Bab 1-Soalan Daya-Daya pada Bahan

(Jun 2011)

Example 13

A bar with a 30 mm diameter and 80 mm length is subjected to a tensile force of 100kN. The ultimate stress is 230 MN/m².  As a result of this force, the bar elongated by 0.0585 mm and the diameter be comes 29.994 mm. Determine:

i)                    The tensile stress

ii)                  The tensile strain in x-x direction

iii)                The tensile strain in y-y direction

iv)                Modulus of elasticity

v)                  Strain energy

vi)                Safety factor

vii)              Poisson’s ratio

Satu bar bergarispusat 30 mm dan panjang 80 mm dikenakan beban kerja sebanyak 100 kN.  Disebabkan daya ini, bar telah memanjang sebanyak 0.0585 mm dan diameternya berubah ke 29.994 mm. Diketahui, tegasan muktamad bagi bar ini ialah 230 MN/m².  Kirakan:

i)                    Tegasan

ii)                   Terikan paksi

iii)                 Terikan sisi

iv)                 Modulus Young

v)                  Tenaga Terikan

vi)                 Faktor keselamatan

vii)               Nisbah poisson

Penyelesaian:

Data diberi:

D₀           = 30 mm

L₀            = 80 mm

D₁           = 29.994mm

DL          = 0.0585 mm

P             = 100 kN

s_muktamad =230 MN/m²

i)        Tegasan

                   P

        s  =  --------

                    A

                   π D²

    Ü A = ---------------

                        4

                π (30 x 10^-3)²

                = ------------------

                       4

           = 7.069 x 10^-4 m² _##

                     P

     Ü s  =  --------

                     A

                      100 x 10³

               =  -------------------------

                  7.069 x 10^-4

              = 141.463 MN/m² @ MPa _##

ii)          Terikan paksi

     L_f –L_o

           e_paksi  = -----------

         L_o

                        0.0585 x 10^-3

                    = ----------------

                           80 x 10^-3

                 

                    = 7.3125 x 10^-4 M  _##

iii)     Terikan sisi

-(D_o –D_f )

             e_sisi  = ------------

      D_o

                      -(30 x 10^-3) –(29.994 x 10^-3 )

                   = -------------------------------------

                                  30 x 10^-3

                   = 2 x 10^-4 M _##

iv)     Modulus Young

                    s   

    Ü E  =    -------

                  e_paksi  

              

                     141.463 x 10⁶

             =   ---------------------

                                     7.3125 x 10^-4

           = 193.454 x10⁹ N/m²_##

v)      Tenaga terikan

       1

U = --- PDL

                      2

                     1

                 = ---- (100 x 10³ ) ( 5.85 x 10^-5 )

                      2

                          = 2.925J_##

vi)        Faktor keselamatan jika tegasan muktamad 432 MPa

             s_max/muktamad

F.K = ---------------

                                                        s_kerja

                                                             230 x 10⁶