8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 1/6

[UNIT 1 – PHYSICS ON THE GO – 2.0 MATERIALS]   1

1.6 STRENGTH OF MATERIALS

1. Hooke’s Law

2. Stress, strain and Young Modulus

3. Elastic and Plastic deformation

. !"aracteristics of a material

#. Elastic strain energ$

1. Hooke’s Law

%"e force e&erted '$ a s(ring, ) is gi*en '$+   F =−k ∆ x  

w"ere k ≡  s(ring constant x ≡  e&tension

 -egati*e sign due to  F   is in t"e o((osite direction  Δ x

 

"ig"er k   indicates a stiffer s(ring

   F ∝ Δ x  

until elastic limit. /e$ond t"is limit, Hooke’s law is no longer

o'e$ed and t"e s(ring undergoes plastic deformation. Limit of (ro(ortionalit$  F ∝ Δ x   ends "ere.

Elastic limit 0 S(ring 'ecomes (ermanentl$ deformed 'e$ond t"is

 (oint.

 

"ic" of t"e a'o*e gra("s s"ow "ig"er stiffness

8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 2/6

2. Stress, Strain and Young Modulus

%ensile stress force (er unit area, is gi*en '$+

  σ =

 F 

 A  

w"ere  F ≡  tensile force, - A ≡  crosssectional area, m2

4nit of σ   is -m2 or Pa

%ensile strengt" is t"us t"e σ   w"en t"e material 'reaks.

%ensile strain e&tension (er unit lengt", is gi*en '$+

   E= Δx x

 -o unit

Young Modulus,

 E=σ 

ε

4nit of  E  is -m2 or Pa

"ic" of t"e a'o*e "as a "ig"er Young Modulus, E

wkquay@gmail.com

8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 3/6

8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 4/6

E&am(le 1

16 m steel ca'le "as a load of 166kg.

7a8 "at s"ould t"e minimum crosssectional area of t"e ca'le 'e if

t"e tensile strengt" of steel is & 169 Pa.

eig"t 5 166 & :.91 5 :91 -

Tensile strength=Tensile Force

Crosssectional Area

4×108=

981

 A 5 2.# m2

7'8 How muc" would t"e ca'le e&tend if t"e Young Modulus of steel

is 2 & 1611 Pa

   E=σ 

ε=

Tensile force

 Area

 Extension

Original length

 

2×1011=

981

2.45

 Extension

10

 

E&tension 5 2 & 1669 m

3. Elastic and Plastic ;eformation

Elastic Plastic

<eturns to its original form afterforce a((lied is remo*ed

<emains in t"e deform (ositionafter force a((lied is remo*ed

. !"aracteristics of a Material

=. /rittle 0 Materials t"at 'reak of crack wit" little

deformation. Eg. !la$==. ;uctile 0 Materials s"owing (lastic deformation. Eg,

!o((er, most metals.

===. Hard 0 Materials resisting (lastic deformation. Eg. ;iamond

=>. Mallea'le Materials s"owing large (lastic deformation

 'efore 'reaking. Eg. ?old, Sil*er, most metals.

>. Stiff 0 Elastic materials w"ic" resists deformation or tensileforce.

>=. %oug" 0 Materials a'le to wit"stand large im(act forces

wit"out 'reaking. Eg. ood, car'on fi're.

wkquay@gmail.com

8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 5/6

[UNIT 1 – PHYSICS ON THE GO – 2.0 MATERIALS]   5

=n safet$ clot"ing 0 safet$ 'oots, "arness.

=n foodstuff 0 cooking utensils

#. Elastic strain energ$

is gi*en '$

 Eel=1

2 k Δ x

2

 

8/18/2019 Unit 1.6 – Materials - Strength of Materials

http://slidepdf.com/reader/full/unit-16-materials-strength-of-materials 6/6

ns for (age @+

1. 6.9 -cm1

2.

a. ) (ro(ortional to & '. 333 -m1

c. 6.63# m

d. #.6 &163 A

3. 966 A

wkquay@gmail.com