Page 89 - Civil Engineering Formulas
P. 89

44                      CHAPTER TWO

                          wyL                         1
                       W =                      –  W =  wyL
                           2                    xL    3
                                           2 2
                               w       w = ky L
                  1  yL  x =  1  yL                  yL
                        –
                  2       2
                      yL
                                                 –  1  y
                   –  1                          x =
                   x =  y                           4
                      2                        G  =  3  y 2
                                                 2
                   2
                  G  =  1  y 2                     80
                      24                         3   1  3
                   3
                  S  = 0                        S  = –  160  y
                     Case 5                      Case 6

                                                          y
                                                         Ú
                                                     W = L    f(x′)dx′
                       W = nP                            0
                   aL    –
                         xL                    –xL     – xL
               P  PPPPPP
                 yL yL yL yL yL yL     W = f(x′)  Ldx
                                                     x′L
                –  n – 1
               x =    y                            yL
                   2
                   2
                                                  y
                2
                       2
              G  =  n – 1  y  =  n + 1  .  a 2  –  L Ú wx′dx′
                    12    n – 1  12           x =  0
                                                   W
               3
                                                  y
               S  = 0                           L wx dx
                                                 Ú
                                                     2
                                              2
                                             G  =  0
                                                   W
                                                  y
                                                 Ú
                                                     3
                                                L wx dx
                                              3
                                             S  =  0
                                                   W
                     Case 7                        Case 8
              FIGURE 2.8 (Continued)
   84   85   86   87   88   89   90   91   92   93   94