There are two theorems of moment of inertia: (1) Perpendicular axis theorem, and (2) Parallel axis theorem. These are explained and proved below. Perpendicular Axis Theorem The moment of inertia of an area about an axis perpendicular to its plane (polar moment of inertia) at any point O is equal to the sum of moments…
The term rdA may be called as moment of area, similar to moment of a force, and hence r 2 dA may be called as moment of area or the second moment of area. Thus, the moment of inertia of area is nothing but second moment of area. In fact, the term โsecond moment of…
A truss is a structure made up of slender members pin-connected at ends and is capable of taking loads at joints. They are used as roof trusses to support sloping roofs and as bridge trusses to support deck. In many machines steel trusses are used. Transmission towers are also the examples of trusses. In the…
To satisfy the condition that there should not be translatory motion of the body subjected to coplanar forces, in this case also the following two conditions are to be satisfied: If the condition ฮฃMA = 0 is satisfied, we can conclude that the resultant R should be a force passing through A. If ฮฃMB = 0 is…
In many problems, it is essential to isolate the body under consideration from the other bodies in contact and draw all the forces acting on the body. For this, first the body is drawn and then applied forces, selfweight and the reactions at the points of contact with other bodies are drawn. Such a diagram…
Before taking up equilibrium conditions of a body, it is necessary to identify the various forces acting on it. The various forces acting on a body may be grouped into: (a) Applied Forces (b) Non-applied Forces (a) Applied Forces These are the forces applied externally to a body. Each of the forces is having contact…
Let F1, F2 and F3 [Fig. 2.18(a)] constitute a system of forces acting on a body. Each force can be replaced by a force of the same magnitude and acting in the same direction at point O and a moment about O. Thus, the given system in Fig. 2.18(a) is equal to the system shown…
General Approach The composition of concurrent forces by graphical method and the analytical method of composition of two force system has been discussed. In this article composition of concurrent coplanar forces is explained by a general analytic method. Analytical method consists in finding the components of given forces in two mutually perpendicular directions and then…
When several forces of different magnitude and direction act upon a body, they constitute a system of forces. If all the forces in a system lie in a single plane, it is called a coplanar force system. If the line of action of all the forces in a system pass through a single point it…
Principles Of Statics The statics is based on the following principles of mechanics: 1. Newtonโs laws of mechanics 2. Law of transmissibility 3. Parallelogram law of forces 4. Principles of physical independence 5. Principles of superposition. Newtonโs Laws of Mechanics As already discussed in first chapter, Newtonโs first law gave definition of the force and…