The maximum normal stress theory is used for brittle materials.

Explanation:
The maximum normal stress theory, also known as the normal stress theory or the Rankine theory, is a failure criterion used to predict the failure of brittle materials under static loading conditions. It is based on the assumption that failure occurs when the maximum normal stress exceeds the ultimate tensile strength of the material.

Characteristics of brittle materials:
1. Limited ductility: Brittle materials have little or no plastic deformation before failure. They typically fail suddenly and without warning once the maximum stress exceeds the material's ultimate strength.
2. High strength: Brittle materials often have high strength and stiffness, making them suitable for applications where strength is critical.
3. Low toughness: Brittle materials have low toughness, which refers to their ability to absorb energy before fracturing. This means that they are prone to catastrophic failure when subjected to sudden or impact loading.
4. Little or no permanent deformation: Unlike ductile materials, brittle materials do not exhibit significant permanent deformation when subjected to stress. They simply fracture or break.

Application of the maximum normal stress theory:
The maximum normal stress theory is commonly used in the design and analysis of structures and components made from brittle materials, such as ceramics, glass, and some types of polymers. It helps engineers determine whether a given design or material is suitable for a specific application by comparing the maximum normal stress under expected loading conditions with the material's ultimate tensile strength.

By applying the maximum normal stress theory, engineers can ensure that the stresses in the structure or component are below the material's ultimate strength, reducing the risk of failure. This theory is particularly useful for brittle materials because it focuses on the maximum normal stress, which is the primary cause of failure in these materials.

In summary, the maximum normal stress theory is used for brittle materials because it predicts failure based on the maximum normal stress exceeding the material's ultimate tensile strength. This theory helps engineers design and analyze structures and components made from brittle materials to ensure their safety and reliability.