Question: Using superposition of the stress field (8.4.15), develop solution (8.4.18) for the equal but opposite biaxial loading on a stress-free hole shown in Fig. 8.15A.

Using superposition of the stress field (8.4.15), develop solution (8.4.18) for the equal but opposite biaxial loading on a stress-free hole shown in Fig. 8.15A. Also justify that this solution will solve the shear loading case shown in Fig. 8.15B. Construct a polar plot (similar to Fig. 8.13) of σθ(a,θ)/T for this case.

Equation 8.4.15

or = T (1)+() TTA = T T 0-7(14) -7 (1+3) 02) + cos T 2a  (1-30 202) + cos 20 sin 20 (8.4.15)

Equation 8.4.18

3a* 0 = 7(1+34-4)cos 20 g 3a4 -7 (1+30)008 20 -T1+ 2a 5,60 -- 7 (1-34 +247) sin 20 (8.4.18)

Fig 8.15 A

(a) T O Biaxial Loading

Fig 8.15 B

(b) T 45 Shear Loading T

Fig 8.13

150/ 180 210 120 240 90 3 2 270 60 (a,0)/T 30 300 -(a,0)/T 0 330


0-1 (1-5) + (+ 49) 00s 20 T 3a4 = 1+ cos 2 A T T **-1 (1+2)-(1+) cos 29 Tre= T 7(1-34 +24) si sin 20 (8.4.15)

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