Design of Columns using Working Stress and Limit State Methods

Design of columns necessitates the calculation of loads from the entire structure that are going to be  transferred to the footing or to the soil surface. It stands as a critical component in ensuring the structural integrity and stability of buildings, bridges, and other infrastructure. As the backbone of any construction project, columns play a pivotal role in supporting the overall load-bearing capacity of the structure.

The load from the floors  or the slabs are transferred to beams and then from beam to slab and from there to column, where the column transfers it to the foundation. Therefore if we design a  column section carefully designed then the entire structure will be stable. 

Design of the columns may be carried out using different methods which also includes limit state design and working stress method. It depends on several factors such as type of material used, type of construction, type of column, slenderness ratio etc.

In this article we are going to discuss in detail the fundamental steps involved in the design of columns using the IS CODES.

Design Of column is nothing but the  designing of the dimensions of the columns that includes its shape, size, length , width and depth of the cross-section,number of  reinforcement bars , and their diameter .

 A very important and essential factor of column design is Euler’s theory of columns, which will be discussed in next articles.

Material for column design

Columns are the structural members that take the compressive loads whether acting axially or eccentrically   from the superstructure to the footing. They act as a medium of transport between the superstructure and the basement. 

 The material used for the construction of the column depends on the design load from the structure and some structural requirements.

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Columns can be constructed with steel structures, timbers, concrete materials, etc. The selection of these materials is mainly based on their strength characteristics. For example, steel columns are preferred for high-strength and lightweight structures and timber columns are generally preferred for temporary structures.

Most commonly used material for construction of any buildings especially in India is Reinforced cement concrete. The design code usually followed is IS456-2000.

Design procedure

The following are the fundamental  steps  essential to ensure that the columns are safe, efficient, and aesthetically pleasing. They also help to optimise the use of materials and resources in the construction process.

Design consideration of column encompasses a multitude of factors, including the material properties, cross-sectional dimensions, and the specific load-bearing requirements of the project. Careful attention to these considerations is paramount in ensuring the column’s structural integrity and longevity.

Determine of effective length 

unsupported length in design of columns as per IS 456 is a crucial parameter that determines the column’s stability and load-bearing capacity. Understanding and adhering to the code’s guidelines on this aspect is essential for civil engineers to design columns that can stand the test of time.

The effective length of the column is determined taking into consideration sway and no sway conditions. For sway conditions it may be taken as 1.2L to 2L depending on end conditions and for non-sway conditions it may be 0.6L to L  where L is the length of the column. 

Column type

Using the effective length , slenderness ratio is calculated from which type of the column i.e short or long type is determined.

Categorization of columns 

The columns are categories based on the type of the material used such as  concrete, steel, wood, or masonry, and the loading condition i.e uniaxial or Bi axial eccentric loading .

Different column types are suitable for different applications. For example, steel or reinforced concrete columns are commonly used in high-rise buildings, while timber columns are often used in residential construction.

Computations of loads and moments 

The  axial load acting on the column from the beams and slabs are to be calculated and the bending moment on the column due to the applied forces and moments from the beams, slabs, walls, and other elements are to be calculated.

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Determine the footing size: 

The footing is the part of the column that rests on the foundation. The size of the footing depends on the load and the soil conditions. In general, a larger footing is required for a larger load or weaker soil.

Determination of column dimensions

The dimensions of the column are determined by the load it must bear  the architectural and functional requirements of the building and the material it is made of. We can use structural engineering software or tables to calculate the dimensions.

Reinforcement details

Reinforcement details such as number of the bars , diameter of the bar rebars used etc of  the column are determined  based on the strength, ductility, durability, and cost criteria.

Verify the design

Check the stability and buckling resistance of the column under different load combinations and slenderness ratios.

Verify the serviceability and performance of the column under different environmental conditions and loading scenarios.

