Centroids and First Moments of AreasB. An area is symmetric with respect to an axis BBif for every point P there exists a point P'suchthat PP'is perpendicular to BB'and is dividedinto two equal parts by BB'.B(a).Thefirstmoment ofanareawithrespecttoaline of symmetry is zero..If an area possesses a line of symmetry,itscentroid lies on that axis. If an area possesses two lines of symmetry, itsBcentroid lies at their intersection..An area is symmetric with respect to a center Oif for every element dA at (x,y) there exists anarea dA' of equal area at (-x,-y). The centroid of the area coincides with thecenterof symmetry6
Centroids and First Moments of Areas • An area is symmetric with respect to an axis BB’ if for every point P there exists a point P’ such that PP’ is perpendicular to BB’ and is divided into two equal parts by BB’. • The first moment of an area with respect to a line of symmetry is zero. • If an area possesses a line of symmetry, its centroid lies on that axis • If an area possesses two lines of symmetry, its centroid lies at their intersection. • An area is symmetric with respect to a center O if for every element dA at (x,y) there exists an area dA’ of equal area at (-x,-y). • The centroid of the area coincides with the center of symmetry. 6
Centroids of Composite Areas·CompositeplatesW3XEW=Ex,WWWYw=Zyw,G3TyEAsCompositeareaC3AZAXZA=ZXAAXYZA-ZJAI7COO7
Centroids of Composite Areas • Composite plates i i i i X W xW Y W yW • Composite area i i i i X A x A Y A y A 7