Statics - Civil Engineering

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A Brief about
  Statics is the branch of mechanics which deals with the study of any object or body or system under static equilibrium i.e. the net force acting on the object or body or system is zero.
  From civil engineering point of view, statics helps in determining stress functions (reactions, shear force, bending moment) in any structural system by using the equations of static equilibrium provided the structure is statically determinate.
  A determinate structure is one which can be easily analyzed through equations of static equilibrium only. By analyzing a structure we mean finding all the unknowns like reactions, internal forces in the structure using equations of static equilibrium only without developing any compatibility equation unlike indeterminate structures in order to find the unknowns.
  We find the application of statics in the static analysis of a structure for a given loading, analyzing force systems including two-dimensional and three dimensional force systems, finding center of mass and centroid, analyzing internal and external effects on beams and frames, flexible cables, analyzing a plane truss by using method of joints and method of sections, application of friction in machines, a three-cabled system under tension at rest, calculating hydrostatic forces in fluids for systems at rest, systems subjected to force but not moving due to static friction, vector operations etc. Thus statics find its application in analyzing both solid and liquid systems at rest. Free-body diagrams are made by balancing all the forces on the system such that net force on the system is zero for the systems at rest. For free-body diagrams of system with acceleration we can still balance the force by treating the acceleration as a pseudo force and covert a dynamic system in to static system thus analyzing the system using equations of static equilibrium, this is also known as D’Alembert’s principle.
  Statics finds its extensive application in structural engineering and strength of materials since by finding stress functions one can draw the shear force diagram, bending moment diagram which are used as inputs in design of the structural system.
  Statics is used in converting a distributed force of system in to a concentrated system so that the effect of different distributed forces can be assumed to act at one place. It should be noted that simplifying a distributed force system to a concentrated force system should only be used to find the reactions only. It should not be used in finding the shear force and bending moment because they depend on the actual position of the loading.
  Statics is also used in drawing influence line diagram for any stress function for statically determinate structures. It should be noted that the structural element (beams, columns, slab) is in static equilibrium at each location of loading thus equations of static equilibrium can be easily used to find the required stress function and drawing influence line diagram for that stress function.
  Availability of number of equations of static equilibrium depends on whether the system is two-dimensional or three-dimensional. For a two-dimensional system, only three equations of static equilibrium are available but for a three-dimensional system six equations of static equilibrium are available. Thus, we can find at most three and six unknowns in two-dimensional and three-dimensional structural systems respectively by using equations of static equilibrium only.
   In any structure, the major load consists of gravity load. Analyzing a structural system for gravity loads is the first step in analyzing any structural system which is done by static analysis by using the equations of static equilibrium. Even in indeterminate structures, if the analysis is being done manually then we have to take certain assumptions so that the structure can be converted to a statically determinate one and all the unknowns can be found easily by using equations of static equilibrium. Assumption includes assuming a contra-flexure at the mid-point of beams, columns etc.
  As a civil engineer, statics is a very important subject because this knowledge is required in designing a structure and we don’t want our structures to move or fall. Even in dynamic conditions like earthquake we want our structure to be in state of static equilibrium at each point of time so that there will be no damage or cracks or failure of any member. In fact, for simple structures we indeed use one method called equivalent static load method to simplify the analysis procedure. This equivalent static load is applied at the base of the structure and structure is analyzed by using equations of static equilibrium only. It should be noted that the equivalent static load method is suitable for simple structures only or to get a preliminary idea as this method is very conservative and doesn’t reflect a true picture of distribution of forces generated due to earthquake.
  Thus statics is a powerful tool in structural engineering and core knowledge of statics can help us to analyze the structure better and design the structures which are safe, economical and effective for a given loading condition.
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