Chapter 1. Properties of solids.docx

8/16/2019 Chapter 1. Properties of solids.docx

1/14

Chapter 1. Properties of solids

Deforming Force

Q. 1 What is Deformation?

Ans.: The change in shape or size of body after application of external forced is calleddeformation.

Q. 2 Dene deforming force. (W!"# W!$# %! W11# %12'

Ans.: Deforming force is dened as the external force which changes the shape and size ofbody after its application.

estoring Force

Q. ) Dene estoring force. (W!"# W!$# W11# %12'

Ans.: Restoring force is dened as internal force developed in a body, in order to regain itsoriginal size and shape after application of deforming force.

*lastic +od,

Q. - What is elastic propert, and elastic +od,? (%11'

Ans.: 1. *lastic propert,: It is a ability of body to regain its original dimensions afterremoval of deforming force.

2. *lastic +od,: It is dened as body which regains its original size and shape after removalof deforming forces.

*lasticit,

Q. Dene elasticit,. (%1)'

Ans.: It is dened as a property of the body by virtue of which it tends to regain its originalshape or size on removal of deforming forces.

Plastic /od,

Q.0 Dene plastic +od,.

Ans.: lastic body is dened as if a body does not regain its original size and shape afterremoval of deforming forces.

Plasticit,

Q." Dene plasticit,. (W1!# %1)'

Ans.: lasticity is dened as a property of the body by virtue of which it tends to remaindeformed and does not regain its original size and shape after removal of deforming forces.

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%tress

Q. $ Dene stress. (W!"# %! W! %1!# W11# W1)'

Ans.: !tress is dened as the internal restoring force per unit cross sectional area of the

body.

%tress Internal RestoringForce

Cross Sectional Area F

A

Q. & %tate % 3nit of stress. (W!"# W!$# %! %11# W11# %12'

Ans.: !. I. "nit of stress is N

m2

4,pes of %tress

Q. 1! %tate t,pes of stress. (%11'

Ans.: There are four types of stress# $. Tensile !tress %&ongitudinal !tress' (. )ompressive!tress %*ormal !tress' +. olumetric !tress - !hear !tress

4ensile %tress

Q. 11 What is tensile stress?

Ans.: Tensile stress is dened as the deforming force applied along the length of the bodyunit cross sectional area.

4ensile stress Aplied Force

Cross Sectional Area F

A Mg

π r2

!.I. unit is

N

m2

Compressi5e %tress

Q. 12 What is compressi5e stress?

Ans.: )ompressive stress %)ompression stress or normal stress' is dened as the restoringforce acting per unit area normal to the surface of the body.

6ol3metric %tress

Q. 1) What is 5ol3metric stress?


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Ans.: olumetric stress is dened as the stress developed in a body due to change in volumeof the body when external force %deforming force' is applied to a body.

6ol3me stress Aplied Force

Area ∴ P

F

A

∴ olume stress )hange in pressure

∴ olume stress d

!.I. unit is N

m2

%hear %tress

Q. 1- What is shear stress? %tate its % 3nit

Ans.: !hear stress is dened as stress developed in a body due change in shape of the bodywithout change in its volume when external force is applied tangentially or parallel to thesurface of the body.

%hearing stress

F

A

!.I. unit is N

m2

%train

Q. 1 Dene strain. (W!"# %! W! %1!# W11# W1)'

Ans.: !train is dened as the ratio of change in dimensions to the original dimensions of thebody.

It has no units.

Q. 10 %tate and e7plain three t,pes of stain. (W1!# %11'

Ans.: There are three types of strain

$. Tensile !train %&ongitudinal !train' (. olumetric !train +. !hear !train

4ensile %train (8ongit3dinal %train'

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Q. 1" What is the tensile strain? (W12'

Ans.: Tensile strain dened as the ratio of change in length of wire to theoriginal length of wire. %/ig. $.$'

Tensile strain Increase∈ Length

Original Length l

L

/ig. $.$

It has no units.

6ol3metric %train

Q. 1$ What is the 5ol3metric strain? (W12'

Ans.: $. olumetric strain is dened as the ratio of the change in volume%dv' without change in shape of body to the original volume %' of thebody when uniform pressure is applied on a body.

(. If 01 is the original volume and 0dv1 is the change in volume then, olume strain

dv

V %/ig. $.('

It has no units.

%hear %train

Q. 1& What is the shear strain?

Ans.: $. !hear strain dened as the ratio of relative displacement between two layers underthe action of force to the distance between two layers.Refer /ig. $.+,

(. Relative displacement between opposite faces of cylinder is dx.

+. &ength of cylinder is 0&1./ig. $.+

∴!hearing strain Relative displacement

Lengthof Object d

L tan θ

2ut tan θ ≈ θ, as θ is very small.

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∴θ d

L

3lastic &imit

Q. 2! Dene elastic limit. (W!0# %!$# W1!# W11'

Ans.: 3lastic limit is dened as maximum stress which can be applied on a body withoutpermanent deformation of a body.

9ooe;s 8a<

Q. 21 %tate and *7plain 9ooe;s la< of elasticit,. (W!$# W!%1!# W1!# %12'

Ans.: !tatement of 4oo5e1s law#

64oo5e1s law of elasticity states that within the elastic limits stress developed in a body isdirectly proportional to strain produced in it.

