Design of Column and Footing

Contents

**Classify Columns on the basis of the following: i. Slenderness Ratio ii. Eccentricity** 1

**Describe the concept of Eccentricity in the Columns** 2

**List various conditions of the effective span of the Column** 2

**Describe IS guidelines for Lateral Reinforcement** 4

**Recall assumptions for the design of axially loaded short columns** 6

**Describe the Load carrying capacity of the Short Columns** 7

**Recall the steps to design axially loaded short columns** 8

**Describe Helical Reinforcement in the Columns** 9

**Recall steps to design Helically Reinforced Columns** 9

**Recall the minimum depth criteria of the Foundation** 11

**Describe the types of Foundations** 11

**Describe general design requirements as per IS:456-2000 for the design of a Footing.** 12

**Describe design procedure for Isolated Footing** 13

**Explain the design steps for Masonry Wall Footing** 15

**Describe Load carrying capacity of the Long Columns** 16

**Recall the steps to design Long Columns.** 18

**Recall the modes of failure in Eccentric compression** 19

**Describe the salient features of PM Interaction Curve** 19

**2. What is a P-M Interaction Curve?** 20

**Recall the steps to design Eccentrically Loaded Columns.** 21

**Classify Columns on the basis of the following: i. Slenderness Ratio ii. Eccentricity**

Classifying columns based on Slenderness Ratio and Eccentricity is an important aspect in the design of Reinforced Concrete Structures (RCC).

i. Slenderness Ratio: Slenderness ratio is the ratio of the effective height of the column to the least radius of gyration of the cross-sectional area. Columns can be classified into short columns and slender columns based on the slenderness ratio. If the slenderness ratio is less than or equal to a certain critical value, the column is considered as a short column. If the slenderness ratio exceeds the critical value, the column is considered as a slender column. The critical value of the slenderness ratio is specified in codes and standards.

**Slenderness ratio** = Kl/r

ii. Eccentricity: Eccentricity is the distance between the centroid of the cross-sectional area of the column and the centroid of the compressive stress. Columns can be classified into centrally loaded columns and eccentrically loaded columns based on the eccentricity. If the eccentricity is zero, the column is considered as a centrally loaded column. If the eccentricity is non-zero, the column is considered as an eccentrically loaded column. The type of loading (central or eccentric) affects the behavior of the column and its design.

All columns shall be designed for minimum eccentricity, equal to the addition of the unsupported length of column divided by 500 and lateral dimensions divided by 30, subject to a minimum of 20 mm.

Classifying columns based on slenderness ratio and eccentricity is important in order to determine the appropriate design procedure to be used for the column and to ensure that the column can safely resist the applied loads.

**Describe the concept of Eccentricity in the Columns**

Eccentricity in columns refers to the offset of the applied axial load from the geometric center of the column cross-section. In other words, when the axis of the load is not coincident with the centroidal axis of the cross-section, it creates an eccentricity in the column. This non-symmetrical distribution of load can lead to lateral buckling, which is a major failure mode in columns, especially in slender columns with low strength. The magnitude of the eccentricity affects the lateral stability of the column, and it is a critical factor in the design of columns. Therefore, it is important to consider eccentricity in the design of columns to ensure their stability and prevent failure.

**List various conditions of the effective span of the Column**

The effective span of a column is an important factor that affects the design of a reinforced concrete column. The effective span is defined as the clear distance between the points of contraflexure or the distance between the points of maximum bending moment. There are several conditions that determine the effective span of a column, including:

- Load conditions: The effective span of a column depends on the type and distribution of loads acting on the column. The loads can be axial, uniaxial bending, biaxial bending, or combined axial and bending loads.
- Restraint conditions: The effective span of a column depends on the type and location of restraints provided to the column. The restraints can be provided at the ends of the column, along the height of the column, or both.
- Member geometry: The effective span of a column depends on the shape, size, and reinforcement of the column. The size of the column, the shape of the cross-section, and the amount of reinforcement all play a role in determining the effective span.
- Material properties: The effective span of a column depends on the material properties of the concrete and reinforcement. The strength, stiffness, and ductility of the concrete and reinforcement all play a role in determining the effective span.
- Environmental conditions: The effective span of a column depends on the environmental conditions in which the column is to be constructed. Factors such as temperature, humidity, and exposure to corrosive environments can affect the effective span of a column.

