The American Institute of Steel Construction Proposed Load and Resistance Factor Design Specification recognizes the ability of connections that function as less than fully rigid to transmit limited moments and to provide some measure of end restraint to columns in its definition of partially restrained (PR) construction. An analytical procedure for determining the response up to collapse of subassemblages in which semirigid beam-to-column connections are present is derived. This employs a nonlinear finite element column analysis together with analytical representation of experimentally determined connection moment–rotation [Formula: see text] curves. To trace the full response under any load path produced by a combination of beam loads and direct column load, it is necessary to allow for possible reversal in the direction of rotation of any of the connections. The program is used to study the effect of different connection types (ranging from very flexible web cleats to almost rigid extended end plates) and different load paths on column behaviour in nonsway subassemblages. It is found that the degree of rotation required from each connection is an important parameter in determining column response. Key words: buckling, columns, connections, frames, stability, steel, structural design, structures.

Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.

Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.