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    Hollow Rectangle

    Defining inequalities

    abs(x)<=a/2 and abs(y)<=b/2 and abs(x)>=c/2 or abs(y)>=d/2

    Definition

    Alternate name
    Lamina properties

    (-a/2, -b/2) | (a/2, -b/2) | (a/2, b/2) | (-a/2, b/2) | (-c/2, -d/2) | (c/2, -d/2) | (c/2, d/2) | (-c/2, d/2)

    8

    0

    A = a b - c d

    x^_ = (0, 0)

    Mechanical properties

    J_x invisible comma x = 1/12 (a b^3 - c d^3)

    J_y invisible comma y = 1/12 (a^3 b - c^3 d)

    J_zz = 1/12 (a^3 b + a b^3 - c d (c^2 + d^2))

    J_x invisible comma y = 0

    r_x = 1/2 sqrt((a b^3 - c d^3)/(3 a b - 3 c d)) r_y = 1/2 sqrt((a^3 b - c^3 d)/(3 a b - 3 c d))

    Distance properties

    a | b | a | b | c | d | c | d

    p = 2 (a + b + c + d)

    sqrt(a^2 + b^2)

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