Short Answer:

A composite bar is a bar made up of two or more different materials joined together so that they act as a single unit when a load is applied. These materials are rigidly connected in such a way that strain is the same in each material, but stress may differ depending on their elastic properties.

In simple words, a composite bar combines different materials like steel, brass, or aluminum to take advantage of their individual strengths. This combination helps achieve higher strength, reduced weight, or better performance under temperature or load variations.

Detailed Explanation:

Composite Bar

Definition and Meaning:
A composite bar is a structural member that consists of two or more materials of different elastic moduli and cross-sectional areas, rigidly connected to act together under the same load. When such a bar is subjected to an axial force (either tension or compression), both materials deform equally (same strain) because they are firmly attached, but the stresses developed in each material may be different due to differences in their stiffness or Young’s modulus.

Composite bars are used in many engineering applications where a single material cannot meet the performance requirements. For example, combining steel and copper can provide both high strength and good electrical conductivity.

Behavior of Composite Bar under Load

When an axial load is applied to a composite bar, it distributes among the individual materials according to their stiffness.

Since the materials are joined together, they experience the same total deformation (strain).
The stresses in different materials are proportional to their Young’s moduli.
The total load is the sum of the loads carried by individual materials.

For a composite bar consisting of two materials (1 and 2):

where
, and .

Because strain () is the same for both materials:

and from Hooke’s law,

This relation shows that the stress in each material is directly proportional to its modulus of elasticity.

Derivation of Relationship in Composite Bar

Consider a composite bar consisting of two materials, material 1 and material 2, of lengths , cross-sectional areas and , and elastic moduli and . The bar is subjected to an axial load .

Let be the total elongation, and , be the stresses in material 1 and 2 respectively.

From Hooke’s law, the strain in each material is:

Since both materials are joined together and deform equally,

Hence,

This shows that the ratio of stresses in two materials equals the ratio of their elastic moduli.

Now, the total load carried by the bar is:

Substitute the relation :

From this, the stress in each material can be found for a given total load .

The total elongation () of the bar is given by:

Substitute for stresses using load distribution equations to get:

or equivalently,

depending on simplifications for uniform load distribution.

Assumptions in Composite Bar Analysis

The bar is perfectly bonded — no slip occurs between the materials.
Both materials have the same initial length and experience equal deformation.
The materials obey Hooke’s Law (within elastic limit).
The load acts along the common axis of the composite bar.
Temperature remains constant (unless thermal effects are analyzed).

Example: Steel and Copper Composite Bar

A steel rod and a copper rod of equal length are joined end-to-end and subjected to a tensile load .

Given:

Then, from the relation:

This means the stress in steel is twice the stress in copper under the same load, because steel is stiffer (higher ). However, since copper has lower stress, it carries less portion of the load.

Applications of Composite Bars

Reinforced Concrete Beams:
- Concrete (weak in tension) is reinforced with steel rods (strong in tension).
Bimetallic Strips:
- Used in thermostats where two metals with different coefficients of expansion are joined to convert temperature change into mechanical movement.
Machine Shafts:
- Composite shafts combine lightweight and strong materials (like steel and carbon fiber).
Bridge and Building Members:
- Composite bars resist combined loads efficiently using different materials.
Aerospace Structures:
- Used for weight reduction with high stiffness and strength (e.g., aluminum + carbon fiber).

Advantages of Composite Bars

Combine strength and flexibility of different materials.
Allow efficient load distribution based on material properties.
Improve thermal resistance and fatigue performance.
Reduce weight while maintaining strength.
Enhance durability in demanding environments.

Disadvantages of Composite Bars

Complex analysis due to different material behavior.
Difficult to manufacture and bond materials perfectly.
Uneven thermal expansion may cause internal stresses.
Expensive compared to single-material members.

Conclusion:

A composite bar is a combination of two or more materials, such as steel and copper, joined so that they act as a single unit under load. The strain is the same in all materials, but stress varies according to their modulus of elasticity. The total load is shared by the components depending on their stiffness. Composite bars are widely used in engineering to achieve the desired combination of strength, stiffness, weight, and durability for modern mechanical and structural applications.