Using the solution from Example 10.7, apply the principle of superposition and solve the problem of a

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Using the solution from Example 10.7, apply the principle of superposition and solve the problem of a stress-free elliptical hole under uniform biaxial tension as shown. In particular show that the circumferential stress is given by:

Jo(9) = Sx (2m+1-2 cos 2p - m m - 2m cos 20+1 To (9) = S( + Sy Finally for the special case of Sx = Sy = S,

= S LI b 1 IT a 8 =Sx =

Data from example 10.7

Consider the problem of a stress-free elliptical hole in an infinite plane subjected to uniform stress 0x =b Ox= S

On the boundary = e, ap = 0 and the circumferential stress is given by (2m+1  2 cos 2 q - m m - 2m cos 2 q+1

25 8 Stress Concentration Factor 15 10 5 0 O 1 2 (op)max/S Circular Case 3 4 5 6 7 Eccentricity Parameter,

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