The effective span of a column must be determined accurately in order to ensure that the column is designed to safely resist the applied loads. The conditions that determine the effective span of a column should be considered carefully during the design process to ensure that the column is designed to meet the required load and restraint conditions.

**Recall IS Codal Provision for the following: i. Minimum Reinforcement ii. Maximum Reinforcement iii. Minimum number of Bars iv. Minimum Clear Cover**

The IS Codal Provision for Reinforced Concrete Column design includes certain guidelines and regulations regarding the minimum and maximum reinforcement, minimum number of bars, and minimum clear cover.

i. Minimum Reinforcement: The minimum reinforcement of a column is determined based on the size and load-bearing capacity of the column. The IS Code specifies the minimum reinforcement in terms of the percentage of the cross-sectional area of the column that must be covered by steel reinforcement.The mild steel reinforcement in either direction in slabs shall not be less than 0.15%. In case of columns minimum reinforcement shall not be less than 0.8%

ii. Maximum Reinforcement: The maximum reinforcement of a column is also specified in the IS Code to prevent the over-reinforcement of the column, which can result in brittle failure. The maximum reinforcement is determined based on the size of the column and the type of loading.

iii. Minimum number of Bars: The minimum number of reinforcement bars in a column is specified in the IS Code to ensure adequate confinement of the concrete and to prevent excessive buckling of the reinforcement.

According to Clause (26.5. 3.1) of IS 456: 2000, the maximum longitudinal steel reinforcement for the column is 6 % of the gross column area.

iv. Minimum Clear Cover: The minimum clear cover of a column is the minimum distance between the outer surface of the reinforcement and the outer surface of the concrete. This is specified in the IS Code to provide adequate protection to the reinforcement from corrosion and to prevent bond failure. The minimum clear cover depends on the type of exposure, the size of the column, and the type of loading.

**Describe IS guidelines for Lateral Reinforcement**

IS guidelines refer to the Indian Standard code of practice for design and construction of reinforced concrete structures. Lateral reinforcement is an essential element in reinforced concrete structures, as it provides resistance against lateral forces like wind, earthquake, and soil pressure. The IS guidelines provide detailed specifications for the design and placement of lateral reinforcement to ensure the stability and safety of the structure.

The following are the IS guidelines for lateral reinforcement:

- Minimum Cross-Sectional Area: The minimum cross-sectional area of lateral reinforcement is specified based on the size of the main longitudinal reinforcement. The cross-sectional area of the lateral reinforcement should not be less than 0.3% of the gross cross-sectional area of the concrete.

Example: For a beam with longitudinal reinforcement of 16 mm diameter, the minimum cross-sectional area of lateral reinforcement would be 0.3% of the gross cross-sectional area of the concrete, which is 16*16*π/4*0.003 = 150 mm².

- Spacing: The maximum spacing between two lateral ties or spirals is specified to ensure that the structure is adequately reinforced against lateral forces. The maximum spacing should not exceed 16 times the diameter of the longitudinal reinforcement or 300 mm, whichever is less.

Example: For a beam with 16 mm diameter longitudinal reinforcement, the maximum spacing between two lateral ties or spirals would be 16*16 = 256 mm, which is less than 300 mm.

- Diameter of Lateral Reinforcement: The diameter of lateral reinforcement is specified based on the size of the main longitudinal reinforcement and the type of structure. The diameter of the lateral ties or spirals should not be less than 6 mm or greater than 1/4th of the diameter of the main reinforcement.

