1. CE 201 - 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

2. CE 201 - 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

3. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Centroid of Area Centroid of Volume x z y y x dV dA

4. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Find Centroid of area ? Example y m h dy b y x

5. CE 201 - 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 4 1 ++ 0.85cm 2cm 0.85cm 2cm

6. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering TOTAL S.N. 1 2 3 4 Shape 36.1441.67130.35 Area cm 2 cm ~ x ~ y cm ~~ xA cm 3 yA cm 3 Semi-Circle Rectangle Triangle Quarter-Circle 6.28 24 9 -3.14 2 2 3.15 6.85 3 2 0.85 12.56 48 -9 -9.89 43.02 72 18 -2.67

7. CE 201 - 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

8. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering TOTAL S.N. 1 2 3 4 Shape 36.14674.24544.4 Semi-Circle Rectangle Triangle Quarter-Circle 5 5 2 6.15 6.85 3 2 0.85 157 600 36 -118.76 294.67 216 36 -2.67 6.28 24 9 -3.14 Area cm 2 dx cm dy cm Adx 2 cm 4 Ady 2 cm 4 I xx cm 2 I yy cm 2 90.87 41.91 1.74 72 18 -0.87 6.24 32 4.5 -0.87 90.87 + 544.4 = 635.27 cm 4 41.91 + 674.24 = 716.15 cm 4

9. CE 201 - 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

10. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Example 1: y dy y x h b