## Friday, November 4, 2016

### Mechanics of solids by R.K RAJPUT

Mechanics-of-solids BY R-K-RAJPUT-S-CHAND

Simple stresses &strains : Concept & types of Stresses and strains, Polson’s ratio, stresses and strain in simple and compound bars under axial loading, stress strain diagrams, Hooks law, elastic constants & their relationships, temperature stress & strain in simple & compound bars under axial loading, Numerical problems.

Numerical Shear Force & Bending Moments : Definitions, SF & BM diagrams for cantilevers, simply supported beams with or without over-hang and calculation of maximum BM & SF and the point of contraflexture under (i) concentrated loads, (ii) uniformly distributed loads over whole span or a part of it, (iii)combination of concentrated loads and uniformly distributed loads, (iv) uniformly varying loads and (v) application of moments, relation between the rate of loading, the shear force and the bending moments, Numerical Problems. . 8 8

Flexural and shear stresses – Theory of simple bending, Assumptions, derivation of equation of bending, neutral axis, determination of bending stresses, section modulus of rectangular & circular (solid & hollow), I,T, Angle, channel sections, composite beams, shear stresses in beams with derivation, shear stress distribution across various beam sections like rectangular, circular, triangular, I, T, angle sections. Combined bending and torsion, equivalent torque,. Numerical problems.

Slope &Deflection : Relationship between bending moment, slope & deflection, moment area method, method of integration, Macaulay’s method, calculations for slope and deflection of (i) cantilevers and (ii) simply supported beams with or without overhang under concentrated load, Uniformly distributed loads or combination of concentrated and uniformly distributed loads, Numerical problems.

**Unit-I**Introduction: Force, types of forces, Characteristics of a force, System of forces, Composition and resolution of forces, forces in equilibrium, principle and laws of equilibrium, Free body diagrams, Lami's Theorem, equations of equilibrium, Concept of center of gravity and centroid, centroid of various shapes: Triangle, circle, semicircle and trapezium, theorem of parallel and perpendicular axes, moment of inertia of simple geometrical figures, polar moment of inertia. Numerical ProblemsSimple stresses &strains : Concept & types of Stresses and strains, Polson’s ratio, stresses and strain in simple and compound bars under axial loading, stress strain diagrams, Hooks law, elastic constants & their relationships, temperature stress & strain in simple & compound bars under axial loading, Numerical problems.

**Unit-II**Principle stresses: Two dimensional systems, stress at a point on a plane, principal stresses and principal planes, Mohr’s circle of stresses,Numerical Shear Force & Bending Moments : Definitions, SF & BM diagrams for cantilevers, simply supported beams with or without over-hang and calculation of maximum BM & SF and the point of contraflexture under (i) concentrated loads, (ii) uniformly distributed loads over whole span or a part of it, (iii)combination of concentrated loads and uniformly distributed loads, (iv) uniformly varying loads and (v) application of moments, relation between the rate of loading, the shear force and the bending moments, Numerical Problems. . 8 8

**Unit-III**Torsion of circular Members: Derivation of equation of torsion, Solid and hollow circular shafts, tapered shaft, stepped shaft & composite circular shafts, Numerical problems.Flexural and shear stresses – Theory of simple bending, Assumptions, derivation of equation of bending, neutral axis, determination of bending stresses, section modulus of rectangular & circular (solid & hollow), I,T, Angle, channel sections, composite beams, shear stresses in beams with derivation, shear stress distribution across various beam sections like rectangular, circular, triangular, I, T, angle sections. Combined bending and torsion, equivalent torque,. Numerical problems.

**Unit-IV**Columns & Struts: Column under axial load, concept of instability and buckling, slenderness ratio, derivation of Euler's formula for crippling load for columns of different ends, concept of equivalent length, eccentric loading, Rankine formulae and other empirical relations, Numerical problems.Slope &Deflection : Relationship between bending moment, slope & deflection, moment area method, method of integration, Macaulay’s method, calculations for slope and deflection of (i) cantilevers and (ii) simply supported beams with or without overhang under concentrated load, Uniformly distributed loads or combination of concentrated and uniformly distributed loads, Numerical problems.

### Mechanics of solid Notes

# Stress and Strain: Basic Terms and Concepts

## Stress Terms

Stress is defined as force per unit area. It has the same units as pressure, and in fact pressure is one special variety of stress. However, stress is a much more complex quantity than pressure because it varies both with direction and with the surface it acts on.

