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191_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011

191_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011 -...

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SL17 Geometry for method of slices: o for each slice must find weight, Wi and base angle, <Xi: o can draw slope with slices to scale and measure with scale and protractor o or can use trigonometry: Xi = R sin <Xi y H Yi = R cos <Xi ~Xi first define the circle center, the circle radius R, the width ~Xi of each slice, and the horizontal distance, Xi, from the circle center to the slice center since X I = R sin (X.i then (X.i = sin· 1 (~ ) the volume of the slice is ~ihi where hi = height of the slice at its center and hi = Rcos(X.j - ~Yj where ~Yi = distance to circle center above slice surface
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Unformatted text preview: circle center above slice surface the weight of the slice, Wi = 1~ihi H =30' AY3 = (tJ v '- 11 . )"') :: ;;l 1. ~ I h 3 = R COS(X3 -AY3 = '(V '(051 f, 11"-'J. "1.S-' = 10. f I ) ') I k W-'VAX h -l:to f(~ (5" (10.5'-: ". Jo k' 3 -,Ui 3 3 -IO()O It. • Slice Geometry Example: toe circle, i = 45°, center above toe, 5' slices, 1= 120 pcf, R = 40', H = 30', Y = 40' , for slice 3: X3 = 1:l5', Ax3 = 5...
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