Working Stress Method

Contents

**Describe the Working stress method to design RCC members** 1

**Recall the Permissible stresses in concrete and steel-reinforcement** 2

**Describe the assumptions of the working stress method** 3

**Recall the different types of sections in RCC members** 4

**State the conditions in which Doubly Reinforced Beam is provided.** 5

**Describe the analysis of Doubly Reinforced Beam by using the Working Stress Design Method** 6

**Define the term Flanged Beam** 7

**Recall the effective Width of the Beam** 11

**Describe the Analysis of Flanged Beam by using the Working Stress Design Method** 12

**Describe the Working stress method to design RCC members**

The working stress method is a design approach used to determine the dimensions and reinforcement requirements for reinforced concrete (RCC) members. This method is based on the concept of working stress, which is defined as the average normal stress that a material is subjected to under normal working loads.

In the working stress method, the dimensions and reinforcement requirements for RCC members are determined by calculating the maximum average normal stress that is expected to occur in the member under normal working loads, and comparing this to the allowable working stress for the material.

To determine the maximum average normal stress, the applied loads are calculated and distributed across the cross-section of the member using appropriate load distribution factors. The stresses in the concrete and reinforcement are then calculated, taking into account the material properties and the geometry of the member.

Once the maximum average normal stress has been calculated, it is compared to the allowable working stress for the material. The allowable working stress is a value that is established based on the strength and deformation properties of the concrete and reinforcement, and it is used to ensure that the member will perform adequately under normal working loads.

If the maximum average normal stress exceeds the allowable working stress, additional reinforcement is added to the member to reduce the stress to an acceptable level. The reinforcement is typically placed in the tension zone of the member, where the highest stress occurs, to improve the strength and stability of the member.

In conclusion, the working stress method is a design approach used to determine the dimensions and reinforcement requirements for RCC members. This method is based on the concept of working stress, and it involves calculating the maximum average normal stress that is expected to occur in the member under normal working loads, and comparing this to the allowable working stress for the material. If the maximum average normal stress exceeds the allowable working stress, additional reinforcement is added to the member to reduce the stress to an acceptable level.

**Recall the Permissible stresses in concrete and steel-reinforcement**

The permissible stresses in concrete and steel reinforcement are values that are established based on the strength and deformation properties of the materials, and they are used to ensure that the reinforced concrete (RCC) members will perform adequately under normal working loads.

Permissible stress in concrete refers to the maximum stress that concrete can withstand without failing or cracking. The permissible stress in concrete is typically expressed as a percentage of its compressive strength, and it is used to determine the dimensions and reinforcement requirements for RCC members.

Permissible stress in steel reinforcement refers to the maximum stress that steel reinforcement can withstand without yielding or undergoing permanent deformation. The permissible stress in steel reinforcement is typically expressed as a percentage of its yield strength, and it is used to determine the dimensions and reinforcement requirements for RCC members.

In the design of RCC members, the permissible stresses in concrete and steel reinforcement are used to calculate the maximum average normal stress that is expected to occur in the member under normal working loads. If the maximum average normal stress exceeds the permissible stress in either concrete or steel reinforcement, additional reinforcement is added to the member to reduce the stress to an acceptable level.

In conclusion, the permissible stresses in concrete and steel reinforcement are values that are established based on the strength and deformation properties of the materials, and they are used to ensure that the RCC members will perform adequately under normal working loads. These values are used to calculate the maximum average normal stress that is expected to occur in the member under normal working loads, and to determine the dimensions and reinforcement requirements for RCC members.

**Describe the assumptions of the working stress method**

The working stress method is a design approach used to determine the dimensions and reinforcement requirements for reinforced concrete (RCC) members. This method is based on a number of assumptions that are made in order to simplify the calculation and design process.

The following are some of the key assumptions of the working stress method:

- Linear elastic behaviour: The working stress method assumes that the concrete and steel reinforcement behave in a linear elastic manner, meaning that the stress-strain relationship is linear and proportional. This assumption simplifies the calculation of stresses in the member and makes it easier to determine the maximum average normal stress.
- Constant section properties: The working stress method assumes that the cross-sectional properties of the member, such as area, moment of inertia, and radius of gyration, remain constant throughout the length of the member. This assumption simplifies the calculation of stresses in the member and makes it easier to determine the maximum average normal stress.
- Isotropic material properties: The working stress method assumes that the concrete and steel reinforcement have isotropic material properties, meaning that the material properties are the same in all directions. This assumption simplifies the calculation of stresses in the member and makes it easier to determine the maximum average normal stress.
- Perfect bond between concrete and steel reinforcement: The working stress method assumes that the bond between the concrete and steel reinforcement is perfect, meaning that the two materials act as a single composite material. This assumption simplifies the calculation of stresses in the member and makes it easier to determine the maximum average normal stress.
- Constant temperature: The working stress method assumes that the temperature of the member remains constant throughout its life, and that no temperature-related effects, such as thermal expansion or contraction, are taken into account.
- No creep or shrinkage: The working stress method assumes that there is no creep or shrinkage of the concrete or steel reinforcement over time. This assumption simplifies the calculation of stresses in the member and makes it easier to determine the maximum average normal stress.