Example: For a beam with 16 mm diameter longitudinal reinforcement, the diameter of the lateral ties or spirals would be between 6 mm and 4 mm, which is 1/4th of the diameter of the main reinforcement.

- Placement of Lateral Reinforcement: The placement of lateral reinforcement should be such that it effectively resists the lateral forces acting on the structure. The reinforcement should be placed close to the compressive face of the concrete to provide effective confinement.

Example: For a beam, the lateral reinforcement should be placed at regular intervals along the length of the beam and close to the compressive face of the concrete to provide effective confinement.

- Special Provisions for Seismic Zones: In seismic zones, the IS guidelines require additional lateral reinforcement to resist the high lateral forces generated by earthquakes. The lateral reinforcement should be provided in the form of closely spaced transverse bars or closed stirrups.

Example: For a building located in a high seismic zone, the IS guidelines require additional lateral reinforcement in the form of closely spaced transverse bars or closed stirrups to ensure the stability and safety of the structure during earthquakes.

In conclusion, the IS guidelines provide detailed specifications for the design and placement of lateral reinforcement in reinforced concrete structures. The guidelines ensure that the structure is adequately reinforced against lateral forces like wind, earthquake, and soil pressure. The guidelines specify the minimum cross-sectional area, maximum spacing, diameter, and placement of lateral reinforcement, and provide special provisions for seismic zones to ensure the stability and safety of the structure.

**Recall assumptions for the design of axially loaded short columns**

The design of axially loaded short columns in Reinforced Concrete (RCC) structures involves making certain assumptions to simplify the calculations. Some of the common assumptions for the design of axially loaded short columns include:

- The column is considered to be short if its height is less than its lateral dimension.
- The column is subjected to axial compression only and no other forces such as bending, torsion, or shear.
- The concrete in the column is considered to be homogeneous, isotropic, and linearly elastic.
- The steel reinforcement in the column is considered to be perfectly bonded with the concrete.
- The steel reinforcement in the column is considered to be perfectly elastic and will follow Hooke’s law.
- The yielding of steel reinforcement in the column is considered to be a plastic phenomenon, and the strain in the reinforcement is proportional to the stress.

These assumptions help to simplify the calculations involved in the design of axially loaded short columns, making it easier to determine the required amount of steel reinforcement, the maximum compressive stress in the concrete and steel, and the maximum deflection of the column.

**Describe the Load carrying capacity of the Short Columns**

The load carrying capacity of short columns refers to the maximum load that a short column can support before failure occurs. Short columns are those that have a slenderness ratio (the ratio of the column’s height to its least radius of gyration) less than or equal to certain limits, as specified by the Indian Standards (IS) codal provisions. The load carrying capacity of short columns is determined by the strength of the concrete, the strength of the reinforcement, and the buckling behavior of the column. The design of axially loaded short columns typically makes use of the working stress method, which involves assuming a certain stress in the concrete and reinforcement and designing the column accordingly to ensure that this stress is not exceeded under normal loading conditions. To determine the load carrying capacity, the design must take into account the effects of axial compression, buckling, and any eccentricities in the loading.

**Recall the steps to design axially loaded short columns**

The following are the steps to design axial loaded short columns:

- Determine the design axial load: The axial load on the column must be determined based on the loads from the structure and the appropriate load factor.
- Determine the effective length of the column: The effective length of the column is determined based on the conditions of restraint, the height of the column, and the type of structure.
- Determine the slenderness ratio: The slenderness ratio is calculated as the effective length divided by the least radius of gyration of the cross-section of the column.
- Select the grade of concrete: The grade of concrete must be selected based on the axial load and the slenderness ratio.
- Determine the longitudinal reinforcement: The minimum and maximum longitudinal reinforcement must be calculated based on the grade of concrete and the axial load.
- Design the cross-section of the column: The cross-section of the column must be designed based on the axial load, the effective length, and the longitudinal reinforcement.
- Check for buckling: The column must be checked for buckling to ensure that it does not fail in compression.
- Check for shear: The column must also be checked for shear to ensure that it does not fail due to shear forces.
- Check for deflection: The deflection of the column must be checked to ensure that it does not exceed the allowable limits.

