Chapter 2 - First-order linear elastic analysis for rigid and semi-rigid frames

Abstract

This chapter introduces the basic concept and formulation of linear elastic analysis of majority of structures, especially steel frames with various connection stiffnesses. A number of manual and computer methods for linear analysis of skeletal structures have been developed over the past century. The slope deflection method, the iterative moment distribution method, and the flexibility and the stiffness methods are used for linear analysis of skeletal structures. However, regardless of the method used, three basic conditions must always be satisfied: the compatibility, the equilibrium, and the material constitutive relationship. All structural analyses require a set of consistent coordinate systems to define the vector quantities. A properly defined coordinate system is essential for the development of a reliable, convenient, and user-friendly analysis computer program. The element stiffness matrix is formulated in a set of local coordinate axes parallel to the principal axes for convenience. The checking of connections concentrates on strength, stiffness, and ductility; and it can be carried out easily by computer analysis.