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 2 h x 3 y 2 h 3 x 3 y + 2 h 3 x h 3 + = From the definition of the Prandtl Stress Funcion σ zy x ϕ d d = σ zy x G θ 2 h x 3 y 2 h 3 x 3 y + 2 h 3 x h 3 + d d = simplify σ zy G θ 2 h x 3 x 2 3 y 2 + ( ) 2 h = Along the x axis, y=0 and thus: σ zy G θ 2 h 2 x h 3x 2 ( ) = σ zx y ϕ d d = σ zx y G θ 2 h x 3 y 2 h 3 x 3 y + 2 h 3 x h 3 + d d = simplify σ zx G θ y h 3 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 2 h 3 h 3 h 3 2
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