Page 305 - Marks Calculation for Machine Design
P. 305

P1: Shashi
                          January 4, 2005
                 Brown˙C07
        Brown.cls
                                   0  15:4 FATIGUE AND DYNAMIC DESIGN   Time      287
                                s max
                              Stress (s)  s     s a
                                  m
                                                     s a
                                 s min

                             FIGURE 7.8  Fluctuating loading (negative stresses).

                      For any of the these three possibilities, the mean stress (σ m ) and the alternating stress
                    (σ a ) can be related to the maximum stress (σ max ) and the minimum stress (σ min ) by the
                    following relationships:
                                                  σ max + σ min
                                             σ m =                              (7.19)
                                                      2
                                                  σ max − σ min
                                             σ a =                              (7.20)
                                                      2
                    Design Criteria.  Data from fatigue tests with fluctuating loading can be plotted in a
                    diagram where the horizontal axis is the ratio of the mean strength (S m ) to either the
                    ultimate tensile strength (S ut ) or the ultimate compressive strength (S uc ) and the vertical
                    axis is the ratio of the alternating strength (S a ) to the endurance limit (S e ). Such a diagram
                    is shown in Fig. 7.9, where the test data (not shown) fall close to the horizontal line in the
                                                ◦
                    compressive region and close to the 45 line in the tensile region.
                         1.2

                         1.0
                        Amplitude ratio S a /S e  0.8


                         0.6

                         0.4

                         0.2

                           0
                          −1.2  −1.0  −0.8  −0.6  −0.4  −0.2  0  0.2  0.4  0.6  0.8  1.0
                                Compression S /S uc             Tension S /S ut
                                           m
                                                                       m
                                                Ratio of the mean
                      FIGURE 7.9  Plot of test data for fluctuating loading.
   300   301   302   303   304   305   306   307   308   309   310