These steps must be followed in accordance with relevant codes and standards, such as Indian Standard (IS) 456, to ensure the strength and stability of the column.

**Describe Helical Reinforcement in the Columns**

Helical Reinforcement in Columns refers to the arrangement of reinforcing bars or tendons that are spirally placed around the circumference of a concrete column. It is used as a supplementary reinforcement for concrete columns in situations where the axial load and/or lateral load demands are high and the column is expected to experience significant levels of axial and/or lateral deformation. The helical reinforcement is placed on the outside of the concrete column and is designed to transfer the axial and lateral loads to the concrete core. The design of helical reinforcement in columns typically involves considering the spacing, size, and number of bars, as well as the pitch of the spirals. It is important to ensure that the helical reinforcement is properly anchored at the ends of the column and is properly tied to the longitudinal reinforcing bars to ensure effective transfer of forces. The use of helical reinforcement in columns can significantly enhance the load carrying capacity of the structure and improve its overall performance.

**Recall steps to design Helically Reinforced Columns**

Helically reinforced columns are RCC (Reinforced Cement Concrete) columns that are reinforced with spirally placed high strength steel bars. These columns are used to resist high axial and lateral loads. Designing a helically reinforced column involves the following steps:

- Determine the load conditions and the load carrying capacity required for the column.
- Calculate the maximum stress in concrete and steel under the loads and determine the required reinforcement area for the column.
- Select the suitable steel reinforcement and its size based on the maximum stress, ductility and bond strength requirements.
- Determine the number and spacing of helical reinforcement bars required to resist the axial and lateral loads.
- Calculate the pitch of the helix and the required length of reinforcement based on the diameter of the column and the helix spacing.
- Detail the reinforcement and the anchorage length required at the ends of the helical reinforcement bars.
- Check the compatibility between the helical reinforcement and the longitudinal reinforcement in the column.
- Ensure that the design satisfies the IS (Indian Standards) guidelines for helical reinforcement and provides adequate confinement to the core concrete.
- Detail the proper placement and fixation of the helical reinforcement in the column formwork.
- Finally, check and validate the design based on load testing and inspection during construction.

**Define the following terms: i. Footings ii. Foundations iii. Allowable Bearing Capacity iv. Safe Bearing Capacity**

i. Footings: Footings are the lower part of the foundation of a building or structure, which serves as the support base for the columns and walls. They help distribute the load of the building evenly to the soil, preventing the building from sinking or collapsing.

ii. Foundations: Foundations are the lower part of a building or structure that lies beneath the ground surface and provides support to the entire structure. They transfer the weight of the building to the ground and ensure stability.

iii. Allowable Bearing Capacity: The Allowable Bearing Capacity is the maximum load that a soil can support without excessive deformation. It is the load capacity that is deemed safe for the soil to bear without causing failure or instability.

iv. Safe Bearing Capacity: The Safe Bearing Capacity is the maximum load that can be safely supported by the soil without causing excessive settlement or failure. It is calculated by considering the soil type, soil structure, and other factors that affect the soil’s ability to support weight.

**Recall the minimum depth criteria of the Foundation**

Foundation depth is an important factor in the design of any structure. It is necessary to have an adequate depth of the foundation to ensure that the structure is stable and not subject to failure due to soil settlement or instability. The minimum depth criteria of the foundation is determined by several factors including the soil type, the load bearing capacity of the soil, the depth of groundwater, and the type of structure being built.

