Page 170 - Marks Calculation for Machine Design
P. 170

P1: Rakesh
                          January 4, 2005
                 Brown˙C03
        Brown.cls
                  152
                            U.S. Customary 14:16  STRENGTH OF MACHINES  SI/Metric
                  Step 6. Using Eq. (3.47), calculate the factor-  Step 6. Using Eq. (3.47), calculate the factor-
                                            √                                 √
                  of-safety (n) at the radial distance ( r i r o )  of-safety (n) at the radial distance ( r i r o )
                  where the principal stress (σ 1 ) is the maximum  where the principal stress (σ 1 ) is the maximum
                  radial stress found in Step 4 and the princi-  radial stress found in Step 4 and the princi-
                  pal stress (σ 2 ) is tangential stress also found  pal stress (σ 2 ) is tangential stress also found
                  in Step 4.                         in Step 4.
                                 1/2                                1/2

                      2   2                              2  2
                     σ + σ − σ 1 σ 2                   σ + σ − σ 1 σ 2
                      1  2           1                  1   2          1
                                   =                                 =
                          S y        n                       S y       n
                                                                  2
                         2
                                                           2
                               2
                    ((4.36) + (4.18) − (4.36)(4.18)) 1/2  1  ((37.5) + (36.1) − (37.5)(36.1)) 1/2  1
                                             =                                  =
                               50              n                  350             n
                    (18.26) 1/2  4.27  1               (1356) 1/2  36.8  1
                           =     =                            =    =
                      50      50   n                     350    350  n
                        50                                350
                    n =   = 11.7                      n =    = 9.5
                       4.27                               36.8
                    Clearly the design is very safe.   Clearly the design is very safe.
                    Notice that the stress element at the inside radius (r i ) has a lower factor-of-safety than
                                        √
                  the one at the radial distance ( r i r o ). This means it is the most important stress element in
                  deciding whether the design is safe or not.
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