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Moment of Inertia of Different Shapes
MOI of shapes in order to calculate MOI of composite sections
16
Civil Engineering
Undergraduate 1
08/26/2012

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Term
Quarter-Circular Arc
Definition
Centroid (x,y)= (2r/π, 2r/π)
MOI= πr/2
Term
Semi-Circular Arc
Definition
Centroid (x,y)= (0, 2r/π)
MOI= πr
Term
Arc of Circle
Definition
Centroid (x,y)= (rsinα/α,0)
MOI= 2αr
Term
Triangular Area
Definition
Centroid (x,y)= (0,h/3)
MOI= bh/3
Term
Quarter circular area
Definition
Centroid (x,y)= (4r/3π, 4r/3π)
MOI= πr²/2
Term
Quarter Elliptical Area
Definition
Centroid (x,y)= (4a/3π, 4b/3π)
MOI= πab/4
Term
Semi Elliptical Area
Definition
Centroid (x,y)= (0, 4b/3π)
MOI= πab/2
Term
Parabolic spandrel (y=kx²)
Definition
Centroid (x,y)= (3a/4, 3h/10)
MOI= ah/3
Term
General spandrel (y=kx^n)
Definition
Centroid (x,y)= ([n+1)/(n+2)]a,[(n+1)/(4n+2)]h)
MOI= ah/n+1
Term
Circular Sector
Definition
Centroid (x,y)= (2rsinα/3α,0)
MOI= αr²
Term
Rectangle
Definition
MOI about centroidal axis(Ix'x',Iy'y')= bh³/12, b³h/12
MOI about axes (Ixx,Iyy)= bh³/3, b³h/3
Polar moment of inertia= Ixx+Iyy
Term
Triangle
Definition
Ix'x'=bh³/36
Ixx=bh³/12
Term
Circle
Definition
Ixx= Iyy= πR^4/4
Jo= πR^4/2
Term
Semicircle
Definition
Ixx= Iyy= πR64/8
Jo= πR^4/2
Ix'x'= 0.11R64
Term
Quarter Circle
Definition
Ixx= Iyy= πR^4/16
Jo= πR^4/8
Term
Ellipse
Definition
Ixx= πab³/4
Iyy= πa³b/4
Jo= πab/4(a²+b²)
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