Matrix Algebra, Nodal forces and nodal displacements, The stiffness matrix of a linear spring in the local coordinate system. The stiffness matrix of two springs in series. Properties of the stiffness matrix. Calculation of the internal forces in the members of plane frames.

The direct stiffness method.

Analysis of trusses: The pinned bar element. Transformation of coordinates from the local to the global coordinate system. The transformation matrix. The stiffness matrix of a bar in the global coordinate system. Application of the direct stiffness method for the analysis of plane trusses.

Beams and frames: The beam element, Calculations of the element stiffness matrix with the unit load method. Analysis of continuous beams subjected to nodal and distributed loads. The stiffness matrix of beams in the global coordinate system. Analysis of frames with the direct stiffness method.

Special Topics: Internal Member Releases, Member End Length Offsets, Diaphragms.