## Introduction of Limit State Method:

The limit state method is a balanced combination of the working stress method and the ultimate load design method. Where the working stress method provides adequate performance at the working load but no observation gives to the conditions at the time of the collapse of the structure.

On the other hand, the ultimate load or load factor method of design is used in construction but the ultimate load method takes to excessive deflection cracking. So it is not preferable. But the limit state method is given the exact value of safety. so that method is more preferable in construction.

This method is used to confirm that the structure should be able to withstand all the load that’s acting on the structure. This method gives an idea about the serviceability requirement of limiting deflection and cracking.

The limit state method is to define the maximum load-carrying capacity and the safety requirements of the structure. The limit state method of design is conferred in section 5 of IS code 456: 2000.

## What Is Limit State Method?

The limit state method is a balanced combination of the working stress method and the ultimate load design method. It is also known as load and resistance factor design in structural engineering.

The limit state method helps us to know the capacity load or working load of the structure. The motive of using the limit state method is to construct a safe and comfortable structure. This method gives an idea about the serviceability requirement of limiting deflection and cracking.

To make a safe structure limit state method obey two criteria, one is the ultimate limit state ana another one is the serviceability limit state. A limit state design makes a structure more safe, durable, and fit for human uses.

It gives the idea that the structure ongoing to build can carry the acting loads like dead loads, live loads, wind loads, and earth quick loads are not.

**Limit State of Serviceability:**

- The condition under which the building analyzed useful is called the limit state of serviceability in civil engineering.
- If the structure is not used if it is not serviceable.
- The limit state is sowing to prevent excessive deflection and cracking.
- At the working load, it ensures the adequate performance of the structure.
- It is calculated on the source of elastic theory or working stress method because it is deformed under the working load but not collapse.
- The two criteria are following in the limit state of serviceability that’s are, limit state of deflection and another is a limit state of cracking.
- Based on the most critical limit the structure should be designed and after that checked other limit states.

## Limit State of Collapse:

- Limit state is the maximum stress condition of the structure just before the collapse.
- Throughout a structured life, it gives proper strength and serviceability by limit state.
- Limit state of collapse deals with the safety of the structure and the limit state of serviceability deals with the durability of the structure in the limit state method.

## Assumption in Limit State of Collapse:

- In concrete, the relationship between the stress-strain distribution is assumed to be parabolic.
- The tensile strength of concrete is ignored.
- The maximum compressive load of the structure takes by the concrete.
- The steel takes the maximum tensile load of the structure and takes a little bit of compressive load.
- There should have a perfect bond between steel and concrete.
- In construction, the maximum strain at the outermost compression fibre is
**0.0035 in bending.** - A section that is plane before bending remains plane after bending.
- The maximum strain in the tension reinforcement of the section at failure is not less.

## Limit State Design

**Introduction,**

**Ultimate Limit State,**

**Serviceability Limit State.**

**#1. Introduction of Limit State Design:**

- Limit state design is known as load and resistance factor design.
- This method is used in structural engineering.
- In this limit state method,
- the structure should be able to fulfil two criteria that are the ultimate limit state and serviceability limit state
- In limit state design when a degree of loading acting on a structure, the structure should be fulfilled the criteria that are structural integrity, fitness for use, durability, or another design requirement.

**#2. ****Ultimate Limit State:**

- The ultimate limit state method is known as the calculation method of all load that’s acting on the structure.
- In this method, the engineers have to ensure that the structure that ongoing to build is stable and strong enough against all loads that are acting on the structure like live loads, wind load, dead load, earth quick load, or their combination load.
- From the calculation of the ultimate limit state, we generally get the load vs capacity ratio.
- From this ratio, we know that the ongoing structure can resist or not the load.
- The maximum value load vs capacity ratio is 1 for the permanent load and 1.30 for the temporary loads.

**#3. Serviceability Limit State:**

- In this stage, we have to calculate that the building that we are going to build that’s are adequately safe, and comfortable for human uses.
- But there has a little condition that is before the calculation of serviceability limit state we have to calculate the ultimate limit state. Because at first, we have to calculate the capacity of the building then the comfort level of the building.
- The serviceability limit is the service of the building like cracking check, deflection check, dampness check, etc.

