Nelson Bustamante: Limit State, Working Stress and Ultimate Load Method of Structural Design

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Structural design is a critical aspect of engineering, ensuring that buildings and infrastructure withstand the forces they encounter. There are three primary methods of structural design: the Working Stress Method (WSM), the Ultimate Load Method (ULM), and the Limit State Method (LSM). These methods are applicable to both reinforced concrete and steel structures.

Methods of Structural Design

  • Working stress method (WSM)
  • Ultimate load method (ULM)
  • Limit state method (LSM)

1. Working stress method (WSM)

The Working Stress Method, a traditional approach to design, encompasses not only reinforced concrete but also structural steel and timber. This method operates under the assumption that structural materials behave linearly elastic, with safety ensured by restricting stresses induced by expected “working loads.”

In WSM, specified permissible stresses remain below material strength, with the ratio of material strength to permissible stress defining the factor of safety. However, this method’s reliance on linear elastic behavior and the assumption that stresses under working loads remain within permissible limits are not always realistic.

Various factors, including long-term effects like creep and shrinkage, stress concentrations, and secondary effects, can lead to significant local increases in stresses and redistribution of loads. Despite resulting in relatively large sections, WSM often yields better performance under typical working loads.

Methods of Structural Design

2. Ultimate load method (ULM)

As awareness grew regarding the limitations of WSM in reinforced concrete design and understanding deepened about material behavior at ultimate loads, the Ultimate Load Method emerged as an alternative. Also known as the Load Factor Method, ULM analyzes stress conditions near structural collapse, leveraging nonlinear stress-strain curves of concrete and steel.

Unlike WSM, ULM doesn’t rely on modular ratios, introducing safety measures through appropriate load factorsβ€”ratios of ultimate load to working load. This method allows different load types to have varying load factors under combined loading conditions, addressing shortcomings of WSM.

ULM often results in more slender sections and economical designs, particularly with high-strength materials. However, these designs may exhibit excessive deflections and crack widths under service loads due to slender sections resulting from high-strength materials. Stress distribution at ultimate loads is based on linear elastic theory, magnified by load factors.

3. Limit state method (LSM)

Representing a significant advancement over traditional design philosophies, the Limit State Method aims for comprehensive solutions by considering safety at both ultimate and service loads. Unlike WSM, which focuses solely on service loads, and ULM, which prioritizes ultimate loads, LSM ensures safety and serviceability.

LSM employs a multiple safety factor format, considering all possible limit statesβ€”Ultimate Limit States (strength, overturning, sliding, buckling, etc.) and Serviceability Limit States (deflection, crack width, vibration, durability, etc.). Limit states signify impending failure, beyond which structures cease to perform satisfactorily.

By incorporating both ultimate and serviceability considerations, LSM provides a rational approach to structural design, ensuring structures perform reliably throughout their service life.

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