Strain

Definition

Strain is a measure of deformation representing the displacement between particles in a material that results from an applied force. It quantifies how much a material stretches or compresses under load and is essential for understanding how materials respond to various forces and moments, as well as their capacity to withstand stress without permanent deformation.

5 Must Know Facts For Your Next Test

1. Strain is a dimensionless quantity often expressed as a percentage or ratio of change in length to the original length.
2. There are different types of strain, including normal strain (change in length) and shear strain (change in angle), each describing different deformation modes.
3. The relationship between stress and strain is crucial for material design; engineers use this information to ensure that structures can safely carry loads.
4. Strain can be elastic (temporary and reversible) or plastic (permanent and irreversible), which is important for predicting material failure.
5. Understanding strain helps engineers analyze stability and equilibrium in structures subjected to various forces and moments.

Review Questions

• How does strain relate to the concepts of stress and elastic modulus in material behavior?
  • Strain is directly related to stress through the elastic modulus, which defines how much a material will deform under applied stress. When a force is applied to a material, it experiences stress, resulting in strain or deformation. The elastic modulus quantifies this relationship, indicating that higher stress leads to greater strain until the material reaches its elastic limit. Understanding this relationship is essential for predicting how materials will behave under load.
• Discuss the significance of differentiating between elastic and plastic strain in engineering applications.
  • Differentiating between elastic and plastic strain is critical in engineering because it affects how materials are selected and used in construction. Elastic strain indicates that a material will return to its original shape after the load is removed, while plastic strain means the material has undergone permanent deformation. Engineers must account for these differences when designing structures to ensure safety and integrity under various loads, preventing catastrophic failures due to unexpected plastic deformations.
• Evaluate the implications of ignoring strain in structural analysis when designing buildings subjected to dynamic loads.
  • Ignoring strain in structural analysis can lead to serious implications, particularly when designing buildings that must withstand dynamic loads such as earthquakes or wind forces. If engineers overlook how materials will deform under such conditions, they risk underestimating the necessary strength and stability of structures, potentially leading to failure during extreme events. A thorough understanding of strain allows engineers to create more resilient designs that accommodate both expected stresses and unexpected deformations, ultimately protecting lives and property.

Related terms

Stress:

Stress is the internal force per unit area within materials that arises from externally applied forces, uneven heating, or permanent deformation, often measured in pascals (Pa).

Elastic Modulus: Elastic modulus, or modulus of elasticity, quantifies a material's ability to deform elastically (i.e., non-permanently) when a stress is applied, indicating the relationship between stress and strain.

Hooke's Law:

Hooke's Law states that, within the elastic limit of a material, the strain is directly proportional to the applied stress, typically expressed as $$ ext{stress} = E imes ext{strain}$$ where E is the elastic modulus.