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Dr. Mustafa Y. Al-Mandil Department of Civil Engineering

Dr. Mustafa Y. Al-Mandil Department of Civil Engineering. Chapter 9. Centroid of Area. Centroid of Volume. z. y. dV. y. dA. x. x. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering. Chapter 9. Example. Find Centroid of area ?. y. m. dy. h. y. x. b.

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Dr. Mustafa Y. Al-Mandil Department of Civil Engineering

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  1. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Chapter 9 Centroid of Area Centroid of Volume z y dV y dA x x

  2. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Chapter 9 Example Find Centroid of area ? y m dy h y x b

  3. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Chapter 9 FIND CENTROID ? y r =2cm 1 + 2 2 3cm 3 3 6cm 6cm + 2cm + 1cm 2cm 4 r =2cm 0 x 3cm 4cm 7cm 7cm 4 2cm + + 1 0.85cm 0.85cm 2cm 2cm 0.85cm

  4. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Chapter 9 ~ ~ ~ ~ S.N. Shape Area cm2 cm y cm xA cm3 yA cm3 x 1 Semi-Circle 6.28 2 6.85 12.56 43.02 2 Rectangle 24 2 3 48 72 3 Triangle 9 18 -1 -9 2 4 Quarter-Circle -3.14 3.15 -9.89 0.85 -2.67 36.14 41.67 130.35 TOTAL

  5. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering y r =2cm 1 + 2 3 6cm 4 r =2cm 0 x 7cm 7cm Chapter 9 FIND MOMENT OF INERTIA Ixx & Iyy ? Parallel - Axis Theorem

  6. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering dx cm Area cm2 Ixx cm2 Iyy cm2 dy cm Adx2 cm4 Ady2 cm4 Chapter 9 S.N. Shape 1 Semi-Circle 6.28 5 6.85 157 6.24 294.67 1.74 2 Rectangle 24 5 3 600 216 32 72 3 Triangle 9 36 2 36 4.5 2 18 4 Quarter-Circle -3.14 6.15 -118.76 0.85 -0.87 -2.67 -0.87 TOTAL 36.14 674.24 544.4 90.87 41.91 90.87 + 544.4 = 635.27 cm4 41.91 + 674.24 = 716.15 cm4

  7. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Chapter 9 Example 1: y Centroid of Rectangle dy h y x b

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