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23 April, 12:35

A spherical container made of steel has 20 ft outer diameter and wal thickness of 1/2 inch. Knowing the internal pressure is 50 psi, estimate the maximum normal stress and the maximum shearing stress in the container

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  1. 23 April, 15:48
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    maximum normal stress = 5975 psi

    maximum shear stress = 2987.50 psi

    Explanation:

    Given data

    dia = 20 ft

    wall thickness = 1/2 inch

    internal pressure = 50 psi

    To find out

    the maximum normal stress and the maximum shearing stress

    Solution

    By the Mohr's circle we will find out shear stress

    first we calculate inner radius

    i. e. r = (diameter/2) - t

    r = (20 * 12 in) / 2 - (1/2)

    r = 120 - 0.5 = 119.5 inch

    Now we find out maximum normal stress by given formula

    normal stress = (internal pressure * r) / 2 t

    normal stress = (50*119.5) / 2 * 0.5

    maximum normal stress = 5975 psi

    and minimum normal stress is 0, due to very small radius

    and maximum shear stress will be

    shear stress = (maximum normal stress - minimum normal stress) / 2

    shear stress = (5975 - 0) / 2

    maximum shear stress = 2987.50 psi
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