Strength of Materials Formulas for GATE ME Exam

# Strength of Materials Formulas for GATE ME Exam | Strength of Materials (SOM) - Mechanical Engineering PDF Download

``` Page 2

Brinell Hardness Number
(BHN)

Elastic constants:

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

Page 3

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 4

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
Page 5

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

Where, T = Applied Torsion , G = Shear modulus or Modulus of rigidity, and J = Polar
moment ofinertia
(iv) Formula to calculate the strain energy due to pureshear:
U  =K  ?  V ² / ( 2GA)  dx limit 0 to L
G = Shear modulus or Modulus of rigidity
A = Area of cross section.
K = Constant depends upon shape of cross section.

(v) Formula to calculate the strain energy due to pure shear, if shear stress isgiven:
U  =  t ² V / ( 2G )

Where, t = ShearStress

G = Shear modulus or Modulus of rigidity
V = Volume of the material.

(vi) Formula to calculate the strain energy , if the moment value isgiven:
U  =  M ² L / (2EI)

Where, M = Bending moment
L = Length of the beam
E = Young’smodulus
I = Moment ofinertia

(vii) Formula to calculate the strain energy , if the torsion moment value isgiven:
U= T ²L /  ( 2GJ)

Where, T = AppliedTorsion

L = Length of the beam

G = Shear modulus or Modulus of rigidity
J = Polar moment of inertia
```

## Strength of Materials (SOM)

37 videos|39 docs|45 tests

## FAQs on Strength of Materials Formulas for GATE ME Exam - Strength of Materials (SOM) - Mechanical Engineering

 1. What are the important formulas in Strength of Materials for the GATE ME Exam?
Ans. Some important formulas in Strength of Materials for the GATE ME Exam include: - Stress formula: Stress = Force/Area - Strain formula: Strain = Change in length/Original length - Young's modulus formula: Young's modulus = Stress/Strain - Shear stress formula: Shear stress = Force/Area - Bending moment formula: Bending moment = Force × Distance from the point of support
 2. How can I calculate the maximum bending stress in a beam for the GATE ME Exam?
Ans. The maximum bending stress in a beam can be calculated using the following formula: Maximum Bending Stress = (M × c) / I where M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the section.
 3. What is the formula to calculate the deflection of a cantilever beam for the GATE ME Exam?
Ans. The formula to calculate the deflection of a cantilever beam for the GATE ME Exam is: Deflection = (F × L^3) / (3 × E × I) where F is the applied load, L is the length of the beam, E is the Young's modulus of the material, and I is the moment of inertia of the cross-section.
 4. How do I calculate the factor of safety for a given material in the GATE ME Exam?
Ans. The factor of safety can be calculated using the following formula: Factor of Safety = Yield Strength / Maximum Working Stress where Yield Strength is the maximum stress that a material can withstand without permanent deformation, and Maximum Working Stress is the maximum stress that the material is subjected to in its intended application.
 5. What is the formula to calculate the torsional stress in a shaft for the GATE ME Exam?
Ans. The formula to calculate the torsional stress in a shaft for the GATE ME Exam is: Torsional Stress = (T × r) / (J × c) where T is the applied torque, r is the radius of the shaft, J is the polar moment of inertia of the shaft, and c is the distance from the center of the shaft to the outermost fiber.

## Strength of Materials (SOM)

37 videos|39 docs|45 tests

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