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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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FAQs on Formula Sheet: Strength of Materials (SOM) - Strength of Materials (SOM) - Mechanical Engineering
| 1. What is the formula for calculating stress in a material? |  |
Ans. The formula for calculating stress in a material is given by stress = force/area. It represents the force applied per unit area of the material.
| 2. How do you calculate the modulus of elasticity for a material? | |
Ans. The modulus of elasticity, also known as Young's modulus, can be calculated by dividing the stress by the strain. It is given by the formula modulus of elasticity = stress/strain.
| 3. What is the formula for calculating the bending moment in a beam? | |
Ans. The formula for calculating the bending moment in a beam is given by bending moment = force x distance. It represents the product of the applied force and the perpendicular distance from the force to the axis of rotation.
| 4. How do you calculate the deflection of a beam? | |
Ans. The deflection of a beam can be calculated using the formula deflection = (force x distance^3)/(3 x modulus of elasticity x moment of inertia). It represents the displacement of a point in the beam under the applied force.
| 5. What is the formula for calculating the shear stress in a material? | |
Ans. The formula for calculating the shear stress in a material is given by shear stress = force/area. It represents the force applied parallel to the surface of the material per unit area.
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