In conclusion, the working stress method is a design approach used to determine the dimensions and reinforcement requirements for RCC members, and it is based on a number of assumptions that are made in order to simplify the calculation and design process. These assumptions include linear elastic behaviour, constant section properties, isotropic material properties, perfect bond between concrete and steel reinforcement, constant temperature, and no creep or shrinkage.

**Recall the different types of sections in RCC members**

Reinforced concrete (RCC) members are commonly used in construction to support loads and provide stability to structures. There are several types of sections that can be used in the design of RCC members, each with unique characteristics and benefits.

- Rectangular section: This section is a simple rectangular shape with a uniform depth and width. It is used primarily in beam and slab designs where the dimensions of the section are determined by the load-bearing capacity required.
- T-section: This section is a combination of two rectangular sections, with one section placed perpendicular to the other. T-sections are commonly used in beam designs and are beneficial in resisting bending moments due to their increased section area.
- L-section: This section is a combination of two rectangular sections, with one section placed adjacent to the other. L-sections are commonly used in beam designs and are beneficial in resisting bending moments due to their increased section area.
- I-section: This section is a beam shape with a wide flange on top and bottom, and a narrow web in the middle. I-sections are commonly used in beam and column designs and are beneficial in resisting both bending moments and axial forces.
- Circular section: This section is circular in shape and is commonly used in column designs. Circular sections are beneficial in resisting both axial compression and bending moments due to their geometric strength.
- Hollow section: This section is a rectangular or circular shape with a void in the middle. Hollow sections are commonly used in column designs and are beneficial in resisting both axial compression and bending moments due to their reduced weight and increased section area.

In conclusion, there are several types of sections that can be used in the design of RCC members, including rectangular, T-section, L-section, I-section, circular, and hollow sections. Each type of section has unique characteristics and benefits, and the appropriate type is selected based on the load-bearing capacity required and the type of member being designed.

**State the conditions in which Doubly Reinforced Beam is provided.**

A doubly reinforced beam is a reinforced concrete (RCC) beam that has reinforcing steel placed both in the tension and compression zones of the beam cross-section. This type of beam is used in specific conditions where the required load-bearing capacity exceeds that which can be achieved by a singly reinforced beam.

The conditions in which a doubly reinforced beam is provided are:

- High Moment demand: When a beam is subjected to high bending moments, a singly reinforced beam may not have sufficient strength to resist the loads. In such cases, a doubly reinforced beam is provided to increase the load-bearing capacity and ensure structural stability.
- Inadequate Depth: If the depth of the beam is not sufficient to accommodate the required reinforcement for the desired load-bearing capacity, a doubly reinforced beam can be used to increase the overall section area and provide additional strength.
- Structural Economy: In some cases, it may be more cost-effective to provide a doubly reinforced beam instead of using a larger single reinforced beam to achieve the required load-bearing capacity.
- Loading Conditions: When the loading conditions are such that the beam experiences both compression and tension forces simultaneously, a doubly reinforced beam can be used to resist both types of forces.

In conclusion, a doubly reinforced beam is provided in specific conditions where the required load-bearing capacity exceeds that which can be achieved by a singly reinforced beam. This type of beam is used to resist high bending moments, when the depth of the beam is inadequate, to achieve structural economy, and when the loading conditions require resistance to both compression and tension forces.

**Describe the analysis of Doubly Reinforced Beam by using the Working Stress Design Method**

The analysis of a doubly reinforced beam using the working stress design method involves determining the required load-bearing capacity of the beam and the reinforcement required to resist the applied loads. The following steps are involved in the analysis:

