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Engineering Statics: Open and Interactive

Daniel W. Baker, William Haynes

Section C.1 Centroids of Common Shapes

Table C.1.1. Centroids of Common Shapes
Shape
Area
\(\bar{x}\)
\(\bar{y}\)
A rectangle with width of b and height of h, centroid at (x-bar,y-bar).
 \(A = b h\)
\(b/2\)
\(h/2\)
A right triangle with right angle at the origin. Width of b and height of h, centroid at (x-bar,y-bar).
 \(\dfrac{bh}{2}\)
\(b/3\)
\(h/3\)
A trapezoid with bottom width of b, top width of a, and height of h, centroid at (x-bar,y-bar).
 \(\dfrac{(a+b) h}{2}\)
\(\dfrac{a^2 +ab + b^2}{3 (a+b)}\)
\(\dfrac{h(2a+b)}{3(a+b)}\)
A circle with radius of r, centroid at (x-bar,y-bar)=(r,r).
 \(\pi r^2\)
\(r\)
\(r\)
A semicircle with radius of r, centroid at (x-bar,y-bar)=(r,4r/(3*pi)).
\(\dfrac{\pi r^2}{2}\)
\(r\)
\(\dfrac{4 r}{3 \pi}\)
 1 
See Example 7.7.14 for proof. \(\dfrac{4 r}{3 \pi} \approx 0.424\ r\)
A quarter circle with radius of r. The center of curvature is at the origin. Centroid at (x-bar,y-bar)=(4r/(3*pi),4r/(3*pi)).
 \(\dfrac{\pi r^2}{4}\) \(\dfrac{4 r}{3 \pi}\) \(\dfrac{4 r}{3 \pi}\)
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