Design of column by working stress method

Previously the working stress method was used in design of columns, but  this method  has certain limitations like it assumes a lesser amount of stress value at failure; hence it gives an uneconomical design.  So this was later replaced by the limit state method .Here are a few points of column designing by working stress method explained.

Load carrying capacity 

P = C_r(σ_scA_sc + σ_ccA_cc) long column

P = σ_scA_sc + σ_ccA_cc

Where

• A_C = Area of concrete, A_C = A_g – A_sc
• σ_SC ⇒ Stress in compression steel
• σ_CC ⇒ Stress in concrete
• A_g ⇒ Total gross cross-sectional area
• A_SC ⇒ Area of compression steel

• C_r = Reduction factor
• C_r = 1.25 – (l_eff/48B)
• l_eff = Effective length of the column
• B = Least lateral dimension

A column with helical reinforcement

In the case of helical reinforcement, the column strength is increased by 5%

P = 1.05(σ_scA_sc + σ_ccA_cc) for short column

P = 1.05 C_r(σ_scA_sc + σ_ccA_cc) for long column

Longitudinal reinforcement

(a) Minimum area of steel = 0.8% of the gross area of the column

(b) Maximum area of steel

(i) When bars are not lapped A_max = 6% of the gross area of the column

(ii) When bars are lapped A_max = 4% of the gross area of the column

Minimum number of bars for reinforcement

For rectangular column 4

For circular column 6

Minimum diameter of bar ⇒ 12 mm

Maximum distance between longitudinal bar ⇒ 300 mm

Pedestal

It is a short length whose effective length is not more than 3 times of least lateral dimension.

Transverse reinforcement (Ties)

φ = max {¼ φ_min and 6 mm}

where Φ_min = Minimum dia of the main longitudinal bar

φ = dia of the bar for transverse reinforcement

Pitch (p)

φ = min {Least lateral dimension, 16 φ_min and 300 mm}

where φ_min = minimum dia of the main longitudinal bar

Helical reinforcement

(i) Diameters of helical reinforcement are selected such that

(ii) Pitch of helical reinforcement (p)

(a) p ≤ 75 mm

(b) p ≤ (1/6)^th d_c

(c) p ≥ 3 φ_h

(d) p ≥ 25 mm

where,

• d_c = Core diameter = d_g – 2 × clear cover to helical reinforcement
• A_G = Gross area = Π(d_g)²/4
• d_g = Gross diameter
• V_h = Volume of helical reinforcement in a unit length of the column
• φ_h = Diameter of steel bar forming the helix
• d_h = centre to centre dia of the helix ⇒ d_g – 2 clear cover – φ_h
• φ_h = diameter of the steel bar forming the helix

Some other IS recommendations

(a) Slenderness limit

(i) Unsupported length between end restrains < 60 times least lateral dimension.

(ii) If in any given plane, one end of the column is unrestrained, then its unsupported length <100 B²/D

(b) All columns should be designed for a minimum eccentricity

Design of Column by Limit State Method

The design of columns by limit state method is carried out based on the IS 456. This design uses the material’s ultimate strength at its failure point; hence, it gives an economical design to the structure. 

The ultimate load on columns is calculated based on the following expression.

P_u = 0.4f_ckA_c + 0.67f_yA_sc

For the column having helical reinforcement, the strength of the column is increased by 5%. Hence it will be ⇒ P_u = 1.05(0.4f_ckA_c + 0.67f_yA_sc)

IS 456 Recommendations

(a) Slenderness limit

(i) Unsupported length between end restrains <60 times least lateral dimension.

(ii) If in any given plane, one end of the column is unrestrained, then its unsupported length <100 B²/D

(b) All columns should be designed for a minimum eccentricity of

Concentrically Loaded Columns

Where e = 0, i.e., the column is truly axially loaded.

P_u = 0.45f_ckA_c + 0.75f_yA_sc

This formula is used for members subjected to combined axial load and bi-axial bending when e > 0.05 D.

In the next article we will discuss the design of the RCC column with a numerical example.

FAQ – design of Columns