According to IS codes, the minimum depth of a foundation should be at least 30 cm below the lowest level at which water is likely to accumulate and should be at least 60 cm below the surface of the ground. Additionally, the minimum depth of the foundation should be such that it is below the maximum level at which the soil is likely to expand due to moisture, and also below the maximum level at which the soil is likely to heave due to frost. The minimum depth of the foundation may also be influenced by the type of structure being built, as well as the size and weight of the structure.

It is important to ensure that the minimum depth criteria of the foundation is met in order to ensure the stability and longevity of the structure.

**Describe the types of Foundations**

The different types of foundations in Reinforced Cement Concrete (RCC) structures are as follows:

- Shallow Foundations: They are also known as spread footings and are used for buildings or structures with relatively low loads. Shallow foundations are mostly used for buildings with small heights.
- Deep Foundations: They are used for buildings or structures with relatively high loads. Deep foundations are usually used for buildings with greater heights.
- Pile Foundations: They are used for buildings or structures where the soil is not strong enough to support the weight of the building. Piles are long cylindrical shaped members made of concrete, steel, or timber, which are driven into the soil to transfer the load of the structure to the deeper, more competent layers.
- Well Foundations: They are used for buildings or structures where the soil is not strong enough to support the weight of the building. A well foundation is a cylindrical shaped structure which is constructed in the soil and filled with concrete.
- Mat or Raft Foundations: They are used for buildings or structures where the soil is not strong enough to support the weight of the building. A mat foundation is a solid reinforced concrete slab that spreads the weight of the structure over a larger area.

All of these foundation types have their own advantages and disadvantages and the choice of the type of foundation depends upon the nature of soil, the type of structure, and other relevant factors.

**Describe general design requirements as per IS:456-2000 for the design of a Footing.**

The Indian Standard IS:456-2000 provides general design requirements for the design of footings in reinforced concrete structures. These requirements include the following:

- Loads: The design of footings must consider all types of loads, including dead loads, live loads, wind loads, seismic loads, and other loads as applicable.
- Footing Dimensions: The size and shape of the footing should be determined based on the loads, soil conditions, and space constraints. Footings should have a minimum thickness of 20 cm or a minimum width of 30 cm, whichever is greater.
- Reinforcement: The reinforcement must be provided in accordance with the IS code requirements. The minimum amount of reinforcement should be determined based on the size of the footing and the loads that it will be subjected to.
- Concrete Strength: The concrete strength must be in accordance with the IS code requirements. A minimum compressive strength of M20 is usually required for footings.
- Soil Conditions: The soil conditions must be considered in the design of the footings. The allowable bearing capacity of the soil should be determined, and the foundation should be designed to ensure that the loads are transmitted safely to the soil without causing excessive settlement or failure.
- Anchorage: The reinforcement must be anchored at the bottom of the footing to ensure that it does not slip under load.
- Column Loads: The loads from the columns must be transferred safely to the footings without causing excessive bending or cracking.
- Connections: The connections between the columns and the footings must be designed to ensure that they are strong and rigid, and to prevent any movement or separation under load.

These are the general design requirements for the design of footings as per IS:456-2000. The design must take into account the specific conditions of each project and should be based on a detailed analysis of the loads, soil conditions, and other relevant factors.

**Describe design procedure for Isolated Footing**

The design procedure for an isolated footing involves the following steps:

- Determine the loads: The first step in designing an isolated footing is to determine the loads that the footing will be subjected to. This includes dead loads, live loads, and wind loads.
- Determine the soil bearing capacity: The soil bearing capacity is a critical factor in the design of an isolated footing. This can be determined through soil tests or from the literature.
- Select the size and shape of the footing: Based on the loads and the soil bearing capacity, the size and shape of the footing can be determined. The size of the footing is generally determined by the maximum load on the footing, while the shape of the footing is typically rectangular or circular.
- Reinforcement: Reinforcement is required to ensure that the footing does not crack or deform under load. The reinforcement can be in the form of steel bars or mesh, and it should be placed in the footing such that the steel is centred over the soil bearing layer.
- Check for stability: Once the size, shape, and reinforcement of the footing have been determined, the stability of the footing should be checked to ensure that it will not tip over or slide. This can be done using a stability factor or a moment calculation.
- Check for punching shear: The punching shear capacity of the footing should also be checked, as this is the shear stress that occurs at the perimeter of the footing when a concentrated load is applied.
- Check for bending and deflection: Finally, the bending and deflection of the footing should be checked to ensure that it does not deform excessively under load.

