Unbraced Slender Column to BS 8110

Basic Structural Element Designs to BS 8110-1:1997

3.2

Unbraced Slender Column

Y-Y axis

X-X Axis

X-X axis

Y-Y Axis

Figure 3.4 : General arrangement


Reference

Calculations

Output

The Column size is 300x500 Consider a Column Segment from Ground to First Floor Level. Determination of Short or Slender Column Bending about X-X Axis

Dimension of column about XX axis Bending h = 500mm Depth of the Beam along Y direction is 675mm. Cl.3.8.1.6.2

Hence Top Condition is 1.

BS 8110-1:1997

Ground Beam Depth is 900mm. Hence Bottom Condition -1

Table 3.2

Hence β = 1.2

BS 8110-1:1997

L ex = βLox = 1.2 × (4000 − 675) = 3990mm (Floor to Floor Height is 4000mm) L ex

=

h

3990 500

= 7.98 < 10

Hence Column is Short for X-X axis Bending.

Bending about Y-Y Axis

Dimension of column about YY axis Bending b = 300mm Depth of the Beam along X direction is 600mm. Cl.3.8.1.6.2

Hence Top Condition is 1.

BS 8110-1:1997

Ground Beam Depth is 900mm. Hence Bottom Condition -1

Table 3.2

Hence β

BS 8110-1:1997

L ey = βLoy = 1.2 × (4000 − 600) = 4080mm L ey

=

b

=

1.2

4080 300

= 13.6 > 10

Hence Column is Slender for YY axis Bending.

Edifice Consultants (Pvt) Ltd

Slender Column


Reference

Calculations

Output

Design Loads from SAP 2000 Model

Column Loads are Extracted from SAP 2000 Modal.

N

=

2767kN

Mxx = 153.8kNm Myy

=

3.42kNm

Cl.3.8.3.1

Additional Moments

BS 8110-1:1997

Since Column is Slender about Y-Y axis only, the additional moment is also about the Y-Y axis only.

Equation 34 BS 8110-1:1997

 ley  βa =   2000  b′  1

1

βa =

2000

2

[13.6]2 = 0.09248

Assume 8 Nos of T25 bars are provided for the Column. Hence A

sc

= 3928mm2

N uz = 0.45f cuA c + 0.95f y A sc N uz = 0.45 × 30 × 300 × 500 + 0.95 × 460 × 3928 = 3741.54kN d = 500 − 30 − 10 − N Equation 33 BS 8110-1:1997

Equation 32 BS 8110-1:1997

Equation 35 BS 8110-1:1997

bal

K=

25 2

= 447.5mm

= 0.25f bd = 0.25 × 30 × 300 × 447.5 = 1006.88kN cu

Nuz − N 3741.54 − 2767 = = 0.36 Nuz − N 3741.54 − 1006.88 bal

a = βKH = 0.09248 × 0.36 × 0.3 = 9.98784 × 10 u

= Na = 2767 × 9.98784 × 10 M add, y u


−3

− 3 = 27.63kNm


Reference

Calculations

Cl.3.8.2.4

Minimum Moments

BS 8110-1:1997

exx = 0.05 × 500 = 25mm > 20mm M = 2767 × 0.020 = 55.34kNm < 153.8kNm xx,min e yy = 0.05 × 300 = 15mm < 20mm M = 2767 × 0.015 = 41.51kNm < 27.63kNm yy, min

Hence Design Moments

M = 153.8kNm xx M

Cl.3.8.4.5 BS 8110-1:1997

YY

= 41.51kNm

Biaxial Bending

b' = 300 − 30 − 10 −

h' = 500 − 30 − 10 −

25 2 25 2

= 247.5mm = 447.5mm

β = 0.3

M xx = 153.8 = 0.34 h′ 447.5 M yy b′

=

41.51 247.5

= 0.17

M M xx > YY h′ b′ Hence Column is Bending about XX axis. M′x = M + β x


h′

447.5 × 41.51 = 176.32kNm M = 153.8 + 0.3 × b′ y 247.5

Output


Reference

Column Design

Calculations Design of Main Reinforcement

Charts by IstructE d

447.5

=

h

≈ 0.90

500 N

=

bhf cu M

ρ=

3

300 × 500 × 30

=

2 bh f cu Hence

2767 × 10

176.32 × 10

= 0.61

3

2 300 × 500 × 30

ρf y

=

f cu

= 0.08

0.4

0.4 × 30 460

A

sc bh

=

A

sc bh

=

A

sc 2

=

0.4 × 30 460 0.4 × 30 460

×

2 300 × 500 = 3913mm

2 1956mm

Provided Reinforcement per Face is 4T25. A

sc,provided

=

2 1964mm

Hence provided Reinforcement is Satisfactory.

Table 3.25

Checks for Minimum Area of Reinforcement

BS 8110-1:1997

100A sc bh A sc =

= 0.4

0.4 × 300 × 500 100

= 600mm2

Hence provided reinforcement satisfied the minimum reinforcement requirement.


Output


Reference

Calculations Checks for Maximum Area of Reinforcement

Cl.3.12.6.1 BS 8110-

100Asc bh

=

6

1:1997 A sc =

6 × 300 × 500 100

= 9000mm2 > 3928mm2

Hence Maximum Area of Reinforcement is Ok. At Laps At a Lap 4T25 bars are lapped. 2 A sc = 12 × 491 = 5892mm A sc =

5892 300 × 500

× 100 = 3.93 < 10%

Cl.3.12.7.1

Design of Links

BS 8110-

Largest Compression bar

1:1997

Hence Diameter of the shear link should be larger than 25/4=6mm.

=25mm

Hence T10 Links were provided. Shear Link spacing should be less than 12 times smallest compression bar. (12x25=300mm) But link details required to mitigate seismic effects are stringent than this. Hence shear link details were provided to mitigate the seismic effects.

Design of Links to mitigate Seismic Effects

Detailing of the shear links were done as per “Reinforcement Detailing to mitigate seismic effects “ published by Society of Structural Engineers, Sri Lanka. Column confinement zone depth ( Adjacent to Beams) is greater of (a) 500mm (b)

lo

6

=

3400/6 ≈ 600mm

(c) Maximum dimension of column (500mm)


Output


Reference

Calculations

Hence Depth of the confinement zone is taken as 600mm. In confinement zones and at laps spacing of links/ cross ties shall be greater of (a) 100mm (b)

Minimum Column Dimension 3 300 3

but greater than 50mm

= 100mm > 50mm

Diameter of the links/ cross ties should be greater than 8mm. Hence T10 links at 100mm spacing provided throughout since column bears are lapped at two location between a given floor height.


Output

Unbraced Slender Column to BS 8110

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