Equilibrium equations and support reactions

Equilibrium Equations:
We know that structures remain at rest, and since they are at rest they have to maintaining the state of equilibrium in between actions and reactions. We can define the geometry of the structure in three dimensional spaces. Since structure is at rest we can say that the actions which are acting on the structure; are in the equilibrium with reactions provided to it. This can be written in the form of equations which are also known as 'Equilibrium Equations' and are as follows:

These are six in numbers. If the structure is built with more than one part, the equilibrium equations will be the six times the number of parts.

If the structure is two dimensional; for example in x y plane, these equations will reduced as follows:

These equations are in three in numbers for each member.

Moreover, for uni-axial members (trusses and cables), the number of equilibrium equations will reduced to just one for each part.

Support Reactions:

Structure is supported with various types of supports. Each support provide a set of support reaction and the magnitude of these reactions itself is the function of loading conditions. For illustration of support reactions click here.

Introduction and classification of structures

A structure is something which is formed by its well connected parts with its supports and supposed to take the load including its own weight satisfactorily during its intended life span. For example buildings, bridges, towers, tunnels etc. 

Analysing structure is a process of estimating and limiting the deformation behaviour of the structure under given loading conditions. Analysis of structure depends on following things:

1)     Loading

2)     Behaviour of structural material

3)     Geometry

4)      Type of structure

The process of analysis is basically done with the help of calculations of unknown parameters of the structure with known set of equations. These equations depends upon certain parameters with some reasonable assumptions which makes calculations easy to handle, however with the help of advanced computer and software it becomes much easier to handle large and complicated computations.  But even now the classical knowledge of structure is beneficial at least to check the computer generated output in order to avoid false results.

Before designing a structure it is important to know that how much strong it has to be so that it can perform its intended purpose satisfactorily during its life. Simultaneously, structure becomes costlier as it becomes stronger so the designer has to optimise it to achieve certain objective of the problem. In order to make the structure safe designer has to take worst situations that may occur during its life span with their probability to occur to get an economical solution as well. Structural analysis is the process of analysing the structure in which its designer gets an idea of how the external loads get distributed throughout the structure and happens to the structure when it’s getting distributed, depending on this he/she can identify the weak and strong zones of the structure which can be further modify to meet the design goals.

In order to simplify the analysis of structures we can classify them into various categories in multiple ways:           
             Based on configuration:

1.  Linear Structure (cables, trusses, beams, shafts etc.)
2. Surface Structure (walls, shells, membranes etc.)
3. Solid Structure (Dams, thick walls etc.)

             Based on geometry in space:

1. One Dimensional (columns, beams, shafts etc.)
2. Two Dimensional (plainer trusses, plainer frames, walls etc.)
3. Three Dimensional (space trusses, space frames etc.)

             Based on functioning:

1. Cables
2. Trusses
3. Arches
4. Frames

             Based on service:

1. Buildings
2. Bridges
3. Towers
4. Mechanical 
5. Aerospace