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Calcs by Checked by Date

Software Consultants (Pty) Ltd

Internet: http://www.prokon.com

E-Mail : [email protected]

C11Rectangular column design

0 1 0 0

2 0 0

300

200

100

0

X X

Y

Y

Rectangular column design by PROKON . (RecCol Ver W2.6.00 - 05 Dec 2012)

Design code : BS8110 - 1997

General design parameters:Given: h = 300 mm b = 200 mm d’x = 20 mm d’y = 20 mm Lo = 5.700 m fcu = 25 MPa fy = 450 MPa

Column design chart (X-X)

M o m e n t m a x = 2 0 8 . 1 k N m @ 3 3 0 k N

-1400

-1200

-1000

-800

-600

-400

-200

200

400

600

800

1000

1200

1400

1600

1800

2000

1 0 . 0

2 0 . 0

3 0 . 0

4 0 . 0

5 0 . 0

6 0 . 0

7 0 . 0

8 0 . 0

9 0 . 0

1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 2 1 0 2 2 0

A x i a l l o a d ( k N )

Bending moment (kNm)

6%5%4%3%2%1%0%

Design chart for bending about the X-X axis:

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Column design chart (Y-Y)

M o m e n t m a x = 1 2 9 . 4 k N m @ 3 3 0 k N

-1400

-1200-1000

-800

-600

-400

-200

200

400

600

800

1000

1200

1400

1600

1800

2000

1 0 . 0

2 0 . 0

3 0 . 0

4 0 . 0

5 0 . 0

6 0 . 0

7 0 . 0

8 0 . 0

9 0 . 0

1 0 0 1 1 0 1 2 0 1 3 0 1 4 0



6%5%4%3%2%1%0%

Design chart for bending about the Y-Y axis:

Therefore:

= Ac b h.

= .2 .3×

= 0.0600 m²

=h’ h d’ x-

= .3 .02-

= 0.2800 m

=b’ b d’ y-

= .2 .02-

= 0.1800 m

Assumptions: (1) The general conditions of clause 3.8.1 are applicable. (2) The section is symmetrically reinforced. (3) The specified design axial loads include the self-weight of the column. (4) The design axial loads are taken constant over the height of the column.

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Design approach:The column is designed using an iterative procedure: (1) The column design charts are constructed. (2) An area steel is chosen. (3) The corresponding slenderness moments are calculated.

(4) The design axis and design ultimate moment is determined . (5) The steel required for the design axial force and moment is read from the relevant design chart. (6) The procedure is repeated until the convergence of the area steel about the design axis. (7) The area steel perpendicular to the design axis is read from the relevant design chart. (8) The procedure is repeated for each load case. (9) The critical load case is identified as the case yielding the largest steel area about the design axis.

Through inspection: Load case 1 is critical.

Check column slenderness:End fixity and bracing for bending about the X-X axis: At the top end: Condition 1 (fully fixed). At the bottom end: Condition 2 (partially fixed). The column is unbraced.∴ ßx = 1.30 Table 3.22

End fixity and bracing for bending about the Y-Y axis: At the top end: Condition 1 (fully fixed). At the bottom end: Condition 2 (partially fixed). The column is unbraced.∴ ßy = 1.30 Table 3.22

Effective column height:

=l ex ß x Lo.

= 1.3 5.7×

= 7.410 m

=l ey ß y Lo.

= 1.3 5.7×

= 7.410 m

Column slenderness about both axes:

= xl ex

h

=7.41

.3

= 24.700

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= yl ey

b

=7.41

.2 = 37.050

Minimum Moments for Design:Check for mininum eccentricity: 3.8.2.4 For bi-axial bending, it is only necessary to ensure that the eccentricity exceeds the minimum about one axis at a time.

For the worst effect, apply the minimum eccentricity about the minor axis:

=eminx 0.05 h.

= 0.05 .3×

= 0.0150 m

=eminy 0.05 b.

