What is allowable stress?

Short Answer:

Allowable stress is the maximum stress that a material or component is permitted to carry safely under working conditions without failure. It is always less than the material’s ultimate or yield strength and provides a margin of safety to prevent damage or permanent deformation.

In simple words, allowable stress is the safe limit of stress used in design calculations. Engineers determine it by dividing the material’s ultimate or yield strength by a suitable factor of safety. This ensures that the structure or machine part remains safe, reliable, and durable during actual operation.

Detailed Explanation :

Allowable Stress

Allowable stress, also known as working stress, is a very important concept in mechanical and structural engineering. It represents the maximum stress that a material can withstand safely without failure when subjected to external loads during normal working conditions. It ensures that the material performs its intended function without reaching its elastic limit or ultimate strength.

The allowable stress is intentionally kept lower than the actual strength of the material to provide a safety margin. This margin accounts for uncertainties such as:

  • Variations in material properties,
  • Inaccurate loading conditions,
  • Imperfections in manufacturing,
  • Environmental effects, and
  • Human errors in design or operation.

By using allowable stress, engineers design components that can handle real-life conditions safely and effectively.

Mathematical Expression

The allowable stress () is calculated using the following formula:

Where,

  •  = allowable or working stress,
  •  = ultimate strength or yield strength of the material,
  • Factor of Safety (FOS) = safety margin applied to prevent failure.

Depending on the type of material and mode of failure, allowable stress can be based on either:

  1. Yield strength, for ductile materials (like steel, aluminum).
  2. Ultimate strength, for brittle materials (like cast iron, concrete).

For example, if the yield strength of steel is 250 MPa and the factor of safety is 2.5, the allowable stress is:

This means that during normal working conditions, the stress on the steel component should not exceed 100 MPa.

Purpose of Allowable Stress

The main purpose of allowable stress is to prevent failure and ensure that the component:

  • Does not deform permanently,
  • Does not fracture or crack under load,
  • Performs safely and reliably throughout its service life.

In simple terms, allowable stress acts as a limit that must not be crossed during operation. It ensures the design remains within the elastic range of the material, meaning the component returns to its original shape once the load is removed.

Factors Affecting Allowable Stress

Several factors influence the value of allowable stress, such as:

  1. Type of Material:
    Different materials have different yield and ultimate strengths. Ductile materials like steel can bear higher allowable stress compared to brittle materials like cast iron.
  2. Factor of Safety (FOS):
    A higher FOS results in a lower allowable stress. Critical applications where safety is important (like aircraft, bridges, or boilers) use higher safety factors.
  3. Type of Loading:
    Static loads require smaller safety margins, while fluctuating, impact, or shock loads need higher safety margins to avoid fatigue or sudden failure.
  4. Environmental Conditions:
    High temperature, corrosion, or humidity can weaken materials, thus reducing allowable stress values.
  5. Manufacturing Accuracy:
    Imperfections such as voids, cracks, or uneven thickness can reduce the actual strength, so allowable stress is lowered accordingly.
  6. Service Life Requirements:
    Components designed for long life or continuous use are given lower allowable stress to prevent fatigue and wear.

Types of Allowable Stress

Allowable stress can be classified based on the type of loading or failure mode:

  1. Allowable Tensile Stress:
    Maximum safe tensile stress a material can handle without failure in tension.
  2. Allowable Compressive Stress:
    Safe limit of compressive stress before the material begins to buckle or crush.
  3. Allowable Shear Stress:
    Maximum shear stress that can be safely applied without causing sliding or shear failure.
  4. Allowable Bearing Stress:
    Safe pressure that can be exerted between contacting surfaces (like bolt and plate) without deformation.
  5. Allowable Bending Stress:
    Limit of stress in bending applications like beams to avoid excessive deflection or cracking.

Each of these allowable stresses is derived from experimental testing and engineering codes or standards.

Importance of Allowable Stress in Design

  1. Ensures Safety:
    Keeping working stress below the allowable limit prevents sudden failures, ensuring safety for people and machinery.
  2. Increases Durability:
    Designs based on allowable stress perform efficiently for long durations without fatigue or damage.
  3. Maintains Elastic Behavior:
    The component always works within its elastic limit, allowing it to return to its original shape after load removal.
  4. Provides Design Standardization:
    Engineering codes like ASME, BIS, and ISO define allowable stress values for materials, ensuring consistency and reliability in designs.
  5. Balances Safety and Economy:
    A properly chosen allowable stress avoids overdesign (which increases cost) and underdesign (which risks failure).

Example of Application

Consider a riveted joint in a steel structure designed to carry 200 kN. If the steel used has a yield strength of 250 MPa and the factor of safety is 2.5, then the allowable stress is 100 MPa. The designer must ensure that the stress developed in the joint during operation does not exceed 100 MPa.

By applying allowable stress, engineers design connections that stay within safe working limits, preventing any permanent deformation or breakage.

Conclusion

In conclusion, allowable stress is the maximum stress that can be safely applied to a material without causing failure or permanent deformation. It is obtained by dividing the material’s ultimate or yield strength by an appropriate factor of safety. Allowable stress helps engineers design strong, safe, and reliable components by maintaining adequate margins against failure. It ensures that mechanical and structural systems work efficiently within safe limits throughout their service life.