Centroids & Centers of Gravity
Centroids & Centers of Gravity
Contents·Introduction（绪论）·CenterofGravityofa2DBody（两维物体的重心）·Centroids and First Moments of Areas（形心与面积的一次矩）·CentroidsofCompositeAreas（组合面积的形心）·Determination ofCentroids by Integration（积分法求形心）·CentroidsofCommonShapesofAreas（常见平面图形的形心）2
Contents • Introduction（绪论） • Center of Gravity of a 2D Body（两维物体的重心） • Centroids and First Moments of Areas（形心与面积的一次矩） • Centroids of Composite Areas（组合面积的形心） • Determination of Centroids by Integration（积分法求形心） • Centroids of Common Shapes of Areas（常见平面图形的形心） 2
Lntroduction. The earth exerts a gravitational force on each of the particlesforming a body. These forces can be replaced by a singleequivalent force equal to the weight of the body and applied at thecenter of gravity for the body. The centroid of an area is analogous to the center of gravity of abody. The concept of the first moment of an area is used to locatethe centroid.3
Introduction • The earth exerts a gravitational force on each of the particles forming a body. These forces can be replaced by a single equivalent force equal to the weight of the body and applied at the center of gravity for the body. • The centroid of an area is analogous to the center of gravity of a body. The concept of the first moment of an area is used to locate the centroid. 3
Center of Gravity of a 2D Body.Center of gravity of a plateAZ,=x=xa=J xdWZM,=JW-y,AW=J ydw4
Center of Gravity of a 2D Body • Center of gravity of a plate y i i x i i M xW x W xdW M yW y W ydW 4
Centroids and First Moments of Areas.Centroid ofan area (assuminguniformthicknessanddensity)xW=[xdWx(pgAt)=[x(pgt)dAxA=[xdA=S,= first moment with respect to yyA=[ydA=Sx= first moment with respectto x5
Centroids and First Moments of Areas first moment with respect to first moment with respect to y x xW x dW x gAt x gt dA xA x dA S y yA y dA S x • Centroid of an area (assuming uniform thickness and density) 5