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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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