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# Formula Sheet: Strength of Materials (SOM) Notes | EduRev

## Mechanical Engineering : Formula Sheet: Strength of Materials (SOM) Notes | EduRev

``` Page 1

Strength of
Material
(Formula & Short Notes)
Page 2

Strength of
Material
(Formula & Short Notes)

Stress and strain
Stress = Force / Area

Page 3

Strength of
Material
(Formula & Short Notes)

Stress and strain
Stress = Force / Area

Brinell Hardness Number
(BHN)

Elastic constants:

where, P = Standard load, D = Diameter of steel ball, and d = Diameter of the indent.

Page 4

Strength of
Material
(Formula & Short Notes)

Stress and strain
Stress = Force / Area

Brinell Hardness Number
(BHN)

Elastic constants:

where, P = Standard load, D = Diameter of steel ball, and d = Diameter of the indent.

Axial Elongation of Bar Prismatic Bar Due to External Load
?=
????
????

Elongation of  Prismatic Bar Due to Self  Weight
?=
????
?????? =
?? ?? ?? ????

Where ?? is specific weight
Elongation of Tapered Bar
• Circular Tapered
?=
?????? ?? ?? ?? ?? ?? ??

• Rectangular Tapered
?=
???? ?????? ?? (
?? 2
?? 1
)
?? . ?? (?? 2
- ?? 1
)

Stress Induced by Axial Stress and Simple Shear
• Normal stress

• Tangential stress

Principal Stresses and Principal Planes
• Major principal stress

• Major principal stress

Page 5

Strength of
Material
(Formula & Short Notes)

Stress and strain
Stress = Force / Area

Brinell Hardness Number
(BHN)

Elastic constants:

where, P = Standard load, D = Diameter of steel ball, and d = Diameter of the indent.

Axial Elongation of Bar Prismatic Bar Due to External Load
?=
????
????

Elongation of  Prismatic Bar Due to Self  Weight
?=
????
?????? =
?? ?? ?? ????

Where ?? is specific weight
Elongation of Tapered Bar
• Circular Tapered
?=
?????? ?? ?? ?? ?? ?? ??

• Rectangular Tapered
?=
???? ?????? ?? (
?? 2
?? 1
)
?? . ?? (?? 2
- ?? 1
)

Stress Induced by Axial Stress and Simple Shear
• Normal stress

• Tangential stress

Principal Stresses and Principal Planes
• Major principal stress

• Major principal stress

Principal Strain

Mohr’s Circle-

STRAIN ENERGY
Energy Methods:
(i) Formula to calculate the strain energy due to axial loads (tension):
U  = ?  P ² / ( 2AE)dx limit 0 toL

Where, P = Applied tensile load, L =  Length of the member ,  A = Area of the member, and
E = Young’smodulus.
(ii) Formula to calculate the strain energy due tobending:
U  = ?   M ² /  ( 2EI) dx limit 0 toL

Where, M = Bending moment due to applied loads, E = Young’s modulus, and I = Moment of
inertia.
(iii) Formula to calculate the strain energy due totorsion:
U  = ?  T ² / ( 2GJ)  dx limit 0 toL
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