A guide about working stress and limit state design

Concrete design has transitioned over time from the traditional working stress method to the more advanced ultimate limit state approach. Until the 1950s, structural design primarily relied on the working stress method. However, starting in the 1970s, the adoption of limit state design became widespread due to its ability to provide safer and more economical designs, accommodating both serviceability and failure loads. Despite this shift, the working stress method remains in use, largely due to its simplicity, familiarity, and relevance for assessing older structures.

Key takeaways

The working stress method is still used occasionally for its simplicity, familiarity, or in specific scenarios such as assessing older structures or during preliminary designs.

Working Stress Method:

Considers loads at service conditions and limits stresses to smaller allowable values.

Assumes an elastic response under loading.

Uses only part of the material’s resistance, leading to larger, less economical sections.

Limit State Method:

Considers ultimate failure loads and stresses, with design based on allowable maximum strain values.

Utilizes the material’s full strength under plastic loading, resulting in more economical designs.

Comparison:

The working stress method produces larger, more conservative sections, while the limit state method optimizes material use for cost-effective designs and provides more safe and reliable design.

Current Practice:

Limit state design is now the standard for structural design due to its efficiency and safety.

History of the development of working stress and limit state design

The development of working stress design (WSD) and limit state design (LSD) codes in the UK , USA, and other regions has been a gradual process spanning over a century. Let us break down in detail the timeline of their evolution:

 Early Development (1800s – 1920s)

Working stress design, also known as allowable stress design or permissible stress design, was the primary method used by civil engineers since the early 1800s. This approach focused on ensuring that stresses in a structure due to loads did not exceed the elastic limit.

In 1900, the building design and construction process began to formalize codes and requirements.

Emergence of Standards (1920s – 1950s)

In 1923, the American Institute of Steel Construction (AISC) published its first “Standard Specification for Structural Steel for Buildings” based on the allowable stress methodology.

In 1931, the American Association of State Highway and Transportation Officials (AASHTO) issued “Standard Specifications for Highway Bridges” based on allowable stress design methodology].

Transition Period (1950s – 1970s)

The 1950s marked the beginning of a shift towards limit state design:

1956: The American Concrete Institute (ACI) introduced Load and Resistance Factor Design (LRFD), then called Ultimate Strength Design, in ACI 318, “Building Code Requirements for Reinforced Concrete”.

1963: ACI 318 gave equal status to both working stress and strength methods.

1971: ACI introduced the “Strength Method” in its code, while identifying Working Stress as an “alternate method”.

1973: AASHTO adopted “Load Factor Design” (LFD) for concrete and steel elements, an interim step between ASD and LRFD.

Widespread Adoption of Limit State Design (1970s – Present)

In the 1970s, limit state theory began to gradually replace allowable or working stress design in structural codes of practice.

1979: The Ontario Ministry of Transportation released the “Ontario Highway Bridge Design Code”, the first reliability-based limit state specification in North America.

1986: AISC introduced LRFD in “Load and Resistance Factor Design Specification for Structural Steel Buildings”.

1994: AASHTO published the first edition of LRFD for highway bridges.

2002: Ten Eurocode sections developed and published, incorporating limit state design principles

2005: AISC unified the provisions for Allowable Stress Design and Load and Resistance Factor Design in a single specification.

Modern application of working stress and limit state design

Modern structural design practices have evolved to incorporate both the working stress method (WSM) and limit state design (LSD) depending on the specific requirements of the project. 

Some countries or some specific disciplines continue to use the work stress method because of its widespread use, familiarity, or simplicity. Even though some regions are slower to fully transition to limit state, particularly countries using Eurocode and most developed world have adopted limit state design for all structural design practices.

Working Stress Method (WSM)

WSM  still has continuing applications in some particular cases. The method is selected  in certain scenarios due to its simplicity and familiarity. Some designers use the method to some extent for solving simple structures and in retrofitting old structures, for double checking and initial design works.

The application of working stress method still is considered for 

-simple structures,due to the simple formulas and assumptions of the method

-geotechnical design because of its simplification of complex soil behaviour,

-in water tank design since it accounts serviceability,

-in some prestress design it continues to be used for limiting stresses under service loads and it has some wider continuing application 

-in timber design because of its popularity and the materials linear behaviour. 

However its use differs from place to place and from design office to design office and is completely replaced by some codes such as eurocodes to be superseded by limit state design.

Limit State Design (LSD)

LSD has become the predominant method in most modern design offices. In US and a few other countries WSM still has greater application for different reasons. However in Europe the LSM is catered by the eurocodes for all types of applications.

Although LSM is the principal design method now,  WSM still in use for some structural design and is used as an alternative in some design works. 

For some type of design works LSM is the best method as listed below:-

1. Complex structures: For high-rise buildings, long-span bridges, and other complex structures, LSD provides a more comprehensive approach to safety and serviceability.

