Rotating construction is an important method in bridge construction,and the calculation of friction force is particularly important for large tonnage rotating bridge,However there is a big difference between the calculate results based on the existing conventional method and the field test results. Therefore,the accurate calculation of friction force needs to be improved. In this paper,the moment of vertical friction resistance is obtained by weighing experiment,and a new stress distribution model of spherical hinge contact surface is proposed based on contact theory. The formula for calculating the moment of vertical friction resistance is established,and then the friction coefficient is obtained. The results are compared with those obtained by conventional method and actual traction force. The results show that the improved optimization formula proposed in this paper is superior to the conventional formula widely used in calculating the surface stress and predicting the static friction coefficient of spherical joints.