Structures are either partly or fully restrained, that is they can not be allowed to move freely. This is done by supports. So reactions of different kinds of supports are to be studied, at first we have to understand reactive forces on that part of the structure, by the support. A fixed support take a moment and 2 reactions, a roller support allows only a vertical reaction it may take a rotation. At a simply supported end moment is zero, it takes 2 reactions. Pinned end is has zero moment and 2 reactions these can be called boundary conditions. This must be known for structural analysis.

Elastic and Linear Behavior 

By Hook law stress/strain is constant, materials obeying this law is called linearly elastic. In stress strain graph it wont go beyond straight line portion. At lower stresses it is true about structures. This behavior is simple to analyse and provides good approximation.

Principle of Superposition

At linear behavior this principle can be applied. This principle states that the deformations resulting from each of a number of forces may be added to obtain the deformations resulting from the sum of forces. For example in a cantilever 3 forces are acting and at A first force makes deflection d1 and 2nd force makes deflection d2 at A, 3rd force makes deflection d3 at A then total deflections at that point is d1+d2+d3. But for this principle is to be true material linearity must be maintained and not allowed large deformations.

Equilibrium Equations

For zero movement in the X direction, algebraic sum of forces along that direction must be zero. It must be hold good along other 2 co ordinate axes. In order to have zero rotations about these 3 axes algebraic sum of moments also must be zero. That is

Fr = Fxi + Fyj + Fzk = 0 , vector form

Mr = Mxi + Myj + Mzk = 0

Free Body Diagram

We know that a stable structure is in equilibrium under the action of external loads and reactions. The magnitude of reactions, are such that the applied loads are balanced according to Newton 3rd law. Any part of the structure is under equilibrium with remaining part of the whole structure. This fact is usedfor finding internal forces by drawing free body diagram. The following steps can be adopted to draw correct free body diagram. Cut it hypothetically some connections or supports

Denote all the possible forces in the structure at the cuts by appropriate force vectors All forces acting on the body in its original state must be included on the diagram. Suppose a fixed end support is represented by one moment and 2 reactions, directions of forces given need not be correct.

Boundary Conditions

For a simply support moment is zero. At a simple support slope is not zero. At a fixed end slope is zero, but moment is not zero..

Bows Notations

Fab denotes force from, a to b, write a to the left of arrow and b to the right of arrow. Fba denote force fro b to a.