= 0.05 .2×

= 0.0100 m

=min emin N .

= .01 4.63×

= 0.0463 kNm

Check if the column is slender: 3.8.1.3

λx = 24.7 > 10

λy = 37.0 > 10

∴ The column is slender.

Check slenderness limit: 3.8.1.7

Lo = 5.700 m < 60× b’ = 12.000 m

∴ Slenderness limit not exceeded.

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Initial moments:The initial end moments about the X-X axis: M1 = Smaller initial end moment = 0.0 kNm M2 = Larger initial end moment = 0.2 kNm

The initial moment near mid-height of the column : 3.8.3.7

=i 0.4 M 1 0.6 M 2. .- +

= 0.4 0 0.6 .2× ×- +

= 0.1200 kNm

=i2 0.4 M 2.

= 0.4 .2×

= 0.0800 kNm

∴ Mi 0.4M2 = 0.1 kNm

The initial end moments about the Y-Y axis: M1 = Smaller initial end moment = 0.0 kNm M2 = Larger initial end moment = 0.3 kNm

The initial moment near mid-height of the column : 3.8.3.7

=i 0.4 M 1 0.6 M 2. .- +

= 0.4 0 0.6 .3× ×- +

= 0.1800 kNm

=i2 0.4 M 2.

= 0.4 .3×

= 0.1200 kNm

∴ Mi 0.4M2 = 0.2 kNm

Deflection induced moments: 3.8.3.1Design ultimate capacity of section under axial load only:

=uz 0.4444 f cu Ac1

1.15 f y A sc. . . . +

= 0.4444 25000 .061

1.15450000 .00024× × × ×+

= 760.513 kN

Maximum allowable stress and strain:

Allowable compression stress in steel

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= sc1

1.15 f y.

=1

1.15

450×

= 391.304 MPa

Allowable tensile stress in steel

= st 1

1.15 f y.

=1

1.15450×

= 391.304 MPa

Allowable tensile strain in steel

=e y f st

E s

=391.3

200000

= 0.0020

Allowable compressive strain in concrete

ec = 0.0035

For bending about the X-X axis:

Balanced neutral axis depth

= xbal h d cx

1e y

c strain

-

+

=.3 .02

1.00196

.0035

-

+

= 0.1795 mm

=bal 0.4444 ß b f cu xbal At

2 f sd f s-( ). . . . . +

= 0.4444 .9 .2 25000 .1796.00024

2391304 391304-( )× × × × ×+

= 359.164 kN

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= K N uz N

N uz N bal

-

-

=762.35 4.63

762.35 359.2

-

-

= 1.879

=a1

2000

l ex

h

2.

=1

2000

7.41

.3

2

×

= 0.3050

Therefore:

=add N ßa K h. . .

= 4.63 .30505 1 .3× × ×

= 0.4237

For bending about the Y-Y axis:

Balanced neutral axis depth

= xbal b d cy

1e y

c strain

-

+

=.2 .02

1.00196

.0035

-

+

= 0.1154 mm

=bal 0.4444 ß h f cu xbal At

2 f sd f s-( ). . . . . +

= 0.4444 .9 .3 25000 .11546.00024

2391304 391304-( )× × × × ×+

= 346.345 kN

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= K N uz N

N uz N bal

-

-

=762.35 4.63

762.35 346.37

-

- = 1.822

=a1

2000

l ey

b

2.

=1

2000

7.41

.2

2

×

= 0.6864

Therefore:

=add N ßa K b. . .

