Design of column

Design of Column

 
Column design
Column design

Working Stress Method<


Slenderness ratio (λ)
image039
If Î» > 12 then the column is long.

Load carrying capacity for short column
image040
where, AC = Area of concrete, image041
σSC Stress in compression steel
σCC Stress in concrete
Ag Total gross cross-sectional area
ASC Area of compression steel

Load carrying capacity for long column
image046
where,
Cr = Reduction factor
image047
where, leff = Effective length of column
B = Least lateral dimension
imin = Least radius of gyration and image048
where, l = Moment of inertia and A = Cross-sectional area

Effective length of column
Effective length of Compression Members
image049
image050
image051


Column with helical reinforcement
Strength of the column is increased by 5%
image052 for short column
image053 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 Amax = 6% of the gross area of column
(ii) When bars are lapped Amax = 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)
image054
where image055 dia of main logitudnal bar
φ = dia of bar for transverse reinforcement
Pitch (p)
image057
where, φmin = minimum dia of main longitudinal bar

Helical reinforcement
(i) Diameters of helical reinforcement is selected such that
image058
(ii) Pitch of helical reinforcement: (p)
image059
where,
dC = Core diameter = dg – 2 × clear cover to helical reinforcement
AG = Gross area image060
dg = Gross diameter
Vh = Volume of helical reinforcement in unit length of column
φh = Diameter of steel bar forming the helix
image062
image063
dh = centre to centre dia of helix
= dg – 2 clear cover - φh
φh = diameter of the steel bar forming the helix
image064
Some others IS recommendations

(a) Slenderness limit

  1.  Unsupported length between end restrains image065 60 times least lateral dimension.
  2. If in any given plane one end of column is unrestrained than its unsupported lengthAll column should be designed for a minimum eccentricity of
image067

Limit state method


  1. Slenderness ratio (λ)
    if image068
    λ<12 Short column
  1. Eccentricity
    image070
    If image071 then it is a short axially loaded column.
    where, Pu = axial load on the column
  2. Short axially loaded column with helical reinforcement
    image072
  3. Some others IS code Recommendations
    image073
(a) Slenderness limit
(i) Unsupported length between end restrains image065 60 times least lateral dimension.
(ii) If in any given plane one end of column is unrestrained than its unsupported length image065 image074
(b) All column should be designed for a minimum eccentricity of
image075
Concentrically Loaded Columns
Where e = 0, i.e., the column is truly axially loaded.
image076
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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