Statics/Geometric Properties of Lines and Areas

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Centroids Of Common Shapes Of Areas And LinesEdit

Triangular AreaEdit

Area = \frac {b*h}{2}

Quarter Circular AreaEdit

Area = \frac { \pi\ r^2}{4}

Semicircular AreaEdit

Area = \frac { \pi\ r^2}{2}

Semiparabolic AreaEdit

Area = \frac {2ah}{3}

Parabolic AreaEdit

Area = \frac {4ah}{3}

Parabolic SpandrelEdit

Area = \frac {ah}{3}

Circular SectorEdit

Area = \alpha\ r^2

Quarter Circular ArcEdit

Area = \frac { \pi\ }{2}

Semi Circular ArcEdit

Area = \pi\ r

Arc Of CircleEdit

Area = 2 \alpha\ r

Area Moments Of Inertia of Common Geometric ShapesEdit


I_{x} = \frac {1}{3}b h^3

I_{y} = \frac {1}{3}h b^3

I_{x'} = \frac {1}{12}b h^3

I_{y'} = \frac {1}{12}h b^3

Right Triangular AreaEdit

I_{x} = \frac {1}{12}b h^3

I_{y} = \frac {1}{4}h b^3

I_{x'} = \frac {1}{36}b h^3

I_{y'} = \frac {1}{36}h b^3

Triangular AreaEdit

I_{x} = \frac {1}{12} bh^3

I_{x'} = \frac {1}{36} bh^3

Circular AreaEdit

J_C = \frac { \pi\ r^4}{2}

I_{x'} = I_{y'} = \frac { \pi\ r^4}{4}

Hollow circleEdit

This is used for hollow cylinders where there is solid material between the outer and inner radius, but no material between the inner radius and the center, like a pipe's cross-section.

I = \frac { \pi\ (r_o^4 - r_i^4)} {4}

 r_o is the outer radius  r_i is the inner radius

Semicircular AreaEdit

I_x = I_y = \frac {1}{8} \pi\ r^4

I_{x'} = (\frac \pi{8}-\frac {8}{9\pi})r^4

I_{y'} = \frac {1}{8} \pi\ r^4

Quarter CircleEdit

 I_{x} = I_{y} = \frac {1}{16} \pi\ r^4

 I_{x'} = I_{y'} = (\frac \pi{16} - \frac {4}{9\pi}) r^4

further readingEdit