mws_civ_sle_txt_gaussian_examples

mws_civ_sle_txt_gaussian_examples - 04.06.1 Chapter 04.06...

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Unformatted text preview: 04.06.1 Chapter 04.06 Gaussian Elimination – More Examples Civil Engineering Example 1 To find the maximum stresses in a compound cylinder, the following four simultaneous linear equations need to be solved. × − = × − × − − × × − × − × × − × 007 . 10 887 . 7 10 6057 . 3 10 2857 . 4 15384 . 5 . 6 15384 . 5 . 6 10 4619 . 5 10 2857 . 4 10 4619 . 5 10 2857 . 4 10 2307 . 9 10 2857 . 4 3 4 3 2 1 5 7 5 7 5 7 5 7 c c c c In the compound cylinder, the inner cylinder has an internal radius of " 5 = a and an outer radius of " 5 . 6 = c , while the outer cylinder has an internal radius of " 5 . 6 = c and an outer radius of " 8 = b . Given psi 10 30 6 × = E , 3 . = ν , and that the hoop stress in the outer cylinder is given by ( ) − + + − = 2 4 3 2 1 1 1 r c c E ν ν ν σ θ , find the stress on the inside radius of the outer cylinder. Find the values of 1 c , 2 c , 3 c and 4 c using naïve Gauss elimination. Solution Forward Elimination of Unknowns Since there are four equations, there will be three steps of forward elimination of unknowns. First step Divide Row 1 by 7 10 2857 . 4 × and then multiply it by 7 10 2857 . 4 × , that is, multiply Row 1 by 1 10 2857 . 4 10 2857 . 4 7 7 = × × . ( ) [ ] [ ] 3 5 7 10 887 . 7 10 2307 . 9 10 2857 . 4 1 1 Row × − × − × = × Subtract the result from Row 2 to get 04.06.2 Chapter 04.06...
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mws_civ_sle_txt_gaussian_examples - 04.06.1 Chapter 04.06...

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