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Slender Column Design1) Column Dimension & Forces

Column mark = External columnConcrete grade, fcu = 35 Nmm-

Steel grade for main bar, fy = 460 Nmm-

Steel grade for link, fyv = 250 Nmm-

Minimum nominal cover, c = 25 mm

Dimater of link, k = 10 mm

Dimater of main bar, m = 16 mm

Width, b = 300 mm

Height, h = 1000 mm

Ultimate axial load, N = 2492 kN

Ultimate bending moment about x-axis, Mux = 49.84 kNm

Ultimate bending moment about y-axis, Muy

= 37.38 kNm

Shear force in y-direction, Vx = 0 kN

Shear force in x-direction, Vy = 0 kN

2) Slenderness Check

Floor-to-floor height with respect x-axis, hox = 4300 mm

Floor-to-floor height with respect y-axis, hoy = 4300 mm

Beam depth in y-direction, dy = 1250 mm

Beam depth in x-direction, dx = 750 mm

Clear height in y-direction, lox = 3050 mm

Clear height in x-direction, Ioy = 3550 mm

End condition for bending about x-axis

x = 1.3

Effective height, lex = 3965

End condition for bending about y-axis

y = 1.3

Effective height, ley = 4615

lex/h = 3.97 short column

ley/b = 15.383 slender column

3) Determination of Cover

h' = h - cover - dia. of link - 1/2 dia. of bar

= 957 mm

b' = 257 mm

3) Design of Slender Column

Assume 100Asc/bh = 1.07 %

Ac= net concrete area = (1-Asc/bh)bh

= 0.9893 bh

xx

y

y

h

b

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= 296790 mm2

Nuz = Design ultimate capacity of a section subjected to axial load only

= 0.45fcuAc+ 0.87fyAsc= 5959.08 kN

Nbal = Design axial load capacity of a balanced section

= 0.25fcubh

= 2625 kN

Factor governing deflection of column due to slenderness, K

= (Nuz- N) / (Nuz- Nbal)

= 1.03989

Deflection in column due to slenderness producing additional moment about x-axis, ax

= (lex/h)2/2000 x Kh

= 8.17 mm (20mm)

= 20.00 mm

Deflection in column due to slenderness producing additional moment about y-axis, ay

= (ley/b)2/2000 x Kb

= 36.91 mm (20mm)

= 36.91 mm

Madd/x = NaxK

= 51.83 kNm

Madd/y = NayK

= 95.66 kNm

4) Biaxial Moment and Direct Load

Mx = Mux+ Madd/x

= 101.67 kNm

My = Muy+ Madd/y

= 133.04 kNm

Mx/h' = 101.67 / 0.957

= 106.24 kN

My/b' = 133.04 / 0.257= 517.67 kN

Mx/h' My/b'

If Mx/h' > My/b' Mx' = Mx+ (h'/b')My

If My/b' > Mx/h' My' = My+ (b'/h')Mx

N/bhfcu = 0.23733

From table, = 0.734

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Modified bending moment about x-axis to account for biaxial bending, Mx'

My' = My + (b'/h')Mx= 153.08 kNm

k = b'/b

= 0.86

e = My' / N

= 0.06143 m

e/b = 0.205

N/bh = 8.31 Nmm-2

For e/b = 0.35 ,

p = 0.4 & N/bh = 7.40

p = 1 & N/bh = 9.44

By linear interpolation, percentage of reinforcement required, p= 0.66667

Ascreq = 2000 mm

Number of main bar required

= 9.9 T 16

Provide 16 T 16

Ascprov = 3216.99 mm 100Asc/bh = 1.07%

> Ascreq OK