Sequencing Model 7. Replacement Model 8. Inventory Control 9. Waiting line theory or […]. Pandey, C. Singh, Balbir Singh. Book Contents This book lucidly explain key manufacturing processes such as: Machining Joining Forming and casting Including a chapter on unconventional machining processes.
Handa, H. But all such second moments are broadly termed as moment of inertia. In this chapter, we shall discuss the moment of inertia of plane areas only. Split up the whole area into a number of small elements. Let a1, a2, a3, If area is in m2 and the length is also in m, the moment of inertia is expressed in m 4. If area in mm2 and the length is also in mm, then moment of inertia is expressed in mm4. By Integration. The reason for the same is that it is equally convenient to use the method of integration for the moment of inertia of a body.
Let us divide the whole area into a no. Consider one of these strips. Now consider an elementary ring of radius x and thickness dx. Find its moment of inertia about the horizontal axis passing through its centre. Now consider a small strip PQ of thickness dx at a distance of x from the vertex A as shown in Fig. This relation holds good for any type of triangle. Determine the moment of inertia of the section about the centre of gravity of the section and the base BC.
We know that moment of inertia of the semicircular section about the base AC is equal to half the moment of inertia of the circular section about AC. Moment of inertia of the section about its centre of gravity and parallel to Y-Y axis.
We also know that moment of inertia of the semicircular section about its centre of gravity and parallel to Y-Y axis. Find the moment of inertia of a rectangular section 60 mm wide and 40 mm deep about its centre of gravity. Find the moment of inertia of a hollow rectangular section about its centre of gravity, if the external dimensions are 40 mm deep and 30 mm wide and internal dimensions are 25 mm deep and 15 mm wide.
Find the moment of inertia of a circular section of 20 mm diameter through its centre of gravity. Calculate the moment of inertia of a hollow circular section of external and internal diameters mm and 80 mm respectively about an axis passing through its centroid. Find the moment of inertia of a triangular section having 50 mm base and 60 mm height about an axis through its centre of gravity and base.
Find the moment of inertia of a semicircular section of 30 mm radius about its centre of gravity and parallel to X-X and Y-Y axes. First of all, split up the given section into plane areas i. Find the moments of inertia of these areas about their respective centres of gravity. The moments of inertia of the given section may now be obtained by the algebraic sum of the moment of inertia about the required axis. First of all, let us find out centre of gravity of the section.
As the section is symmetrical about Y-Y axis, therefore its centre of gravity will lie on this axis. Split up the whole section into two rectangles viz.
Let bottom of the web be the axis of reference. Related Papers. Mechanics of Solids by S. By Vikas Ahlawat. By kamran anjum. By Summit Beast. Meriam best. By wabii dhuguma. Download pdf. Centre of Gravity, 7.
Moment of Inertia, 8. Principles of Friction, 9. Applications of Friction, Principles of Lifting Machines, Simple Lifting Machines, Support Reactions, Analysis of Perfect Frames Analytical Method , Virtual Work, Linear Motion, Motion Under Variable Acceleration, Relative Velocity, Projectile Motion, Motion of Rotation, Combined Motion of Rotation and Translation, In order to take up his job more skilfully, an engineer must pursue the study of Engineering Mechanics in a most systematic and scientific manner.
The subject of Engineering Mechanics may be divided into the following two main groups: 1. Statics, and 2. It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies at rest. It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies in motion. The subject of Dynamics may be further sub-divided into the following two branches — 1.
Kinetics, and 2. It is the branch of Dynamics, which deals with the bodies in motion due to the application of forces.
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