= 4.63 .68635 1 .2× × ×

= 0.6356

Design ultimate load and moment:Design axial load: Pu = 4.6 kN

For bending about the X-X axis, the maximum design moment is the greatest of: 3.8.3.7 (a) 3.8.3.2

= M 2 M add +

= .2 .42371+

= 0.6237 kNm

(d) 3.8.3.2

= emin N . = .015 4.63×

= 0.0694 kNm

Thus 3.8.3.2

M = 0.6 kNm

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Moment distribution along the height of the column for bending about the X-X: At the top, Mx = 0.6 kNm Near mid-height, Mx = 0.1 kNm At the bottom, Mx = 0.0 kNm

Mxadd=0.4 kNm

Mxadd=0.4 kNm

Mxtop=0.2 kNm

Mxbot=0.0 kNm

Moments about X-X axis( kNm)

Initial Additional Design

Mx=0.6 kNm

Mxmin=0.1 kNm

+ =

For bending about the Y-Y axis, the maximum design moment is the greatest of: 3.8.3.7 (a) 3.8.3.2

= M 2 M add +

= .3 .63556+

= 0.9356 kNm

(d) 3.8.3.2

= emin N

.

= .01 4.63×

= 0.0463 kNm

Thus 3.8.3.2

M = 0.9 kNm

Moment distribution along the height of the column for bending about the Y-Y: At the top, My = 0.9 kNm Near mid-height, My = 0.2 kNm

At the bottom, My = 0.0 kNm

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Myadd=0.6 kNm

Myadd=0.6 kNm

Mytop=0.3 kNm

Mybot=0.0 kNm

Moments about Y-Y axis( kNm)

Initial Additional Design

My=0.9 kNm

Mymin=0.0 kNm

+ =

Design of column section for ULS:Through inspection:

The critical section lies at the top end of the column.

The column is bi-axially bent. The moments are added vectoriallyto obtain the design moment: Mx/h’ = 2.2 < My/b’ = 5.2

The effective uniaxial design moment about the Y-Y axis:

= 1

7

6 N

b h f cu. .

.

-

= 1

7

6

4630

.2 .3 2500×104

× ×

×

-

= 0.9964

=’ y M y ß b d cy

h d cx M x

-( )

-

.. +

= .93556.9964 .2 .02

.3 .02.62371

-( )

-

××+

= 1.335 kNm

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For bending about the design axis:


M o m e n t m a x = 1 2 9 . 4 k N m @ 3 3 0 k N

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-400

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200

400

600

800

1000

1200

1400

1600

1800

2000

1 0 . 0

2 0 . 0

3 0 . 0

4 0 . 0

5 0 . 0

6 0 . 0

7 0 . 0

8 0 . 0

9 0 . 0

1 0 0 1 1 0 1 2 0 1 3 0 1 4 0



6%5%4%3%2%1%0%

Minimum reinforcement required for bending about the Y-Y axis only: From the design chart, Asc = 245 mm² = 0.41%

For bending about the design axis - use the Y-axis:


M o m e n t m a x = 1 2 9 . 4 k N m @ 3 3 0 k N

-1400

-1200

-1000

-800

-600

-400

-200

200

400

600

800

1000

1200

1400

1600

1800

2000

1 0 . 0

2 0 . 0

3 0 . 0

4 0 . 0

5 0 . 0

6 0 . 0

7 0 . 0

8 0 . 0

9 0 . 0

1 0 0 1 1 0 1 2 0 1 3 0 1 4 0



6%5%4%3%2%1%0%

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Summary of design calculations:

Design results for all load cases:

Load case Axis N (kN) M1 (kNm) M2 (kNm) Mi (kNm) Madd (kNm) Design M (kNm) M’ (kNm) Asc (mm²)

DL

LL

DES

X-XY-Y 4.6

0.00.0

0.20.3

0.10.2

0.40.6

Y-YTop

0.60.9 1.3

245 (0.41%)245 (0.41%)

X-XY-Y 1.7

0.00.0

0.00.0

0.00.0

0.20.2

Y-YTop

0.20.2 0.3

245 (0.41%)245 (0.41%)

X-XY-Y 11.3

0.00.0

0.20.3

0.10.2

1.01.5

Y-YTop

1.21.9 2.6

245 (0.41%)245 (0.41%)

Load case 1 is critical.

Date post:	06-Jul-2018
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