Civil engineering problem:
The following matrix is the simultaneous linear equations to find the maximum stresses in a pipe.
𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑠𝑖𝑡𝑦 = 𝐸 = 30 × 106 𝑝𝑠𝑖
𝑝𝑎𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝑣 = 0.3
𝜎𝜃 =
𝐸
1−𝑣
(1
+
𝑣)
+
𝑐
(
)]
[𝑐
3
4
1 − 𝑣2
𝑟2
Find the stress on the inside radius of the outer pipe
Find the values of 𝑐1 , 𝑐2 , 𝑐3 and 𝑐4 using Gaussian elimination method, Gaussian elimination by partial
pivoting and LU Decomposition (Excel and Matlab)
Ahmad Alyafei