Design of Column

Design of Column

Working Stress Method(Not in the GATE Syllabus)

Slenderness ratio (λ)

If λ > 12, then the column is long.

Load carrying capacity for short column

where A_C = Area of concrete, 

σ_SC Stress in compression steel

σ_CC Stress in concrete

A_g Total gross cross-sectional area

A_SC Area of compression steel

Load carrying capacity for long column

where,

C_r = Reduction factor

where l_eff = Effective length of the column

B = Least lateral dimension

i_min = Least radius of gyration and 

where, l = Moment of inertia and A = Cross-sectional area

The effective length of a column

The effective length of Compression Members

A column with helical reinforcement

The strength of the column is increased by 5%

 for short column

 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)

where Φ_min = dia of the main longitudinal bar

φ = dia of the bar for transverse reinforcement

Pitch (p)

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)

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 of

Limit state method

1. Slenderness ratio (λ)
   if 
   λ<12 Short column

1. Eccentricity
   
   If e_min≤0.05 D, it is a short axially loaded column.
   where P_u = axial load on the column
2. A short axially loaded column with helical reinforcement
   
3. Some other IS code 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.

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

For more information about the design of column, you can refer to the following video on the Byju Exam Prep's official youtube channel.

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