Understanding Yield Stress in Plastic Method of Analysis for Steel Structures

The plastic method of analysis is a structural design approach that considers the non-linear behavior of materials, specifically their ability to yield and form plastic hinges. Unlike elastic analysis, which assumes materials remain elastic under service loads, plastic analysis allows for the redistribution of stresses after yielding occurs, up to the point of collapse.

Why Yield Stress Matters in Plastic Analysis

Yield stress, denoted by \(f_y\), is a critical material property. It represents the stress level at which a material begins to deform permanently. In the plastic method of analysis, the formation of plastic hinges at points where the yield stress is reached is fundamental to understanding the structural behavior and determining the collapse load. The material must exhibit sufficient ductility after yielding to allow for stress redistribution and the full development of the plastic mechanism.

Limit on Yield Stress for Plastic Analysis

For the plastic method of analysis to be reliably applied to steel structures, the steel grade used must possess adequate ductility. Indian Standard code IS 800:2007, which deals with steel structures, provides guidelines for the application of different design methods, including plastic analysis. Clause 5.2.2 of IS 800:2007, specifically related to material properties and plastic analysis, puts a restriction on the maximum yield stress for steel sections designed using the plastic method.

According to IS 800:2007, the nominal yield stress (\(f_y\)) of the grade of steel used for plastic analysis shall not exceed 450 MPa. This limit ensures that the steel has the necessary ductility to undergo plastic deformation and stress redistribution without brittle failure before the full plastic capacity is reached.

Let's look at the given options:

• 250 MPa: This is a common yield strength for Fe 250 grade steel, which is well below the limit for plastic analysis.
• 415 MPa: This is close to the limit and represents a high-strength steel grade, potentially usable if ductility requirements are met and the yield stress is confirmed to be within the limit.
• 450 MPa: This value matches the maximum allowed yield stress as per IS 800:2007 for plastic analysis.
• 500 MPa: This value exceeds the maximum allowed yield stress of 450 MPa, making steel with this yield strength generally unsuitable for design strictly based on the plastic method as per the code.

Therefore, based on the code provisions for the plastic method of analysis in steel structures, the value of the yield stress of the grade of steel shall not exceed 450 MPa.

Revision Table: Key Concepts in Plastic Analysis

Additional Information: Ductility Requirements

The restriction on yield stress to 450 MPa for plastic analysis is directly related to ensuring adequate ductility in the steel. High-strength steels (with yield strengths significantly above 450 MPa, like Fe 500 or higher) often have a lower ratio of ultimate tensile strength to yield strength (\(f_u/f_y\)) and reduced elongation compared to lower-strength steels (like Fe 250 or Fe 415). Sufficient \(f_u/f_y\) ratio and elongation are crucial for plastic hinge formation and rotation capacity before fracture. A higher yield stress can imply less strain hardening and a shorter plastic plateau, which might not provide the required rotation capacity for plastic analysis assumptions to be valid.

Therefore, while higher strength steels offer advantages in elastic design by reducing material weight, their application in plastic analysis requires careful consideration of their ductility characteristics, which is why codes like IS 800:2007 limit the maximum permissible yield stress for this method.