Solid Mechanics

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A cast iron block of 5Cm^2 cross section carries an axial compressive load of 50KN.Calculate the magnitude or normal and shear stresses on a plane whose normal is inclined at 30 deg.to the axis of the block,also determine the maximum shear stress in the block?

  • Solid Mechanics -

    I'll give it a try.

    We have 50kN on 5cm², or 0.0005 m².
    So the axial stress
    σx = 105 kPa
    =100 MPa

    σy=0

    So draw the Mohr's circle (in the σ/τ plane) with between (0,0) and (100,0) as a diameter.
    The centre is at (50,0).

    To find the stresses at θ=30°
    draw a diameter passing through the centre at 2*30=60° with the axis.
    The stresses in that plane is shown by the extremities of the diameter, namely
    σ=50±50cos(60°), and
    τ=±50sin(60°).

    Maximum shear stress is at θ=45° where
    σx=σy=50, and
    τxy=50

    Hope that helps.

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