## Limit State Method of RCC Design:

- Limit state method of RCC design in which we can know the permissible load that can carry the RCC structure safely.
- Plane cement concrete has high compressive strength but low tensile strength. So the beam or column made by plane cement concrete has a low load-carrying capacity and fails by cracking in the tension zone.
- So the reinforced steel bar is placed in the concrete in the tension zone. The steel bars take the tensile stress and concrete take compressive stress. That makes the beam strong.
- The steel bars that are provided in the tension zone are called the main bar.
- In this process, we can know the condition of the buildings or structure.
- And after knowing the condition of the building or structure we can decide that the building need services or repairs are not.
- Using this limit state method we can design the RCC beam-column or structure.

## What Is Working Stress Method?

**Working Stress Design Method** is a **method** used for the reinforced concrete **design** where concrete is assumed as elastic, steel and concrete act together elastically where the relationship between loads and **stresses** is linear.

## Working Stress Method:

- Plane cement concrete has high compressive strength but low tensile strength. So the beam or column made by plane cement concrete has a low load-carrying capacity and fails by cracking in the tension zone.
- So the reinforced steel bar is placed in the concrete in the tension zone. The steel bars take the tensile stress and concrete take compressive stress. That makes the beam strong.
- The steel bars that are provided in the tension zone are called the main bar.
- By the working stress method, we can design the above column or beam.

## Assumptions in Working Stress Method:

- A section that is plane before bending remains plane after bending.
- The steel and concrete behave as a linear elastic element.
- The concrete takes the compressive load but not takes the tensile load.
- On the other hand, the steel takes the compressive load but not takes the compressive load.
- The moduli elasticity of concrete and steel are constant.
- The bonds between concrete and steel reinforcement should be perfect.
- Under the working load, the stress-strain relationship of concrete and steel is a straight line.

### Limitations of Working Stress Method:

The limit state method gives a reasonable measure of strength. Where the working stress method does not give a reasonable measure of strength.

**Working Stress Method of Design:**

- This method is used for reinforcing the concrete design.
- Where steel and concrete simultaneously act elastically.
- The relationship between stress and load is linear.
- The moduli elasticity of concrete and steel are constant.
- In this method, we don’t get the true margin of the load that’s acting on the structure.
- In this method, concrete is assumed elastic material.

## Frequently asked questions (FAQs) that could be included in your article on the Limit State Method and Working Stress Method:

**What is the Limit State Method in structural design?**

The Limit State Method is a design philosophy that ensures structures can withstand all expected loads without collapsing or failing beyond acceptable limits. It considers both ultimate and serviceability limits.

**How does the Limit State Method differ from the Working Stress Method?**

The Limit State Method balances safety and performance by accounting for potential failure modes like excessive deflection and cracking, whereas the Working Stress Method assumes elastic behavior and does not explicitly consider these failure modes.

**What are the key advantages of the Limit State Method?**

The Limit State Method provides a more accurate assessment of structural safety under various loads, including live, wind, and seismic loads. It also considers durability and serviceability requirements, such as deflection and cracking limits.

**When should one use the Limit State Method over the Working Stress Method?**

The Limit State Method is preferred when designing structures that require rigorous safety assessments and consideration of non-elastic behavior under load. It is mandated in many modern building codes for its comprehensive approach to structural design.

**What are the main limitations of the Working Stress Method?**

The Working Stress Method does not provide a clear margin of safety under loads and can underestimate structural capacities, especially under non-linear load conditions or unexpected stresses.

**How does the Limit State Method address safety and serviceability?**

The Limit State Method ensures safety by considering ultimate limit states (preventing collapse) and serviceability limit states (ensuring comfort and functionality). It calculates load-carrying capacities based on safety factors derived from statistical analyses of material strengths and load variations.

**What are the basic assumptions in the Working Stress Method?**

Assumptions include linear elastic behavior of materials (concrete and steel), perfect bond between concrete and reinforcement, and a proportional relationship between stress and strain up to the yield point of materials.

**Which design approach is more widely used in modern construction and why?**

The Limit State Method is more widely used today due to its ability to account for uncertainties in loads and material strengths, providing a safer and more reliable structural design compared to the Working Stress Method.

**How does the Limit State Method impact construction costs and project timelines?**

While initial design calculations under the Limit State Method may be more involved, resulting in potentially higher design costs, it generally leads to more robust structures that require less maintenance over their lifetime, thereby reducing overall life-cycle costs.

**Is the Limit State Method mandated by building codes and standards?**

Yes, many national and international building codes now require the use of the Limit State Method due to its comprehensive approach to ensuring structural safety, durability, and serviceability.