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    Right Triangular Laminae

    Definition

    Defining inequalities

    y>=0 and a b>=a y + b x and x>=0

    Lamina properties

    (0, 0) | (a, 0) | (0, b)

    3

    a>0 and b>0

    (data not available)

    b

    A = (a b)/2

    x^_ = (a/3, b/3)

    Mechanical properties

    J_x invisible comma x = (a b^3)/12

    J_y invisible comma y = (a^3 b)/12

    J_zz = 1/12 a b (a^2 + b^2)

    J_x invisible comma y = -1/24 a^2 b^2

    r_x = b/sqrt(6) r_y = a/sqrt(6)

    Distance properties

    a | sqrt(a^2 + b^2) | b

    sqrt(a^2 + b^2)

    p = sqrt(a^2 + b^2) + a + b

    r = 1/2 (-sqrt(a^2 + b^2) + a + b)

    R = 1/2 sqrt(a^2 + b^2)

    sqrt(a^2 + b^2)

    χ = 1

    s^_ = (2 a^5 b + 4 a^3 b^3 + a b^4 (sqrt(a^2 + b^2) + 2 b) + a^4 b sqrt(a^2 + b^2) + (a^2 + b^2)^(3/2) (b^3 log((sqrt(a^2 + b^2) + a)/b) + a^3 log((sqrt(a^2 + b^2) + b)/a)) + 2 a^3 b^3 coth^(-1)((a + b)/sqrt(a^2 + b^2)))/(15 a b (a^2 + b^2)^(3/2))

    A^_ = (a b)/24

    Classes

    convex laminae | polygonal laminae | right triangular laminae | triangular laminae

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