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solid mechanics

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a steel bar 10m long and 10cm*10cm in section .it is subjected to an axial pull of 250KN .determine the intensities of normal and tangential stresses on a plane section at 60 degree to the longitudinal axis .

  • solid mechanics -

    normal stress
    σ = F/A = 250000/0.1•0.1 = 2.5•10⁷ N/m²
    Tangential stress
    τ = F /(A/cosα) = Fcosα/A =
    =250000•0.5/0.1•0.1=1.25•10⁷ N/m²

  • solid mechanics -

    If I am not mistaken, tangential stress on a plane section at 60° to the longitudinal axis would be the shear stress, γ, and the normal stress on the same plane is the normal stress, σ.

    σx=250 kN / (0.1²) m²
    =25 MPa

    Using the Mohr circle, we have
    Tangential stress
    =(σx-σy)/2 * sin(2*α)
    =25/2 * sin(2*60°) MPa
    =6.25√3 MPa

    Normal stress
    =((σx+σy)/2 + (σx-σy)/2 * cos(2*α)
    = 12.5 + 12.5cos(2*60°)
    =6.25 MPa

  • solid mechanics -

    Sorry, typo above:
    shear stress should have read τ. γ would have been shear strain.

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