20_ch 03 Mechanical Design budynas_SM_ch03

20_ch 03 Mechanical Design budynas_SM_ch03 -...

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Chapter 3 33 The uniform stress assumption is common practice but is not exact. If interested in the details, see p. 570 of 6th edition. 3-17 From Eq. (3-15) σ 3 ( 2 + 6 4) σ 2 + [ 2(6) + ( 2)( 4) + 6( 4) 3 2 2 2 ( 5) 2 ] σ [ 2(6)( 4) + 2(3)(2)( 5) ( 2)(2) 2 6( 5) 2 ( 4)(3) 2 ] = 0 σ 3 66 σ + 118 = 0 Roots are: 7.012, 1.89, 8.903 kpsi Ans. τ 1 / 2 = 7 . 012 1 . 89 2 = 2 . 56 kpsi τ 2 / 3 = 8 . 903 + 1 . 89 2 = 5 . 40 kpsi τ max = τ 1 / 3 = 8 . 903 + 7 . 012 2 = 7 . 96 kpsi Ans. Note: For Probs. 3-17 to 3-19, one can also find the eigenvalues of the matrix [ σ ] = ± σ x τ xy τ zx τ xy σ y τ yz τ zx τ yz σ z ² for the principal stresses 3-18 From Eq. (3-15) σ 3 (10 + 0 + 10) σ 2 + ³ 10(0) + 10(10)
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