By following these steps, a safe and efficient design for an isolated footing can be developed.

**Describe the Design procedure for the following: i. Rectangular Combined Footing ii. Trapezoidal Combined Footing**

The design procedure for rectangular and trapezoidal combined footings in Reinforced Cement Concrete (RCC) is a critical aspect of building design and construction. The combined footings are used to distribute the load of a structure over a larger area, reducing the pressure on the soil and providing a stable foundation.

For the design of rectangular combined footings, the following steps are followed:

- Determination of Loads: The loads acting on the structure, such as dead load, live load, wind load, and earthquake load, must be calculated and added to find the total load acting on the structure.
- Determination of Soil Data: The soil bearing capacity and its properties must be determined to assess the stability of the footing.
- Selection of Footing Dimensions: Based on the load calculations and soil data, the dimensions of the rectangular footing must be selected to ensure adequate stability and support.
- Reinforcement Calculation: The reinforcement required for the rectangular footing must be calculated based on the loads acting on the structure and the soil data.
- Design of Beam: The beams that rest on the combined footing must be designed to ensure adequate strength and stability.
- Design of Column: The column must be designed to ensure that it can transfer the loads from the structure to the footing.

For the design of trapezoidal combined footings, the steps are similar to those for rectangular combined footings with a few modifications:

- Determination of Loads: The loads acting on the structure must be calculated, including dead load, live load, wind load, and earthquake load, to find the total load acting on the structure.
- Determination of Soil Data: The soil bearing capacity and its properties must be determined to assess the stability of the footing.
- Selection of Footing Dimensions: Based on the load calculations and soil data, the dimensions of the trapezoidal footing must be selected to ensure adequate stability and support.
- Reinforcement Calculation: The reinforcement required for the trapezoidal footing must be calculated based on the loads acting on the structure and the soil data.
- Design of Beams: The beams that rest on the combined footing must be designed to ensure adequate strength and stability.
- Design of Column: The column must be designed to ensure that it can transfer the loads from the structure to the footing.

In conclusion, the design of combined footings is a critical aspect of building design and construction, and it is essential to follow the proper design procedures to ensure stability and support for the structure. The steps for the design of rectangular and trapezoidal combined footings are similar, with a few modifications, and must be carefully followed to ensure that the structure is safe and secure.

**Explain the design steps for Masonry Wall Footing**

Masonry Wall Footing design is an important aspect of the overall design of a building’s foundation. The design of a Masonry Wall Footing involves several steps, which include:

- Determine the load and the type of soil: The load to be carried by the footing must be determined, which includes the weight of the wall, any live loads, and any other loads that may be present. The type of soil must also be determined, as this will affect the design of the footing.
- Determine the allowable bearing capacity: The allowable bearing capacity of the soil must be determined, which is the maximum load that the soil can bear without experiencing excessive settlement or failure.
- Determine the size and shape of the footing: The size and shape of the footing must be determined based on the load to be carried, the type of soil, and the allowable bearing capacity.
- Determine the depth of the footing: The depth of the footing must be determined, taking into consideration the type of soil and the load to be carried. In general, the minimum depth criteria for a Masonry Wall Footing is 600mm.
- Determine the reinforcement requirements: Reinforcement is required in a Masonry Wall Footing to provide additional strength and stability. The amount of reinforcement required will depend on the load to be carried, the type of soil, and the size and shape of the footing.
- Detailing of Footing: The detailing of the footing must be done in accordance with IS:456-2000. This includes details such as the thickness of the footing, the size and spacing of the reinforcement bars, and the details of the bond between the footing and the wall.
- Analysis of Footing: A structural analysis of the footing must be performed to determine its load carrying capacity, taking into consideration the load to be carried, the type of soil, and the size and shape of the footing.
- Verification of Design: Finally, the design of the Masonry Wall Footing must be verified to ensure that it is safe, stable, and able to carry the load without excessive settlement or failure. This verification can be done through hand calculations or computer simulations.