2. Seismic design: LSD is preferred for structures in earthquake-prone regions, as it better accounts for extreme loading conditions.

3. Steel structures: The majority of steel design codes worldwide now use LSD principles, allowing for more efficient use of materials.

4. Geotechnical engineering: LSD has been widely adopted in foundation design and slope stability analysis.

5. Marine structures: Offshore platforms and port structures typically employ LSD due to the complex loading conditions and environmental factors.

 Hybrid Approaches

Some design offices use a combination of WSM and LSD:

1. Concrete structures: While LSD is the primary method, some designers use WSM for initial sizing before refining with LSD.

2. Renovation projects: When dealing with older structures originally designed using WSM, engineers may use a hybrid approach to ensure compatibility with existing elements.

While LSD has become the dominant method in most modern structural design practices, WSM still finds application in specific scenarios where simplicity or historical precedent are valued. The choice between methods often depends on local codes, project requirements, and the designer’s expertise.

What is the difference between work stress method and limit state method.

The Working Stress Method (WSM) and the Limit State Method (LSM) are two fundamental approaches used in structural design, particularly in reinforced concrete. Each method has distinct philosophies, assumptions, and applications.

What are the  Basic Principles

– Working Stress Method (WSM):

  – Based on linear elastic behavior of materials.

  – Designs structures to ensure safety under working loads only, without considering ultimate failure conditions.

  – Utilizes a single factor of safety applied to the yield or ultimate strength of materials to derive permissible stresses.

  – Assumes that the structure behaves elastically up to the point of service load, ignoring potential inelastic behavior during extreme conditions.

– Limit State Method (LSM):

  – Incorporates both ultimate strength and serviceability considerations. The method utilizes the strength of the material, which is not considered by the working stress method, as shown in light blue in the loading response diagram of concrete.

  – Structures are designed to remain safe under both service loads and potential failure scenarios, ensuring they do not exceed defined limit states.

  – Uses partial safety factors for different types of loads (e.g., dead, live) and material strengths, reflecting a more probabilistic approach to safety.

  – Considers nonlinear behavior of materials, allowing for more realistic modeling of stress distributions and material performance under load.

While the Working Stress Method is simpler and focuses on ensuring safety under normal working conditions, the Limit State Method provides a more robust framework that incorporates various failure modes and serviceability requirements. As such, LSM is increasingly preferred in modern structural engineering practices due to its comprehensive approach to safety and performance.

Design examples of Work stress method and limit state design

Design example showing steps of Concrete Design

– Design a reinforced concrete section subjected to 80 kN/m load and having a length of 5m. Assume the beam is simply supported at its ends. Consider the following section’s characteristics.

  f_ck = 30 MPa, f_yk = 500 MPa 

  b = 500 mm, W = 80 KN/m

Working stress method example:-

Solution :

  W = 80

M = W × L² / 8 = 250 kNm**  

L = 5 m

Assume a cover of 30 mm:  

c = 30 mm 

fc= 10 MPa, fst=230 MPa, n = 9.33 

k_c = n × fc/ (fst+ n × fc)  

k_c = 9.33 × 10 / (230+9.33×10)

= 0.288  

J = 1 – k / 3 = 0.904

= 1.304  

Q=0.5x fc x j x k = 0.5x10x0.904×0.2886=1.304

d = √(M / (Qxb)  

= 619 mm 

Hence, the working stress method results in a section height of h = 650 mm.

-Calculating the area of steel

  M = As × fs × jd = As × 230 × 0.904 × 0.619  

=> 250 × 10⁶ => As = 1942 mm²  

Provide ϕ 20 => 7ϕ 20  

Limit state method example according to eurocode

Design moment = 1.5M = 1.5 × 250 = 375 kNm

Calculating the size of the section required  

M = k × b × d² × f_ck**  

M = 0.196 × 500 × d² × 30 = 375 × 10⁶  

=> **d = 357 mm ≈ 360 mm**  

—Provide the size of the section of height h=400mm

Moment arm calculation:

   

where:

–

–

   

   

-To calculate , we’ll use the formula

   

Calculating are of steel:

–

–

–

–

   

   

Provide ϕ 24 => 8ϕ 24, by providing a larger height the steel reinforcement can be reduced.

Hence, as the design shows the size of the section is larger when designed with the working stress method.

Sources:

The Evolution of Structural Design Specifications in the United States

https://www.eng-tips.com/threads/1920s-concrete-beam-analysis-working-stress-design.355047/

https://www.researchgate.net/publication/292829093_A_history_of_the_safety_factors

https://www.sciencedirect.com/topics/engineering/allowable-stress-design

https://www.midasbridge.com/en/blog/working-stress-vs-limit-state-method

https://www.eng-tips.com/threads/limit-state-vs-working-stress-design.225903/

https://www.researchgate.net/publication/329170391_Quantified_Advantage_of_Limit_State_over_Working_Stress_as_Design_Methods