**Compression**- Stress that acts to shorten an object.
**Tension**- Stress that acts to lengthen an object.
**Normal Stress**- Stress that acts perpendicular to a surface. Can be either compressional or tensional.
**Shear**- Stress that acts parallel to a surface. It can cause one object to slide over another. It also tends to deform originally rectangular objects into parallelograms. The most general definition is that shear acts to change the angles in an object.
**Hydrostatic**- Stress (usually compressional) that is uniform in all directions. A scuba diver experiences hydrostatic stress. Stress in the earth is nearly hydrostatic. The term for uniform stress in the earth is
**lithostatic**. **Directed Stress**- Stress that varies with direction. Stress under a stone slab is directed; there is a force in one direction but no counteracting forces perpendicular to it. This is why a person under a thick slab gets squashed but a scuba diver under the same pressure doesn't. The scuba diver feels the same force in all directions.

**In geology we never see stress.**We only see the results of stress as it deforms materials. Even if we were to use a strain gauge to measure in-situ stress in the rocks, we would not measure the stress itself. We would measure the deformation of the strain gauge (that's why it's called a "

*strain*gauge") and use that to infer the stress.

## Strain Terms

Strain is defined as the amount of deformation an object experiences compared to its original size and shape. For example, if a block 10 cm on a side is deformed so that it becomes 9 cm long, the strain is (10-9)/10 or 0.1 (sometimes expressed in percent, in this case 10 percent.) Note that strain is dimensionless.

**Longitudinal or Linear Strain**- Strain that changes the length of a line without changing its direction. Can be either compressional or tensional.
**Compression**- Longitudinal strain that shortens an object.
**Tension**- Longitudinal strain that lengthens an object.
**Shear**- Strain that changes the angles of an object. Shear causes lines to rotate.
**Infinitesimal Strain**- Strain that is tiny, a few percent or less. Allows a number of useful mathematical simplifications and approximations.
**Finite Strain**- Strain larger than a few percent. Requires a more complicated mathematical treatment than infinitesimal strain.
**Homogeneous Strain**- Uniform strain. Straight lines in the original object remain straight. Parallel lines remain parallel. Circles deform to ellipses. Note that this definition rules out folding, since an originally straight layer has to remain straight.
**Inhomogeneous Strain**- How real geology behaves. Deformation varies from place to place. Lines may bend and do not necessarily remain parallel.

### Terms for Behavior of Materials

**Elastic**- Material deforms under stress but returns to its original size and shape when the stress is released. There is no permanent deformation. Some elastic strain, like in a rubber band, can be large, but in rocks it is usually small enough to be considered infinitesimal.
**Brittle**- Material deforms by fracturing. Glass is brittle. Rocks are typically brittle at low temperatures and pressures.
**Ductile**- Material deforms without breaking. Metals are ductile. Many materials show both types of behavior. They may deform in a ductile manner if deformed slowly, but fracture if deformed too quickly or too much. Rocks are typically ductile at high temperatures or pressures.
**Viscous**- Materials that deform steadily under stress. Purely viscous materials like liquids deform under even the smallest stress. Rocks may behave like viscous materials under high temperature and pressure.
**Plastic**- Material does not flow until a threshhold stress has been exceeded.
**Viscoelastic**- Combines elastic and viscous behavior. Models of glacio-isostasy frequently assume a viscoelastic earth: the crust flexes elastically and the underlying mantle flows viscously.

### HEAT AND MASS TRANSFER NOTES LINK-(by Asst Prof. CP SAINI)

**----HERE ARE THE DIRECT LINKS TO THE SELECTED TOPICS---**

HEAT AND MASS TRANSFER BY RK RAJPUT

1. CONDUCTION

1.1 BASICS

1.2 ONE DIMENSIONAL STEADY STATE HEAT CONDUCTION

1.3 EXTENDED SURFACE HEAT TRANSFER

1.4 UNSTEADY STATE HEAT CONDUCTION

2. CONVECTION (BASICS)

3. RADIATION

4. HEAT EXCHANGERS

### Heat Transfer Unit-1(By: Asst Prof. C.P. SAINI)

Solids, on the other hand, have atoms/molecules which are more closely packed which cannot
move as freely as in gases. Hence, they cannot effectively transfer energy through these same
mechanisms. Instead, solids may exhibit energy through vibration or rotation of the nucleus. Hence,
the energy transfer is typically through lattice vibrations.
Another important mechanism in which materials maintain energy is by shifting electrons into
higher orbital rings. In the case of electrical conductors the electrons are weakly bonded to the
molecule and can drift from one molecule to another, transporting their energy in the process. Hence, flow of electrons, which is commonly observed in metals, is an effective transport
mechanism, resulting in a correlation that materials which are excellent electrical conductors are
usually excellent thermal conductors.

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