Battering Ram

As a part of their offensive, the orcs of Mordor want to break through the gate of Minas Tirith. In a parallel-universe Middle-earth, no progress is made even after calling for Grond, a fire spitting battering ram. Feeling hopeless, Sauron eventually decides to prop up another battering ram horizontally between the gate and a newly built perfectly rigid wall. He then orders to heat the ram so as to exploit thermal expansion properties of its material to break the gate. Find out by how much (in Kelvins) the ram needs to be heated. Assume that the ram has the shape of a cylinder with axis perpendicular to the gate. The material of the ram has linear expansion coefficient $\alpha$ $= 1.2*10^{-5} K^{-1}$ , Young’s modulus of compression $Y = 211 GPa$ and the maximum compressive stress that the gate endures is $\sigma_{max}$ $= 400 MPa$ . Consider the thermal expansion process to be fully linear and assume that there is no deformation of the gate until it yields.Give answer rounded off to nearest integer.

Problem adapted from PUPC Physics Brawl November 2015.