## Strength of Materials: Mechanical Basics

Strength of Materials is a fundamental branch of engineering mechanics that deals with the behavior of materials under various types of loads. It helps engineers understand how materials will respond to stresses and strains, which is crucial for designing structures, components, and machines.

### Key Concepts

#### 1. Stress:

**Normal Stress:**Force per unit area acting perpendicular to a plane.**Shear Stress:**Force per unit area acting parallel to a plane.

#### 2. Strain:

**Normal Strain:**Change in length per unit original length.**Shear Strain:**Change in angle between two originally perpendicular lines.

#### 3. Hooke's Law:

- Within the elastic limit, stress is directly proportional to strain.
- E = Ïƒ/Îµ (where E is Young's modulus, Ïƒ is stress, and Îµ is strain)

#### 4. Elasticity and Plasticity:

**Elastic Deformation:**Material returns to its original shape when the load is removed.**Plastic Deformation:**Material does not return to its original shape after the load is removed.

#### 5. Poisson's Ratio:

- The ratio of lateral strain to longitudinal strain.

#### 6. Modulus of Rigidity (G):

- A measure of a material's resistance to shear deformation.

#### 7. Factor of Safety:

- The ratio of the ultimate strength of a material to the working stress.

### Types of Loads

**Axial Load:**A load acting along the longitudinal axis of a member.**Torsional Load:**A load causing twisting of a member.**Bending Moment:**A moment that causes a member to bend.**Shear Force:**A force that causes a member to shear.

### Failure Theories

**Maximum Normal Stress Theory:**Failure occurs when the maximum normal stress exceeds the allowable stress.**Maximum Shear Stress Theory:**Failure occurs when the maximum shear stress exceeds the allowable shear stress.**Distortion Energy Theory:**Failure occurs when the total strain energy per unit volume exceeds the allowable strain energy.

### Applications

**Design of structures:**Buildings, bridges, and dams.**Machine elements:**Shafts, beams, columns, and springs.**Material selection:**Choosing appropriate materials for specific applications.**Failure analysis:**Investigating the causes of failures in components.

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## SOM SFD BMD PROPERTY OF MATERIAL NORMAL STRESS & STRAIN SHORT NOTES

**SOM (Strength of Materials)**is a fundamental subject in engineering that deals with the behavior of materials under various types of loads.

**SFD (Shear Force Diagram)**is a graphical representation of the shear force along the length of a beam.

**BMD (Bending Moment Diagram)**is a graphical representation of the bending moment along the length of a beam.

**Property of Material**refers to the characteristics of a material that determine its behavior under different conditions.

**Normal Stress**is the internal force per unit area acting perpendicular to a cross-section of a material.

**Strain**is the deformation of a material per unit length due to an applied stress.

## SHORT NOTES

- SFD and BMD are used to analyze the stresses and deflections in beams.
- The slope of the SFD at a point gives the bending moment at that point.
- The slope of the BMD at a point gives the shear force at that point.
- The area under the SFD between two points gives the change in bending moment between those points.
- The area under the BMD between two points gives the change in shear force between those points.
- The maximum bending moment occurs at the point where the shear force is zero.
- The maximum shear force occurs at the point where the bending moment is zero.
- The normal stress in a beam is given by the formula: Ïƒ = M*y/I, where Ïƒ is the normal stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia of the cross-section.
- The strain in a beam is given by the formula: Îµ = Î”L/L, where Îµ is the strain, Î”L is the change in length, and L is the original length.
- The relationship between stress and strain is linear up to the elastic limit. Beyond the elastic limit, the material undergoes plastic deformation.
- The modulus of elasticity (E) is the ratio of stress to strain in the elastic region.
- The Poisson's ratio (Î½) is the ratio of lateral strain to longitudinal strain.

These notes provide a brief overview of the concepts of SFD, BMD, properties of materials, normal stress, and strain in the context of SOM.