- Determine Loads: The first step in the analysis of a doubly reinforced beam is to determine the loads that will be applied to the beam. This includes dead loads, live loads, and any other loads that the beam will be subjected to.
- Calculate Moments: The next step is to calculate the bending moments in the beam at various points along its length. This is done by using the equation for bending moment, which is equal to the product of the applied load and the distance from the neutral axis to the point of interest.
- Select Section: Based on the calculated moments, the appropriate cross-sectional dimensions of the beam can be selected. The depth of the beam must be sufficient to accommodate the required reinforcement.
- Determine Permissible Stresses: The permissible stresses in concrete and steel reinforcement are used to determine the maximum stress that each material can withstand before failure occurs. These values are based on the properties of the materials and are given in codes and standards.
- Determine Required Reinforcement: The next step is to determine the amount of reinforcement required to resist the applied loads. This is done by calculating the maximum tensile stress in the steel reinforcement and the maximum compressive stress in the concrete. The amount of reinforcement required is determined based on the difference between these two stresses.
- Design Reinforcement: Based on the calculated reinforcement, the steel reinforcement is designed in accordance with codes and standards. This includes determining the size and spacing of the reinforcement bars and the size of the hooks and stirrups that are used to anchor the reinforcement.
- Check Deflection: The final step is to check the deflection of the beam and ensure that it is within the permissible limits. This is done by using a deflection formula and comparing the calculated deflection to the permissible deflection given in codes and standards.

In conclusion, the analysis of a doubly reinforced beam using the working stress design method involves determining the loads that will be applied to the beam, calculating the bending moments, selecting the appropriate cross-sectional dimensions, determining the permissible stresses, determining the required reinforcement, designing the reinforcement, and checking the deflection. The goal of the analysis is to ensure that the beam has sufficient load-bearing capacity and that it will not fail due to excessive deflection or material failure.

**Define the term Flanged Beam**

A flanged beam, also known as a T-beam, is a type of reinforced concrete (RCC) beam that has a wider flange on one side than the other. The flange is designed to provide additional strength and stability to the beam, making it suitable for use in a variety of structural applications.

The wider flange of the T-beam serves as the compression member, while the thinner web or stem acts as the tension member. The flange provides a large cross-sectional area for the concrete to resist compressive forces, while the web provides the necessary tensile strength to resist the applied loads.

Flanged beams are typically used in floor and roof systems, where they provide additional support and stability to the structure. They are also used in bridge construction, where they are used to support the roadway and provide lateral stability.

The design of a flanged beam involves determining the required load-bearing capacity, selecting the appropriate cross-sectional dimensions, and determining the required reinforcement. The reinforcement must be designed in accordance with codes and standards to ensure that the beam has sufficient strength and stability to resist the applied loads.

In conclusion, a flanged beam is a type of RCC beam that has a wider flange on one side than the other. It provides additional strength and stability to the structure and is used in a variety of structural applications, including floor and roof systems and bridge construction. The design of a flanged beam involves determining the required load-bearing capacity, selecting the appropriate cross-sectional dimensions, and determining the required reinforcement.

**Classify the Flanged Beam**

In reinforced concrete construction, a flanged beam refers to a specific type of beam that is designed with flanges or horizontal extensions on the sides of the main beam section. These flanges provide additional strength and stiffness to the beam, enabling it to support heavier loads and span longer distances compared to regular rectangular beams.

Flanged beam is broadly classified as:

i) Monolithic Beam: A monolithic beam, also known as a continuous beam or a continuous reinforced concrete beam, is a beam that extends over multiple supports without any intermediate joints or interruptions. It is constructed as a single, continuous element, with the reinforcing steel running continuously throughout its length. Monolithic beams provide structural continuity and distribute loads more evenly across the supports.

The main advantages of monolithic beams include:

- Increased Strength and Load Capacity: The absence of joints or interruptions in a monolithic beam results in increased strength and load-carrying capacity. The continuous reinforcement provides better resistance against bending and shear forces.
- Reduced Deflection: Monolithic beams tend to exhibit lower deflections compared to isolated beams since they distribute the load more uniformly over the supports.
- Crack Control: The absence of joints in a monolithic beam reduces the likelihood of cracks occurring at the beam’s ends or supports, enhancing its durability.

Monolithic beams are commonly used in various applications, including building construction, bridges, and infrastructure projects where longer spans or higher load capacities are required.

ii) Flanged beams are commonly used in structures where large spans or heavy loads need to be supported, such as bridges, multi-story buildings, and industrial structures. The flanges distribute the load over a wider area, reducing the bending moment and deflection of the beam.

Flanged beams can be classified based on various criteria, including the shape of the flanges and the overall configuration of the beam. Here are a few common classifications:

- T-Beam: This type of flanged beam has a horizontal flange at the top, forming a T-shape. The flange provides additional strength to resist bending moments, while the vertical web section connects the flange to the beam’s bottom. T-beams are often used in reinforced concrete floor and roof systems.
- L-Beam: An L-beam, also known as an inverted T-beam, has a horizontal flange at the bottom, resembling the letter “L” when viewed from the side. The flange helps distribute the load and increase the overall strength of the beam.

iii) Isolated Beam: An isolated beam, also known as a simply supported beam, is a beam that is supported at its ends or on discrete supports, such as columns or walls. Unlike a monolithic beam, an isolated beam is not continuous and may have joints or interruptions between supports.

