Engineering Mechanics: Static Force Analysis

Structures are made to support loads. Structure is an assembly of number of members arranged in certain manner. When load acts on a structure this load is distributed to the constituent members of the structure in different proportions. Members experiencing large forces can be made stronger, members experiencing less force can be made lighter and redundant members with no force to support can be removed altogether. Thus static force analysis of structures can help to build cost effective, light and strong structures.


Force acting on a member of a structure can be compressible or tensile. For the purpose of force analysis a sign convention can be assigned to the forces. Tensile forces, acting outwards the members and having a tendency to extend the member, is assigned positive sign. The force acting inwards any member and tending to compress the member is called as compressive force and assigned negative sign. Although a sign convention opposite to this one can also be followed with equal validity but the same sign convention should be adhered to throughout the analysis of a structure.

There are mainly two approaches for static force analysis in structures. One approach is to section the structure under consideration and find the unknown forces by balancing the forces. Other approach is based on the principle that net force at any joint or node for static structure is zero. In either of the approaches force calculation is started from the support points as it is easier to determine the forces at the support points and further calculation of forces in the members of the structure becomes easier after knowing the forces at supports.

Section Approach

In the Section Approach the structure under consideration is sectioned at certain part such that the number of unknown forces is not more than two, for two dimensional structures. Unknown forces are assigned variables and components of the forces are taken along and perpendicular to any one of the unknown forces. For each of the two directions force balance equations are framed and solved for the unknowns. The components of the forces can also be taken along any fixed coordinate axis. For three dimensional structures the section taken can have up to three unknown forces.

Nodal Approach

In the other approach, to find forces in the members of a structure, net force at any joint is set to zero. Any joint connecting two or more members can be called as a node. One by one different nodes are considered for force analysis. To start with such a node will be taken which has not more than two unknown forces. Unknown forces are determined by writing net forces along any set of orthogonal axes and equating them to zero.

For a simple structure one of the two approaches may be sufficient to determine the forces in members. But for complex structures single force analysis approach can become cumbersome for force analysis, therefore, a tricky combination and use of the two approaches can simplify the static force analysis in structures.

This post is part of the series: Basics of Engineering Mechanics

A bicycle moves down the street and carry us with a little effort on our part. Water falls from the height of dam and run large turbines. How these machines work? How the different bodies interact? Engineering Mechanics, the study of forces and motion of bodies in mechanisms, answers these questions
  1. Basics of Engineering Mechanics: Introduction
  2. Basics of Engineering Mechanics: Statics
  3. Force Analysis in Statics in Engineering
  4. Engineering Mechanics: Contact Forces