Consider the expansion loop displayed in the diagram below, which is part of a long pipeline.  The loop is made up of a uniform pipe section and is subjected to a temperature raise of ΔT.  The total length of this loop is L and the coefficient of thermal expansion is α.  Determine the restraining bending moment M and force N induced by the temperature change in each end of the loop.

Q2) For a Vogt material under a stress along with a constant rate find e (t). C (t) = 1/E [ 1- exp((-t)/(τ 2))]?