__STRENGTH OF MATERIALS__

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### Strength of Materials Made Easy GATE Handwritten Notes PDF Download

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**Topics Covered in this book :**

- Properties of materials
- Simple and temperature stresses (Hooke’s Law)
- Shear force and bending moment
- Shear stress and bending stress distribution
- Principle stresses
- Theories of failure
- Torsion of shaft
- Deflection of beams
- Pressure vessel
- Theory of columns
- Principle axis

The following are the terms basic to the study of mechanics, which should be understood clearly.

#### Mass :

The quantity of the matter possessed by a body is called mass. The mass of a body will not change unless the body is damaged and part of it is physically separated. If the body is taken out in a space craft, the mass will not change but its weight may change due to the change in gravitational force. The body may even become weightless when gravitational force vanishes but the mass remain the same.

#### Time :

The time is the measure of succession of events. The successive event selected is the rotation of earth about its own axis and this is called a day. To have convenient units for various activities, a day is divided into 24 hours, an hour into 60 minutes and a minute into 60 seconds. Clocks are the instruments developed to measure time. To overcome difficulties due to irregularities in the earths rotation, the unit of time is taken as second which is defined as the duration of period of radiation of the cesium-133 atom.

#### Space :

The geometric region in which study of body is involved is called space. A point in the space may be referred with respect to a predetermined point by a set of linear and angular measurements. The reference point is called the origin and the set of measurements as coordinates. If the coordinates involved are only in mutually perpendicular directions, they are known as cartesian coordination. If the coordinates involve angles as well as the distances, it is termed as Polar Coordinate System.

#### Length :

It is a concept to measure linear distances. The diameter of a cylinder may be 300 mm, the height of a building may be 15 m, the distance between two cities may be 400 km. Actually metre is the unit of length. However depending upon the sizes involved micro, milli or kilo metre units are used for measurements. A metre is defined as length of the standard bar of platinum-iradium kept at the International Bureau of weights and measures. To overcome the difficulties of accessibility and reproduction now metre is defined as 1690763.73 wavelength of krypton-86 atom.

#### Continuum :

A body consists of several matters. It is a well known fact that each particle can be subdivided into molecules, atoms and electrons. It is not possible to solve any engineering problem by treating a body as conglomeration of such discrete particles. The body is assumed to be a continuous distribution of matter. In other words the body is treated as continuum.

#### Particle :

A particle may be defined as an object which has only mass and no size. Theoretically speaking such a body cannot exist. However in dealing with problems involving distances considerably larger compared to the size of the body, the body may be treated as a particle, without sacrificing accuracy.

For example:

— A bomber aeroplane is a particle for a gunner operating from the ground.

— A ship in mid sea is a particle in the study of its relative motion from a control tower.

— In the study of movement of the earth in celestial sphere, earth is treated as a particle.

#### Force :

Force is an important term used in solid mechanics. Newton’s first law states that everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external agency acting on it. This leads to the definition of force as ‘force is an external agency which changes or tends to change the state of rest or uniform linear motion of the body’.

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