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 column

B = Least lateral dimension

i_min = Least radius of gyration and 

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

Effective length of column

Effective length of Compression Members

Column with helical reinforcement

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 column

(b) Maximum area of steel

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

(ii) When bars are lapped A_max = 4% of the gross area of 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 lest lateral dimension.

Transverse reinforcement (Ties)

where  dia of main logitudnal bar

φ = dia of bar for transverse reinforcement

Pitch (p)

where, φ_min = minimum dia of main longitudinal bar

Helical reinforcement

(i) Diameters of helical reinforcement is 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 

d_g = Gross diameter

V_h = Volume of helical reinforcement in unit length of column

φ_h = Diameter of steel bar forming the helix

d_h = centre to centre dia of helix

= d_g – 2 clear cover - φ_h

φ_h = diameter of the steel bar forming the helix

Some others 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 column is unrestrained than its unsupported length 

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

Limit state method

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

1. Eccentricity
   
   If  then it is a short axially loaded column.
   where, P_u = axial load on the column
2. Short axially loaded column with helical reinforcement
   
3. Some others 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 column is unrestrained than its unsupported length  

(b) All column 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 member subjected to combined axial load and bi- axial bending and also used when e > 0.05 D.

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