column design

SheetJob Number

Job Title

Client

Calcs by Checked by Date

Software Consultants (Pty) Ltd

Internet: http://www.prokon.com

E-Mail : [email protected]

C11Example: Short column with bi-axial bending

Rectangular column design by PROKON. (RecCol Ver W2.5.17 - 26 Oct 2012)

Design code : BS8110 - 1997

Input tables

Loadcase Description

Ultimate Limit State Design Loads

P (kN) Mx top (kNm) My top (kNm) Mx bot (kNm) My bot (kNm)

1 DL 495 50 25

2 DL+LL 783 35 12

General design parameters and loads:

h (mm)

b (mm)

d'x (mm)

d'y (mm)

Lo (m)

fcu (MPa)

fy (MPa)

345

230

45

45

2.8

30

450

0 10

0

20

0

400

300

200

100

0

X X

Y

Y

General design parameters:Given: h = 345 mm b = 230 mm d'x = 45 mm d'y = 45 mm Lo = 2.800 m fcu = 30 MPa fy = 450 MPa

Column design chart (X-X)

Mom

ent

max =

283.2

kN

m @

524 k

N

-1800-1600-1400-1200-1000-800-600-400-200

200 400 600 800

10001200140016001800200022002400260028003000

20.0

40.0

60.0

80.0

100

120

140

160

180

200

220

240

260

280

300

Axia

l lo

ad (

kN

)

Bending moment (kNm)

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

Design chart for bending about the X-X axis:

SheetJob Number

Job Title

Client





Column design chart (Y-Y)

Mom

ent

max =

160.5

kN

m @

476 k

N

-1800-1600-1400-1200-1000-800-600-400-200

200 400 600 800

10001200140016001800200022002400260028003000

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100

110

120

130

140

150

160

170

Axia

l lo

ad (

kN

)


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

Design chart for bending about the Y-Y axis:

Therefore:

=Ac b h.

= .23 .345×

= 0.0793 m²

=h' h d'x -

= .345 .045 -

= 0.3000 m

=b' b d'y -

= .23 .045 -

= 0.1850 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.

SheetJob Number

Job Title

Client





Design approach:The column is designed using the following procedure: (1) The column design charts are constructed. (2) The design axis and design ultimate moment is determined . (3) The steel required for the design axial force and moment is read from the relevant design chart. (4) The area steel perpendicular to the design axis is read from the relevant design chart. (5) The procedure is repeated for each load case. (6) The critical load case is identified as the case yielding the largest steel area about the design axis.

Through inspection: Load case 1 (DL) is critical.

Check column slenderness:End fixity and bracing for bending about the X-X axis: At the top end: Condition 2 (partially fixed). At the bottom end: Condition 1 (fully fixed). The column is braced.∴ ßx = 0.80 Table 3.21

End fixity and bracing for bending about the Y-Y axis: At the top end: Condition 2 (partially fixed). At the bottom end: Condition 1 (fully fixed). The column is braced.∴ ßy = 0.80 Table 3.21

Effective column height:

=lex ßx Lo.

= .8 2.8×

= 2.240 m

=ley ßy Lo.

= .8 2.8×

= 2.240 m

Column slenderness about both axes:

=λxlex

h

=2.24

.345

= 6.493

SheetJob Number

Job Title

Client





=λyley

b

=2.24

.23

= 9.739

Minimum Moments for Design:Check for mininum eccentricity: 3.8.2.4

Check that the eccentricity exceeds the minimum in the plane of bending:

=eminx 0.05 h.

= 0.05 .345×

= 0.0172 m

=eminy 0.05 b.

= 0.05 .23×

= 0.0115 m

=Mmin emin N.

= .01725 495×

= 8.539 kNm

Check if the column is slender: 3.8.1.3

λx = 6.5 < 15

λy = 9.7 < 15

∴ The column is short.

Initial moments:The column is bent in double curvature about the X-X axis: M1 = Smaller initial end moment = 25.0 kNm M2 = Larger initial end moment = 50.0 kNm

The initial moment near mid-height of the column : 3.8.3.2

=Mi 0.4 M1 0.6 M2. .- +

= 0.4 25 0.6 50× ×- +

= 20.000 kNm

SheetJob Number

Job Title

Client





=Mi2 0.4 M2.

= 0.4 50×

= 20.000 kNm

∴ Mi ≥ 0.4M2 = 50.0 kNm

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

The initial moment near mid-height of the column : 3.8.3.2

=Mi 0.4 M1 0.6 M2. .- +

= 0.4 0 0.6 0× ×- +

= 0.0000×100

kNm

=Mi2 0.4 M2.

= 0.4 0×

= 0.0000×100

kNm

∴ Mi ≥ 0.4M2 = 0.0 kNm

Design ultimate load and moment:Design axial load: Pu = 495.0 kN

Moment distribution along the height of the column for bending about the X-X: At the top, Mx = 50.0 kNm Near mid-height, Mx = 20.0 kNm At the bottom, Mx = 25.0 kNm

Mxtop=50.0 kNm

Mxbot=25.0 kNm

Moments about X-X axis( kNm)

Initial Additional Design

Mx=50.0 kNm

Mxmin=8.5 kNm

+ =

SheetJob Number

Job Title

Client





Design of column section for ULS:Through inspection: The critical section lies at the top end of the column.

The column is designed to withstand the uni-axially applied moment aboutthe major axis.

For bending about the design axis:

Column design chart (X-X)

Mom

ent

max =

283.2

kN

m @

524 k

N-1800-1600-1400-1200-1000-800-600-400-200

200 400 600 800

10001200140016001800200022002400260028003000

20.0

40.0

60.0

80.0

100

120

140

160

180

200

220

240

260

280

300

Axia

l lo

ad (

kN

)


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

Reinforcement required about the X-X axis: From the design chart, Asc = 324 mm² = 0.41%

SheetJob Number

Job Title

Client





For bending perpendicular to the design axis:

Column design chart (Y-Y)

Mom

ent

max =

160.5

kN

m @

476 k

N

-1800-1600-1400-1200-1000-800-600-400-200

200 400 600 800

10001200140016001800200022002400260028003000

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100

110

120

130

140

150

160

170

Axia

l lo

ad (

kN

)


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

Reinforcement required about the Y-Y axis: From the design chart, Asc = 324 mm²

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)

1

2

X-XY-Y 495.0

25.0 0.0

50.0 0.0

50.0 0.0

0.0 0.0

X-XTop

50.0 0.0 50.0

324 (0.41%) 324 (0.41%)

X-XY-Y 783.0

12.0 0.0

35.0 0.0

35.0 0.0

0.0 0.0

X-XTop

35.0 0.0 35.0

324 (0.41%) 324 (0.41%)

Load case 1 (DL) is critical.

column design

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