To find the maximum stresses in a compound cylinder, the following four simultaneous linear equations need to be solved. 4.2857 × 10 - 9.2307×105 0 0 C₁ -7.887 × 103 4.2857x107 -5.4619×105 -4.2857x107 5.4619×105 C₂ 0 -6.5 0 -0.15384 0 6.5 4.2857x107 0.15384 -3.6057×105 C3 0.007 0 In the compound cylinder, the inner cylinder has an internal radius of a=5" and an outer radius of c=6.5", while the outer cylinder has an internal radius of c=6.5" and an outer radius of b=8". Given E=30×10 psi, v=0.3, and that the hoop stress in the outer cylinder is given by E 1-12 [(1+r)+c (17)]. find the stress on the inside radius of the outer cylinder. Find the values of C₁, C2, C3 and C using naïve Gauss elimination.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 40E
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To find the maximum stresses in a compound cylinder, the following four simultaneous
linear equations need to be solved.
4.2857 × 10 - 9.2307×105
0
0
C₁
-7.887 × 103
4.2857x107
-5.4619×105 -4.2857x107
5.4619×105 C₂
0
-6.5
0
-0.15384
0
6.5
4.2857x107
0.15384
-3.6057×105
C3
0.007
0
In the compound cylinder, the inner cylinder has an internal radius of a=5" and an outer
radius of c=6.5", while the outer cylinder has an internal radius of c=6.5" and an outer
radius of b=8". Given E=30×10 psi, v=0.3, and that the hoop stress in the outer
cylinder is given by
E
1-12
[(1+r)+c (17)].
find the stress on the inside radius of the outer cylinder.
Find the values of C₁, C2, C3 and C using naïve Gauss elimination.
Transcribed Image Text:To find the maximum stresses in a compound cylinder, the following four simultaneous linear equations need to be solved. 4.2857 × 10 - 9.2307×105 0 0 C₁ -7.887 × 103 4.2857x107 -5.4619×105 -4.2857x107 5.4619×105 C₂ 0 -6.5 0 -0.15384 0 6.5 4.2857x107 0.15384 -3.6057×105 C3 0.007 0 In the compound cylinder, the inner cylinder has an internal radius of a=5" and an outer radius of c=6.5", while the outer cylinder has an internal radius of c=6.5" and an outer radius of b=8". Given E=30×10 psi, v=0.3, and that the hoop stress in the outer cylinder is given by E 1-12 [(1+r)+c (17)]. find the stress on the inside radius of the outer cylinder. Find the values of C₁, C2, C3 and C using naïve Gauss elimination.
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