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Lecture 26

ENGR-1100 Introduction to Engineering Analysis. Lecture 26. Today Lecture outline. Composite areas. Read Chapter 5 !!. Distributed forces. Concentrated forces. Distributed area: the moment about an axis. Composite areas. y. a. b. x. y. a. b. x. Composite body. Composite body. y.

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Lecture 26

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  1. ENGR-1100 Introduction to Engineering Analysis Lecture 26

  2. Today Lecture outline • Composite areas Read Chapter 5 !!

  3. Distributed forces Concentrated forces

  4. Distributed area: the moment about an axis

  5. Composite areas y a b x

  6. y a b x Composite body

  7. Composite body y y x x a b = a b y + x

  8. Example 5-39 Locate the centroid of the slender rod shown in the Figure.

  9. 1 2 5 4 3 (Page 212) A.Xc = My A.Yc = Mx h yc My1 = -171.5in3 Mx1 = 171.5in3 xc b My5 = 0in3 Mx5 = 0in3 My4 = -57.16in3 Mx4 = -57.16in3 My3 = 171.5in3 Mx3 = -171.5in3 My2 = 114.32in3 Mx2 = 114.32in3 A1 = A3 = 72 = 49in2, A2 = 1/4pr2 = 1/4p(7)2 = 38.48in2 A4 = 0.5.7.7 = 24.5in2, A5 = pr2 = p(3)2 = 28.27in2 Xc1 = -3.5in, Yc1 = 3.5in, Xc2 = Yc2 = 4r/(3p) = 2.971in Xc3 = 3.5in, Yc3 = -3.5in, Xc4 = -2.333in, Yc4 = -2.333in Xc5 = Yc5 = 0

  10. 1 2 5 4 3 A.Xc = SAiXci = My  Xc = My/A = 57.2/132.71 = 0.431in A.Yc = SAiYci = Mx Yc = Mx/A = 57.2/132.71 = 0.431in

  11. Class assignment: Exercise set 5-40 Locate the centroid of the slender rod shown in the Figure. Xc=75.5 mm Yc=87.2 mm

  12. Class assignment: Exercise set 5-41 Locate the centroid of the slender rod shown in the Figure. Xc=4.23 in Yc=8.33 in

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