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CE231_Homework3 Answer

# CE231_Homework3 Answer - CE 231 HW#3(Collected 9/10/4...

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CE 231 HW #3 (Collected 9/10/4) Hibbler Problem 9.4 Determine the stress components acting on the inclined plane AB in Figure 1 using method of equilibrium. 2 ksi 4 ksi A 3 ksi 30 o B Figure 1 x’ Section 1 Taking Section 1 and the sum of the forces in each direction are = 0 the following equations are determined. τ x’y’ 4* A*sin(30) 4* A*cos(30) 2* A*cos(30) y’ 3* A*sin(30) F x’ A x 60 o y

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x' x' 2 2 x' F 0 0 F * A 2* A*cos(30)*cos(30) 4* A*cos(30)*sin(30) 3* A*sin(30)*sin(30) 4* A*sin(30)*cos(30) F 8*cos(30)*sin(30) 3*sin (30) 2*cos (30) 2.71 ksi + = = + = + = − / / / y' x'y' 2 2 x'y' F 0 0 * A 4* A*cos(30)*cos(30) 3* A*cos(30)*sin(30) 4* A*sin(30)*sin(30) 2* A*sin(30)*cos(30) 5*cos(30)*sin(30) 4*sin (30) 4*cos (30) 4.17 ksi =4.17 ksi + = = τ + + + τ = − + = − 2 3 The result is shown in Figure 2. y’ Figure 2 4.17 ksi x’ 4.17 ksi 2.71 ksi y’ y x 60 o
Hibbler Problem 9.5 Determine the stress components acting on the inclined plane AB in Figure 1 using the stress-transformation equations.

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CE231_Homework3 Answer - CE 231 HW#3(Collected 9/10/4...

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