STATICS Flashcards
controid of composite areas: x-axis
x̄ = ∑ xi Ai / ∑ Ai
controid of composite area: y-axis
ȳ =∑ yi Ai / ∑ Ai
Polar moment of inertia
J = Ix + Iy
Radius of gyration: x-axis
rx = √ Ix / A
radius of gyration: y-axis
ry = √ Iy / A
section modulus: x-axis
Sx top/bottom = Ix / Cy top/bottom
Section modulus: y-axis
Sy top/bottom = Iy / Cx top/bottom
Polar section modulus (Zp)
Zp = J / C
Circle (Area)
A = πR²
Circle (moment of inertia):
I = πR⁴ / 4
Rectangle (area):
A = b(h)
Rectangle (moment of inertia): x-axis
Ix = b(h)³ / 12
Rectangle (moment of inertia): y-axis
Iy = h(b)³ / 12
Triangle (area):
A = ½ bh
Triangle (moment of inertia): x-axis
Ix = b(h)³ / 36
Triangle (moment of inertia): y-axis
Iy = h(b)³ / 36
Semicircle (area):
A = ½ π R²
Semicircle (moment of inertia):
Ix = ⅛ (π ) (R⁴ )
Parallel axis theorem (moment of inertia): x-axis
Ix = ∑Ix + ∑A dy²
Parallel theorem (moment of inertia): y-axis
Iy = ∑Iy + ∑A dx²
