1. 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

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

3. CE 201 - STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering + 7cm 3cm4cm 6cm r =2cm 0 6cm 2 1 y x 4 1 + 3 3 2 4 + 0.85cm 2cm 0.85cm 2cm + 3cm FIND CENTROID ? + 2cm 1cm

4. 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

5. 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

6. 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

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