Material Science > QUESTIONS & ANSWERS > University of Texas - MSCI 353Homework+4+answer+key ALL ANSWERS CORRECT (All)

University of Texas - MSCI 353Homework+4+answer+key ALL ANSWERS CORRECT

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Homework 4 Answer Key 4.1 (a) In a polyvinyl chloride (PVC) plate, there is an elliptical, through-thethickness cavity. The dimensions of the cavity are: Major axis=1 mm Minor axis=0.1 mm Compute ... the stress concentration factor Kt at the extremities of the cavity. (2 pts) Solution: ρ a K t = 2 mm mm mm a b 0.005 12 2 0.1 2 2 = ⎞⎟⎠ ⎛⎜⎝ ⎞⎟⎠ ⎛⎜⎝ ρ = = 20 0.005 1/ 2 ∴ = 2 = mm mm K t (b) Calculate the maximum tensile stress at the surfaces of a circular hole (in the case of a thin sheet) and a spherical hole (in the case of a thick specimen) subjected to a tensile stress of 200 MPa? The material is Al2O3 with v=0.2 (3 pts) Solution: Circular hole: Using Inglish’s formula for elliptical hole and setting a=b, we obtain: 3 600MPa σ max = ⋅σ = Spherical hole: Using the formula by Goodier for the equatorial plane (θ = π / 2 ) and setting r=a in order to obtain the stress at the surface of the hole, ( ν ) ( ν ) σ ν σ θθ ⎤⎥⎦ ⎡⎢⎣ ⋅ − ⋅ + − − = + 5 5 3 3 2 7 5 9 2 7 5 4 5 1 ar ar ⎥ ⎦ = ⋅ = ⎤ ⎡⎢⎣ = + + σ 2 σ 12 9 12 [Show More]

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