Formula Sheet: Strength of Materials (SOM) | Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering PDF Download

 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