A Centroidal Method of Rigid-Frame Analysis

The object of this paper is to present a method for the analysis of rigid frames. Rotations and translations of the ends are represented by a resultant vector at the centroid. By use of this vector and the circle of inertia the amount and direction of the thrust are found. The distance from the centroid to the line of action of the thrust is shown to be a function of the relative rota tion of the ends. In a structure with intermedia te loads which has been made determinate by release of joints the rotation and the displacement at the centroid determine the thrust required to return it to its original indeterminate position. The moments in the structure are _the algebraic sum of the determinate and indeterminate moments. A method of finding the deflection and rotation of any point on the structure is shown. The method is developed analytically and illustrative examples are solved graphically.