Q3: Stress Relaxation in Elevated Temperature Flange Bolts A flange in a high temperature pipeline is sealed by tightening 6 steel bolts with Young's modulus is E = 172E3 MPa. The flange is required to operate for 10,000 hours without leakage, which is known to occur when the stress in the bolts is 30 MPa or lower. a) Assuming steady state creep occurs in the bolts according to the Norton power law Esc with Norton's law parameters: = Bon B = 40.0x10-16, n = 3.6 determine the minimum initial preload stress required in the bolts to ensure that the stress does not relax to below 36 MPa (i.e. the 30MPa seal preload multiplied by a design factor of 1.2) after 10,000 hours in service conditions. 1 (MPa)"h [7 Marks] b) Assuming sealing condition of 30 MPa bolt stress applies, determine the maximum time at which the bolts must be re-tightened to prevent leakage./nNOTE: Part b(i), calculating c. Part b(i) requires you to determine c. This involves solving a cubic equation. You may do thi by any suitable method you choose, including use of mathematical software. For students not familiar with such software, the simplest way is probably to use a graphical method in Excel. All the values in the moment equation are known except c. In Excel, calculate and plot M for an appropriate range of values of c. From the plot, determine the value of c that gives M = 14kNm. Moment kNm C

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