Overall, the design of a Masonry Wall Footing is a complex process that requires careful consideration of many factors, including the load to be carried, the type of soil, the allowable bearing capacity, the size and shape of the footing, the reinforcement requirements, and the detailing of the footing.

**Describe Load carrying capacity of the Long Columns**

The load carrying capacity of long columns in Reinforced Cement Concrete (RCC) structures is an important factor to be considered in the design process. The load capacity of a long column is determined by its ability to resist buckling. Buckling is a type of instability that occurs when the compression force in a column exceeds its critical load.

There are two types of buckling in long columns, lateral buckling and Euler buckling. Lateral buckling occurs when the column is subjected to compressive forces along its length and the lateral deformations cause the column to buckle. Euler buckling occurs when the column is subjected to compressive forces along its length and the axial deformations cause the column to buckle.

To determine the load carrying capacity of a long column, the critical buckling load must be calculated. This is done by considering the geometric properties of the column, its material properties, and the type of loading. The load carrying capacity of a long column can be improved by increasing its cross-sectional area, reducing its slenderness ratio, and providing lateral reinforcement.

To prevent the buckling of longitudinally reinforced column, provide Transverse reinforcement

- D≥ maximum {dmax/4, 6 mmm
- S ≥ Minimum { LLD, 16d, 300 mm

The IS 456:2000 codal provisions provide guidelines for the design of long columns in RCC structures. These guidelines include

the minimum reinforcement= 0.8%

maximum reinforcement= 6％ gross area (practically it is 4 % due to lapping)

minimum number of bars= 4 for rectangular and 6 bars for circular columns

minimum clear cover = 40 mm or diameter of bar whichever is greater

**Recall the steps to design Long Columns.**

The design of long columns is done to ensure that the column can withstand the load that it is subjected to. Long columns are generally subject to both axial and lateral loads, which must be considered during the design process. The steps to design long columns are as follows:

- Determine the load intensity on the column: The load intensity on the column is determined by considering the self-weight of the structure, live loads, and any other applied loads.
- Calculate the effective length of the column: The effective length of the column is the length between two points where the deformation of the column is considered to be zero.
- Determine the slenderness ratio of the column: The slenderness ratio is the ratio of the effective length of the column to the least radius of gyration.
- Calculate the critical load for buckling: The critical load for buckling is calculated using the following equation: Pcr = π2 * E * I / (KL)
^{2}, where E is the modulus of elasticity, I is the moment of inertia, K is the effective length factor, and L is the effective length of the column. - Determine the load intensity at the critical load: The load intensity at the critical load is calculated by dividing the critical load by the cross-sectional area of the column.
- Check the adequacy of the cross-sectional area: The adequacy of the cross-sectional area is checked by comparing the calculated load intensity at the critical load with the permissible stress for the material used.
- Design the longitudinal reinforcement: The longitudinal reinforcement is designed to resist the axial load and the buckling load. The reinforcement must be placed such that the stress in the reinforcement is within the permissible limit.
- Design the lateral reinforcement: The lateral reinforcement is designed to resist the lateral load and prevent buckling. The lateral reinforcement must be placed such that the stress in the reinforcement is within the permissible limit.

These steps must be followed as per IS 456-2000 to ensure that the design of long columns is safe and effective.

**Recall the modes of failure in Eccentric compression**

The mode of failure in Eccentric compression refers to the way in which the column fails under compressive loads when the load is applied in an eccentric manner. This means that the load is not applied directly on the axis of the column, but instead is applied at some distance away from it. Eccentric compression can cause failure in a number of different ways, including buckling, lateral-torsional buckling, and crippling.