!tress ∝ !train

∴ Stress

Strain )onstant

6)onstant of proportionality is called 7odulus of 3lasticity.

∴ 7odulus of elasticity Stress

Strain

!.I. unit is

N

m2 .

67odulus of elasticity is a characteristic of material.

*lastic Coe=cient

Q. 22 Dene >o3ng;s mod3l3s of elasticit,. (W!0# %!"# W!$# %! W! %12# W1)'

Ans.: 8oung1s modulus is dened as the ratio of tensile stress to tensile strain when the bodyis within elastic limits.

8 Longit!dinal Stress

Longit!dinal Strain "ensile Stress

"ensile Strain

Mg / π r2

l L

Mg L

l π r2

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!.I "nits

N

m2

2ul5 7odulus

9:; ?@, !>?A, =>?B, !>$(, =>$+'

Cns. # 2ul5 modulus is dened as ratio of volumetric stress to volumetric strain when thebody is within the elastic limits.

It is denoted by 01.

∴

E. *Fm(

*egative sign indicates that when pressure increases volume decreases and vice versa.

6The ratio is always negative.

)ompressibility

9:;


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%=>?@, !>?A, !>?, =>?B, !>$(, =>$+'

Cns. # 7odulus of rigidity is dened as the ratio of shear stress to shear strain when the bodyis within elastic limit. Its !I unit is *Fm(.

It is denoted by 0η1.

η

∴η θ

∴η

E * F m(

oisson1s Ratio

9:; $+'

Cns. # oisson1s ratio is dened as within elastic limit the ratio of lateral strain to longitudinal

strain. It is denoted by 0δ1.

∴δ

9:;


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9:; ?@, !>?A, =>?B, !>$('

Cns. #

Relation between 8oung1s modulus %8', bul5 modulus %' and rigidity modulus %η' of elasticity

is given by,

Nr

8

where 8 8oung1s modulus of elasticity

η 7odulus of rigidity

2ul5 modulus of elasticity

Relation between and )ompressibility

9:; $+'

Cns. #

It is dened as the ratio of volume stress to volume strain within elastic limit i.e. itcorresponds to changes in volume.

olume strain

and olume stress dp

4ence, bul5 modulus %5' and can be written as,

2ul5 modulus %5'

2ul5 modulus is possessed by solids, liLuids and ass. 2ul5 modulus has the same unity asthose of 8oung1s modulus. The reciprocal of bul5 modulus is called as compressibility.

2ehaviour of wire under continuously increasing load

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9:;


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(. The load values are observed and noted from dial of the machine and correspondingchanges in the gauge length are recorded simultaneously. =ith the help of an extensometerattached to the specimen of metal.

+. =hen stress is uniformly and continuously applied to a metal wire or metal bar, thematerial exhibits strain linearly up to point C %/ig $.-.'. Thus between points N and C appliedstress is directly proportional to the strain. Therefore region NC is perfectly elastic region andthe material obeys 4oo5e1s law. oint 0C1 is called as 3lastic limit.

-. oint 021 is called Oyield pointP and stress corresponding to it is 5nown as yielding stress.

H. Region 0)D1 is called plastic range. In this region steady increase in strain occurs withnegligible increase in stress.

@. 2eyond 0D1, the material loses its shape and becomes thinner and thinner in diameter. Thematerial of wire ultimately brea5s at point 031. 4ence point 031 is called brea5ing point of thewire.

"ltimate !tress or 2rea5ing !tress

9:;


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Cns. # /actor of safety is dened as the ratio of ultimate stress to the wor5ing stress.

/actor of safety

/actor of safety depends on #

%a' =ear and tear of material at actual

%b' 7agnitude of maximum load subMected on specimen.

%c' )haracteristic of load such as xed or variable.

3lasticity

9:; $('

Cns. # The elastic properties of solids vary due to following parameters #

$. 3Ject of stress # Due to application of constant large and repeated cycles of stress on abody, elasticity of body decrease gradually.

3lasticity α

(. 3Ject of temperature # Qenerally, a rise in temperature shows a decrease in elasticproperties of metals.

+. 3xample # Ct room temperature, carbon lament shows elastic behavior. =hen it is heatedby passing current through it, carbon lament shows plastic behavior.

-. 3Ject of hammering and rolling # =hen crystals are hammered or rolled, the grains arereduced to smaller units that results in an increase in elastic properties of crystal.

H. 3Ject of annealing # Cnnealing is process of heating and then gradually cooling thematerial.

@. The annealing process of a metal produces a uniform large crystal grains which results indecrease of elastic properties.

A. 3Ject of impurities # Cddition of imparity increases the compactness of material. Due tothis elastic property of the material also increases.

. 3xample # =hen small amount of impurities li5e carbon and potassium are added tomolten iron and gold, it increases their elastic property.

Important /ormulae

!r. Important /ormulae !. I.


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*o. "nits

$.

!tress

*Fm(

(.

!train

*o unit

+.

8

∴ 8

*Fm(

-. ⋅

*egative sign indicates that when pressure increases volume decreases andvice versa.

*Fm(

H.

)ompressibility ⋅

m(F*

@.

η

*Fm(



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A. oisson1s ratio % δ '

*egative sign indicates that as longitudinal strain increases lateral strain

decreases and vice versa

*o unit

.

Relation between 8, and η.

: or

8

θθθ

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Chapter 1. Properties of solids.docx