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10 September, 19:38

A thin-walled pressure vessel is constructed by rolling a 6 mm thick steel sheet into a cylindrical shape, welding the seam along line A-B, and capping the ends. The vessel is subjected to an internal pressure of 1.25 MPa. What is the normal stress normal to line A-B?

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  1. 10 September, 19:58
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    41.015

    Explanation:

    Solution

    Given that:

    Th first step to take is to find the longitudinal stress in the cylinder

    σl = PD/4t

    P = the pressure

    D = the diameter

    t = the thickness

    Thus,

    σl = 1.25 * ^ 6 * 0.45 / 4 * 6 * 10 ^ ⁻3

    =23.475Mpa

    Now. we find the hoop stress in the cylinder∠

    σh = PD/2t

    σh = 1.25 * ^ 6 * 0.45 / 2 * 6 * 10 ^ ⁻3

    σh = 46.875 Mpa

    Then

    we find the normal stress in the line of the 30° angle with the longitudinal axis stated below:

    σab = σh + σl/2 + (σh - σl/2) cos 2θ + t sin 2θ

    So,

    σab = 46.875 + 23.4375/2 + (46.875 - 23.4375/2) cos 2 (30°) + 0

    σab = 41.015

    Therefore the normal stress to line A-B is 41.015
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