Equilibrium
In mechanics, the stress-strain relationship describes how a material deforms and becomes internally stressed as a result of an external load. The body is in equilibrium when the sum of all forces acting on it is equal to zero. A body is also in equilibrium if it is at rest or moving at a constant velocity. Stress and strain are related through the material's elastic modulus, which describes how much a material will deform under a given load.
Rigid body
In the context of mechanics, stress and strain refer to the forces acting on and the resulting deformation of a body. A rigid body is one that does not deform or bend under the influence of external forces. Therefore, when a rigid body is subjected to external forces, it experiences only stress, not strain. Stress is defined as the force per unit area acting on the body, while strain is the ratio of deformation to original size. In a rigid body, there is no deformation, so the strain is zero.
Deformable body
Deformable or body, when it is subjected to external forces, it experiences both stress and strain. Stress is the force per unit area acting on the body, while strain is the ratio of deformation to original size. As the body is deformable, there will be a change in its shape and size, and the strain will be non-zero.
When a deformable body is subjected to external forces, it experiences both stress and strain. Stress is the force per unit area acting on the body, while strain is the ratio of deformation to original size. The relationship between stress and strain is governed by the elastic modulus of the material, which can be different for different materials.
Deformable bodies are commonly used in engineering and construction, such as in the design of bridges, buildings, and other structures, as well as in the automotive and aerospace industries.
CONCEPT OF STRESS
The concept of stress refers to the force per unit area that acts on a body. It is a measure of the intensity of the internal forces within a body that are trying to deform it. Stress is a scalar quantity and is measured in units of force per unit area, such as Pascals (Pa) or pounds per square inch (psi).
There are different types of stress that a body can experience, including:
- Tensile stress: Occurs when a body is stretched or pulled apart. It is a positive stress and is measured in units of force per unit area.
- Compressive stress: Occurs when a body is compressed or squeezed. It is a negative stress and is also measured in units of force per unit area.
- Shear stress: Occurs when a body is subject to a force that causes one part of the body to slide or move in relation to another part of the body. It is measured in units of force per unit area.
- Bending stress: Occurs when a body is subject to a force that causes it to bend. It is measured in units of force per unit area.
- Torsional stress: Occurs when a body is subject to a force that causes it to twist. It is measured in units of force per unit area.
It's important to note that the relationship between stress and strain is governed by the elastic modulus of the material, which can be different for different materials. This relationship is usually defined by Hooke's law which states that the stress is proportional to the strain within the elastic limit of the material.
Concept of strain
The concept of strain refers to the ratio of deformation to original size in a body caused by external forces. It is a measure of how much a body changes shape or size when it is subjected to stress. Strain is a dimensionless scalar quantity, usually represented as a decimal or percentage.
There are different types of strain that a body can experience, including:
- Tensile strain: Occurs when a body is stretched or pulled apart. It is a positive strain and is usually represented as a decimal or percentage.
- Compressive strain: Occurs when a body is compressed or squeezed. It is a negative strain and is also represented as a decimal or percentage.
- Shear strain: Occurs when a body is subject to a force that causes one part of the body to slide or move in relation to another part of the body. It is represented as a decimal or percentage.
- Bending strain: Occurs when a body is subject to a force that causes it to bend. It is represented as a decimal or percentage.
- Torsional strain: Occurs when a body is subject to a force that causes it to twist. It is represented as a decimal or percentage.
It's important to note that the relationship between stress and strain is governed by the elastic modulus of the material, which can be different for different materials. This relationship is usually defined by Hooke's law which states that the stress is proportional to the strain within the elastic limit of the material.
Behaviour of tensile material under tension
Limit of proportionality: The point at which the relationship between stress and strain in a material deviates from linearity and Hooke's law no longer applies. Beyond this point, the material begins to exhibit plastic deformation.
- Elastic limit: The point at which a material begins to exhibit permanent deformation. When a material is loaded and then unloaded within the elastic limit, it returns to its original shape and size.
- Upper yield point: The point at which a material begins to exhibit a significant increase in deformation without an increase in load. It is also known as the upper yield stress.
- Lower yield point: The point at which a material begins to exhibit a significant increase in deformation without an increase in load. It is also known as the lower yield stress.
- Ultimate point: The point at which a material reaches its maximum strength and can sustain no further load without failure.
- Breaking point: The point at which a material fails under load, usually due to the formation of cracks or fissures.
- Nominal stress: The stress calculated based on the original dimensions of the material before deformation.
- Actual stress: The stress calculated based on the deformed dimensions of the material.
- Yield stress: The stress at which a material begins to exhibit a significant increase in deformation without an increase in load.
- Ultimate stress: The maximum stress a material can sustain without failure.
- Working stress: The stress at which a material is designed to operate in a safe and reliable manner.
- Factor of safety: The ratio of the strength of a material to the working stress. It is used to ensure that a design is safe and reliable.
Shear stress
Shear stress is a measure of the force that causes two layers of a material to slide against each other in opposite directions. It is often represented by the symbol "Ï„" (tau) and is measured in units of force per unit area, such as Pascals (Pa) or pounds per square inch (psi). Shear stress is important in understanding the behavior of materials under load and is commonly encountered in engineering and physics applications
Shear strain
Shear strain is a measure of how much a material deforms or changes shape when a shear stress is applied to it. It's a ratio of the change in the material's dimensions to its original dimensions. It is usually represented by the symbol "γ" (gamma) and is unitless. Shear strain is an important concept in understanding the behavior of materials under load, especially in the fields of engineering
Hook's Law
Hook's Law states that within the elastic limit, the amount of deformation (stretch or compression) a material experiences is directly proportional to the amount of force applied to it. This means that the material will return to its original shape once the force is removed. It is often used to predict and design the behavior of structures and materials under load in engineering applications such as bridges, buildings, and mechanical systems. Mathematically, it can be represented by the equation:
Stress = Elastic Modulus x Strain
Where Stress is the force applied per unit area, Elastic Modulus is a constant of proportionality for a material and Strain is the change in length per unit length.
Young's modulus
The Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It is defined as the ratio of the stress applied to a material to the resulting strain. The units of Young's modulus are typically gigapascals (GPa) or gigapounds per square inch (Gpsi). The modulus is a fundamental property of a material, and it is used to predict how a material will behave under load. Materials with a high Young's modulus, such as steel, are relatively stiff and strong, while materials with a low Young's modulus, such as rubber, are relatively flexible and weak.
Young's modulus is one of three moduli that describe the elasticity of solids, the other two are shear modulus and bulk modulus.
Modulus of rigidity
The modulus of rigidity, also known as the shear modulus or the modulus of elasticity in shear, is a measure of the stiffness of a material when it is subjected to a shearing force. It is defined as the ratio of the shear stress applied to a material to the resulting shear strain. The units of modulus of rigidity are typically gigapascals (GPa) or gigapounds per square inch (Gpsi).
It is used to calculate the deformation of a material when it is subjected to a shearing force. Materials with a high modulus of rigidity, such as steel, are relatively stiff and strong, while materials with a low modulus of rigidity, such as rubber, are relatively flexible and weak.
Modulus of rigidity can be calculated using the following formula:
G = (τ) / (γ)
Where G is the modulus of rigidity, τ is the shear stress and γ is the shear strain.
It is one of three moduli that describe the elasticity of solids, the other two are Young's modulus and bulk modulus.
