Problem_06_15

Problem_06_15 - Problem 6.15 Derive the relation for the...

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Problem 6.15 Derive the relation for the shear stress distribution on the x axis for the equilateral triangle in Fig. 6.10. Solution: From Eq. 6.48, page 215: ϕ G θ 2h x3 y 3 y + 3 x h 3 + = From the definition of the Prandtl Stress Funcion σ zy x ϕ d d = σ zy x G θ y 3 y + 3 x h 3 + d d = simplify σ zy G θ x 3x 2 3y 2 + () = Along the x axis, y=0 and thus: σ zy G θ 2x h 2 = σ zx y ϕ d d = σ zx y G θ y 3 y + 3 x h 3 + d d = simplify σ zx G θ y h3 x + h = Along the x axis, y=0 and thus: σ zx 0 = Here is some extra work: Note that at x h 3 = σ zy G θ 2 h 3 h 3 h 3 2 = G θ h 2 2 3 1 3
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