Buckling is a type of failure that occurs when a column is unable to support its load and begins to deform in a lateral manner. This can occur when the load is applied along the axis of the column, or when it is applied in an eccentric manner.

Lateral-torsional buckling occurs when the load applied to the column causes it to bend both laterally and in torsion. This type of failure is more likely to occur when the column is slender and the load is applied in an eccentric manner.

Crippling is a type of failure that occurs when the compressive stress in the column exceeds its crushing strength. This type of failure is most likely to occur when the column is very short and the load is applied in an eccentric manner.

It is important to understand the modes of failure in eccentric compression in order to design columns that can withstand such loads and prevent failure. This information is used to determine the size, shape, and reinforcement of the column, as well as the type and amount of lateral reinforcement that is required.

Minimum eccentricity:

Every column must be designed for minimum eccentricity to account for constructional defects and material imperfection:

emin= maximum { Unsupported/500 + b or D/30, 20 mm

**Describe the salient features of PM Interaction Curve**

The P-M interaction diagram/curve is used to design reinforced concrete members in which axial force and bending moment act simultaneously. The reason the P-M curve is needed for designing members in which axial force and bending moment act simultaneously are because the equilibrium equation “C=T” (C: Compression force, T: Tension force) of the** **internal couple does not hold due to the effect of the axial force. Therefore, the moment of the member to which the axial force acts should be calculated on the plastic centroid axis. In summary, a structural member supported only by bending moment and shear without axial force is called a beam, and a structural member with bending moment, shear, and axial force acting on it are called a column.

**2. What is a P-M Interaction Curve?**

The P-M interaction curve indicates the capacity for P and M that reinforced concrete can resist. There are many programs that can calculate the P-M required for design; midas Civil is one of those programs and provides a function to create a P-M curve. Please refer to the link below for an explanation of the function for creating a P-M curve in midas Civil.

**Recall the steps to design Eccentrically Loaded Columns.**

The design of Eccentrically Loaded Columns is a crucial aspect of reinforced concrete structure design. The following steps outline the procedure for designing Eccentrically Loaded Columns:

- Determine the loads acting on the column: The first step in designing an Eccentrically Loaded Column is to determine the loads that will be acting on the column. These loads could be axial, bending, and/or torsion loads.
- Determine the effective length of the column: The effective length of the column is the length of the column between two points of lateral support. It is the length of the column that is free to deform under the load and is used in determining the buckling load.
- Determine the slenderness ratio: The slenderness ratio is a measure of the slenderness of the column and is defined as the effective length of the column divided by the least radius of gyration. The slenderness ratio is used in determining the critical buckling load.
- Determine the moment of inertia: The moment of inertia of the column cross-section is required for determining the buckling load and for determining the location of the neutral axis.
- Determine the stress distribution in the column: The stress distribution in the column must be determined for both the compression and tension regions. This information is used to determine the maximum and minimum reinforcement required in the column.
- Determine the reinforcement requirements: The minimum and maximum reinforcement required in the column must be determined. The minimum reinforcement is the reinforcement required to prevent the development of cracks in the column. The maximum reinforcement is the reinforcement required to prevent failure of the column under the applied loads.
- Design the column: Based on the information obtained in the previous steps, the final design of the column can be performed. This will include determining the size, shape, and reinforcement of the column.

These steps provide a basic outline of the procedure for designing Eccentrically Loaded Columns. It is important to note that the actual design procedure may vary depending on the specific design codes and standards used. The Indian Standard IS:456-2000 provides guidelines for the design of Eccentrically Loaded Columns.

Minimum eccentricity:

Every column must be designed for minimum eccentricity to account for constructional defects and material imperfection:

emin= maximum { Unsupported/500 + b or D/30, 20 mm)