Broken bridge

This bridge on Royal Deeside had been hit by a tree in flood waters and put out of action. Suppose the tree had a mass of 1 tonne (1000kg) and was travelling at 30km/h, which is about 8 m/s. That would give it a kinetic energy of 35000J. Elastic strain energy is given by 0.5kx^2 where k is the spring constant and x is the extension. Suppose the bridge is 15m long and the middle is displaced by 30cm. By Pythagoras, that means an extension of each half by about 0.5cm. That means spring constant would be 1.4 x 10^9 N/m.