The main features of isolated beams include:

- Defined Support Points: Isolated beams have well-defined support points, such as columns or walls, where they rest. These supports provide reaction forces to the beam, enabling it to resist loads.
- Clear Span: The span of an isolated beam refers to the distance between the supports. The beam is designed to transfer the loads it carries to the supports, and the span length determines the magnitude of the bending moment and shear forces.
- Potential for Expansion Joints: Isolated beams may incorporate expansion joints or discontinuities to allow for movement and accommodate temperature variations or other factors that can cause dimensional changes in the structure.

Isolated beams are commonly used in various structural systems, such as building frames, where shorter spans or separate structural components are desired. They are often found in residential and commercial buildings, where the beams rest on columns or walls and provide support for floor slabs or other elements.

Flanged beams are commonly used in structures where large spans or heavy loads need to be supported, such as bridges, multi-story buildings, and industrial structures. The flanges distribute the load over a wider area, reducing the bending moment and deflection of the beam.

**Recall the effective Width of the Beam**

The effective width of a beam can be determined using a different formula depending on the beam’s configuration and loading conditions. Here are some commonly used formulae for calculating the effective width in specific cases:

- Simply Supported Beam with Rectangular Cross-section:
- For uniform load distribution: The effective width (b_eff) is usually taken as the actual width (b) of the beam. b
_{eff}= b - For concentrated load at mid-span: The effective width is often approximated as 1.5 times the actual width. b
_{eff}= 1.5 * b

- For uniform load distribution: The effective width (b_eff) is usually taken as the actual width (b) of the beam. b
- T-Beam:
- For the flange width (b
_{f}) of a T-beam subjected to uniform load distribution: The effective width (b_eff) is generally taken as the actual width (b_{f}) of the flange. b_{eff}= b_{f} - For the web width (b
_{w}) of a T-beam subjected to uniform load distribution: The effective width is determined based on the contribution of the web to resisting the loads. Design codes provide formulas or tables for determining the effective width of the web, taking into account parameters such as the thickness of the flange and the spacing of the transverse reinforcement.

- For the flange width (b
- Continuous Beam:
- For continuous beams with multiple spans, the effective width depends on the distribution of bending moments and shears along the beam’s length. Design codes typically provide simplified methods or empirical formulas for calculating the effective width based on the specific beam configuration. These methods often consider factors such as the span lengths, support conditions, and the relative stiffness of adjacent spans.

b_{t}=6L_{0}+b_{w}+6D_{f}

- For continuous beams with multiple spans, the effective width depends on the distribution of bending moments and shears along the beam’s length. Design codes typically provide simplified methods or empirical formulas for calculating the effective width based on the specific beam configuration. These methods often consider factors such as the span lengths, support conditions, and the relative stiffness of adjacent spans.

It’s essential to consult the applicable design codes and guidelines specific to your project to determine the appropriate formula or method for calculating the effective width of the beam. These resources provide detailed information and recommendations to ensure the structural integrity and safety of the design.

**Describe the Analysis of Flanged Beam by using the Working Stress Design Method**

The analysis of a flanged beam using the working stress design method involves determining the capacity of the beam to resist various loads and stresses, such as bending, shear, and axial forces. The following steps outline the general process of analyzing a flanged beam using the working stress design method:

- Determine loads and loads distribution: The first step is to determine the loads and their distribution on the beam. This may include dead loads, live loads, wind loads, and any other loads that the beam may be subjected to.
- Determine the design moment: The next step is to determine the design moment, which is the maximum bending moment that the beam will experience. This is done by considering the loads and their distribution, as well as the span of the beam and the type of loading.
- Determine the effective width of the compression face: The effective width of the compression face is the width of the beam that is subjected to compression forces. This is an important factor in determining the capacity of the beam to resist compression forces.
- Calculate the permissible stresses: The next step is to calculate the permissible stresses in concrete and steel reinforcement. The permissible stresses are based on the strength of the materials, as well as any applicable design codes and standards.
- Determine the reinforcement required: The next step is to determine the amount of reinforcement required to resist the design moment. This may include the size and spacing of the steel reinforcement, as well as the size and spacing of any stirrups or other types of secondary reinforcement.
- Check the beam for shear: The final step is to check the beam for shear, which is the horizontal force that the beam experiences. This involves determining the shear capacity of the beam, which may include calculating the amount of shear reinforcement required and checking the beam for shear cracks.

In conclusion, the analysis of a flanged beam using the working stress design method involves determining the capacity of the beam to resist various loads and stresses. The process includes steps such as determining the loads and their distribution, calculating the permissible stresses, and determining the reinforcement required to resist the design moment and shear forces. The analysis must be done in accordance with any applicable design codes and standards.