CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Center of Gravity & Centroid Method of Weighted average x y z W1W1 W4W4 W3W3 W2W2 WnWn

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Center of Gravity x y z Dw=  dv This is called Centroid of Volume.  Center of Gravity = Centroid for Uniform materials

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Centroid of Area Centroid of Volume x z y y x dV dA

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Find Centroid of area ? Example y m h dy b y x

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering x 7cm r =2cm 0 6cm 3 4 2cm + r =2cm 2 1 y FIND CENTROID ? 2 + 3cm 6cm 3 + 2cm 1cm 3cm4cm cm 2cm 0.85cm 2cm

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering TOTAL S.N Shape Area cm 2 cm ~ x ~ y cm ~~ xA cm 3 yA cm 3 Semi-Circle Rectangle Triangle Quarter-Circle

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering + 7cm r =2cm 0 6cm 2 1 y x 3 4 FIND MOMENT OF INERTIA I xx & I yy ? Parallel - Axis Theorem

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering TOTAL S.N Shape Semi-Circle Rectangle Triangle Quarter-Circle Area cm 2 dx cm dy cm Adx 2 cm 4 Ady 2 cm 4 I xx cm 2 I yy cm = cm = cm 4

CE STATICS y x y x ~ ~ dA Dr. Mustafa Y. Al-Mandil Department of Civil Engineering MOMENT OF INERTIA PARALLEL AXIS THEOREM CENTROIDAL MOMENT OF INERTIA + x x dy y ~ dA

CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Example 1: y dy y x h b