Short Answer:

Compressive stress and strain describe how materials behave when they are subjected to a pushing or squeezing force. Compressive stress is the internal resistance developed per unit area in a material when it is compressed by external forces. It is the ratio of applied compressive load to the original cross-sectional area of the material.

Compressive strain is the deformation produced due to compressive stress. It represents the fractional decrease in length of the material and is given by the ratio of change in length to the original length. These properties are important for studying the strength of materials under compression.

Detailed Explanation :

Compressive Stress and Strain

When a body is subjected to a load that tends to shorten it, the type of stress developed inside the material is known as compressive stress, and the resulting deformation is called compressive strain. These concepts are very important in mechanical engineering because many structural and machine components such as columns, beams, concrete blocks, and shafts often experience compressive forces during operation.

Compressive stress and strain help engineers understand how materials behave under squeezing forces and ensure that structures do not collapse when subjected to compression.

Compressive Stress

Compressive stress is defined as the resisting force developed per unit area within a material when it is subjected to a compressive load. When a compressive force acts on a body, it tries to reduce its length. The material resists this reduction in length through internal forces. This internal resistance distributed over the cross-sectional area is known as compressive stress.

Mathematically, it is expressed as:

The unit of compressive stress is N/m² or Pascal (Pa), similar to other types of stress.

For example, if a steel cube is placed under a hydraulic press and a force acts on its top surface, the stress produced inside the cube that resists the compression is compressive stress.

Compressive stress acts opposite to tensile stress. While tensile stress tries to stretch the material, compressive stress tends to shorten it. The amount of compressive stress that a material can bear before failing depends on its compressive strength. Brittle materials like cast iron and concrete have high compressive strength but low tensile strength, while ductile materials like steel have good strength in both tension and compression.

Compressive Strain

Compressive strain is the ratio of the decrease in length to the original length of a material when it is subjected to compressive stress. It shows how much a material is shortened under the applied load.

It is given by the formula:

Compressive strain is a dimensionless quantity because it is a ratio of two lengths.

For example, if a steel rod 1 meter long shortens by 0.001 meters under a compressive load, then the compressive strain is 0.001 / 1 = 0.001. This means the rod has shortened by 0.1% of its original length due to the load.

The relationship between compressive stress and strain within the elastic limit of the material follows Hooke’s Law, which states:

Here, E is the Young’s Modulus or Modulus of Elasticity of the material. This constant represents the stiffness of the material — the higher the modulus, the less it deforms under a given stress.

Behavior of Materials under Compression

Different materials behave differently under compressive loads. For example:

1. Brittle Materials:
   Materials like concrete, stone, and cast iron are strong in compression but weak in tension. They can withstand large compressive loads before failure but cannot handle much elongation.
2. Ductile Materials:
   Materials such as mild steel and copper can resist both tensile and compressive stresses effectively. They deform more before breaking, which makes them suitable for applications involving both tension and compression.
3. Elastic Materials:
   Rubber and similar materials exhibit large compressive strains even under small stresses. They return to their original shape when the load is removed, showing elastic behavior.

In engineering design, the ability of a material to bear compressive stress is very important for components like columns, pillars, engine blocks, bridges, and bearings that constantly face compressive forces during use.

Practical Example

Consider a concrete column in a building structure. The weight of the roof and upper floors exerts a compressive load on the column. The internal resistance developed in the column due to this load is the compressive stress, and the small shortening of the column is the compressive strain. If the stress becomes greater than the compressive strength of concrete, the column will fail or crush.

Similarly, in mechanical components like pistons and shafts, compressive forces act during operation, and understanding compressive stress and strain helps in designing these components safely.

Conclusion

In conclusion, compressive stress is the internal resistance developed per unit area of a material when a compressive load acts on it, while compressive strain is the ratio of decrease in length to the original length. These two properties are fundamental in studying how materials behave under compressive forces. They are used to ensure that mechanical and structural components can bear loads safely without failure. Understanding compressive stress and strain helps engineers design durable and efficient systems in various fields of mechanical and civil engineering.