fig. 7.7.

s max
Stress (s) s m s a

0
s a Time
s min

FIGURE 7.7 Fluctuating loading (positive and negative stresses).

The third possibility is that the mean stress (σ m ) is negative and the alternating stress
(σ a ) has a magnitude such that the maximum stress (σ max ) and the minimum stress (σ min )
are also negative, as shown in Fig. 7.8.