Assignment9-solution

Assignment9-solution - Problem 6.6: Consider the split beam...

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Problem 6.6 : Consider the split beam with loading shown in Figure 6.27. Both loadings in the figures 6.11 and 6.27 are antisymmetric, and both are Mode II fracture problems. For the same value of P, which loading is more efficient in cracking the beam? Assume that the material is aluminum 2024-T651 with E = 70 GPa 3 . 0 a = 10x10 -2 m, t =2x10 -2 m L = 15x10 -2 m, h =1x10 -2 m Figure 6.27 Figure 6.11 Solution: From example 6.4 for the loading in Fig. 6.11, the strain energies calculated at the three segments shown on the figure are: 1 2 2 1 2 EA a P U U where ht A A 2 1 (1)  3 2 2 3 2 3 2 ) ( 2 2 / 2 / EI a L h P dx EI Ph Ph U L a where 3 3 3 12 8 ) 2 ( 12 1 th h t I (2) P P x a L 1 2 3 3 Ph b P P 2h t x a L 1 2 3
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The total strain energy is the sum of the three as, 3 2 2 1 2 3 2 1 2 ) ( 2 2 EI a L h P EA a P U U U U (3) Strain energy release rate da dU t G 1 (4) Substituting (3) along with
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Assignment9-solution - Problem 6.6: Consider the split beam...

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