Page 3 - ZSi-Foster Channel Loads
P. 3

Beam Load Support Formulas






                                                         Cantilever Beams

                  P                                                                   P
                                                                                    a     b
                                V max. = P                        V max. = W                     V max. = P
                       L                                 L               WL             L
                                M max. = PL                       M max. =   2                   M max. = Pb
                                                                                                         2
                                       PL 3                              WL 3                          Pb (3L-b)
                                 max. =                            max. =                         max. =
                                       3EI        V                      8EI    V                        6EI
                V

                M                                 M                             M

                                                          Simple Beams

                      P                                                             P
                   L
                    2            P                             W                a    b
                              R=                            R=                            R =  Pb
                                 2                             2                           1  L
                      L              P              L              W             L           Pa
                 R         R  V max. =        R          R  V max. =        R         R   R =
                                     2                             2         1         2   2  L
               V              M max. =  PL   V              M max. =  WL   V              V max. =  Pa
                                     4                             8                             L
                                     PL 3                         5WL 3                         Pab
                               max. =                        max. =                       M max. =
                                    48EI                          384EI                          L
                                                                                                Pab(a+2b)     3a(a+2b)
               M                            M                              M               max. =
                                                                                                      27EIL
                                            Beams Fixed At One End & Supported At The Other
                      P                                                                 P
                  L                                                                              Pb 2
                    2             5P                               3W               a    b    R =  3  (a+2L)
                                                                                               1
                               R =                              R =                              2L
                                1  16                            1  8
                      L                                L                              L
                                                                                                      2 2
                R              V max. =  11P                    V max. =  5W                  R =  Pa  (3L -a )
                 1                    16         R 1                   8        R 1        R 2  2  2L 3
               V               M max. =  3PL    V               M max. =  WL  V
                                      16                               8                      M at point of load = R a
                                                   3L                                                        1
                                                    8
                                max. at x = 0.447L               max. at x = 0.4215L
                                                                                              M at fixed end =  Pab (a+L)
                                                                         3
                                                                                                            3
               M                            PL 3  M              max. =  WL    M                          2L
                                max. = 0.009317       3L              185EI
                                            EI         4
                                                     Beams Fixed At Both Ends
                       P                                                                   P
                    L                                                                                 2
                     2                 P                                 W            a     b    R =  Pb  (3a+b)
                                                                                                  1
                                V max. =                          V max. =                           L 3
                                       2                                 2
                       L               PL                L               WL             L             2
                                M max. =                          M max. =                       R = Pa  (a+3b)
                                        8                                12        R 1        R 2  2  L 3
                V                max. =   PL 3    V                max. =  WL 3  V
                                      192EI                             384EI                           2
                                                                                                 M  =  Pab
                                                                                                   1   2
                                                                                                      L
                                                                                                       2
                                                                                                 M  =  Pa b
                                                                                                   2  L 2
                M                                 M                             M              M
                                                                                  1             2
                 R – Reaction                        W – Total Uniform Load                   – Deflection
                 M – Moment                          V – Shear                            E – Modulus of Elasticity
                 P – Concentrated Load               L – Length                           I – Moment of Inertia
            ZSi-Foster Engineering Catalog                                                                    – 3 –
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