One of the most famous analysis methods to analyze continuous beams is “Moment Distribution Method”, which is based on the concept of transferring the loads on the beams to the supports at their ends. Each support will take portion of the load according to its K; K is the stiffness factor, which equals EI/L. As you can see E, and L is constant per span, the only variable here is I; moment of inertia. I depends on the cross section of the member. So, if you want to use this analysis method, you have to assume a cross section for the spans of the continuous beam. If you want to use this method to analyze a simple frame, it will work, but it will not be simple, and if you want to make the frame a little bit more complicated (simple 3D frame) this method alls short to accomplish the same mission.

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Hence, a new more sophisticated method emerged, which depends fully on matrices, this method called “Stiffness Matrix Method”, the main formula of this method is: [P] = [K] x [Δ] [P] is the force matrix = Dead Load, Live Load, Wind Load, etc [K] is the stiffness factor matrix. = K=EI/L [Δ] is the displacement matrix. • The stiffness analysis implemented in STAAD is based on the matrix displacement method. • In the matrix analysis of structures by the displacement method, the structure is first idealized into an assembly of discrete structural components (frame members or finite elements). Each component has an assumed form of displacement in a manner which satisfies the force equilibrium and displacement compatibility at the joints • First structural software which adopted Matrix Methods for the method of analysis was STAAD • Methods used:- Modified Cholesky’s method (Decomposition) Most efficient accurate and time saving method also well suited for Gaussian Elimination Process. • A STRUCTURE can be defined as an assemblage of elements.

STAAD is capable of analyzing and designing structures consisting of both frame, and Finite elements. Almost any type of structure can be analyzed by STAAD. • Frame elements – Beam elements – 2 nodes • Finite elements – 1.) Plate – 3 or 4 nodes 2.) Solid – 4 to 8 nodes Remember for staad - Node becomes Joint it has a number and xyz cordinates Beam becomes Member it has a number and nodes at its ends Plate becomes Element it has a number and node at its corners. • A TRUSSstructure consists of truss members which can have only axial member forces and no bending in the members • A PLANEstructure is bound by a global X-Y coordinate system with loads in the same plane • A SPACE structure, which is a three dimensional framed structure with loads applied in any plane, is the most general.

• A FLOORstructure is a two or three dimensional structure having no horizontal (global X or Z) movement of the structure [FX, FZ & MY are restrained at every joint]. The floor framing (in global X-Z plane) of a building is an ideal example of a FLOOR structure. Columns can also be modeled with the floor in a FLOOR structure as long as the structure has no horizontal loading.

If there is any horizontal load, it must be analyzed as a SPACE structure.

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