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MP2001 Chap 7 part 2

MP2001 Chap 7 part 2 - Example 7.02(a Rework Ex 7.01 using...

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1 1 Example 7.02 (a) Rework Ex 7.01 using Mohr’s circle construction & find (b) Principal planes, (c) Principal stresses, (d) Max shearing stress and corresponding normal stress. 2 = Y σ xy τ = x σ • Construction of Mohr’s circle ( ) ( ) ( ) ( ) MPa 50 40 30 MPa 40 MPa 30 20 50 MPa 20 2 10 50 2 2 2 = + = = = = = = + = + = = CX R FX CF OC y x ave σ σ σ xy τ = = Y σ x σ

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2 3 p θ 2 • Principal planes and stresses 50 20 max + = + = = CA OC OA σ MPa 70 max = σ 50 20 min = = = BC OC OB σ MPa 30 min = σ ° = = = 1 . 53 2 30 40 2 tan p p CP FX θ θ 0 0 6 . 116 , 6 . 26 = p θ p θ MPa 30 min = σ MPa 70 max = σ (ref from x axis) 4 70 max = σ 30 min = σ A E B D 0 1 . 53 2 = p θ 50 max = τ 0 90 d b a 0 45 20MPa ' = σ 20MPa ' = σ MPa 0 5 max = τ MPa 70 max = σ MPa 30 min = σ p θ e R = max τ ave σ σ = MPa 50 max = τ MPa 20 = σ • Maximum shear stress Same answers as Ex 7.01! 20 ' = = ave σ σ (in-plane)