prokon - circular column

SheetJob Number

Job Title

Client

Calcs by Checked by Date

Software Consultants (Pty) LtdInternet: http://www.prokon.comE-Mail : [email protected]

C12Example: Braced slender column with bi-axial momentCircular column design by PROKON. (CirCol Ver W2.5.06 - 01 Sep 2011)

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+LL 20 10 10 0 0

General design parameters and loads:

(mm)

d' (mm)

Lo (m)

fcu (MPa)

fy (MPa)

300416

25460

0 100

200

300

300

200

100

0

X X

Y

Y

General design parameters:Given: d = 300 mm d' = 41 mm Lo = 6.000 m fcu = 25 MPa fy = 460 MPa

Therefore:

=Acp d2

4

.

=p 300 2

4

= 70.69103 mm

=diax' dia d' - = 300 41 -

= 259.000 mm

=diay' dia d' - = 300 41 -

= 259.000 mm

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 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.

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 3 (pinned). The column is braced.\ x = 0.95 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 3 (pinned). The column is braced.\ y = 0.95 Table 3.21

Effective column height:

=lex x Lo.

= .95 6

= 5.700 m

=ley y Lo.

= .95 6

= 5.700 m

Column slenderness about both axes:

=lxlexdia

=5.7.3

= 19.000

=lyleydia

=5.7.3

= 19.000

SheetJob Number

Job Title

Client



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:

=emin 0.05 d.

= 0.05 .3

= 0.0150 m

=Mmin emin N.

= .015 20

= 0.3000 kNm

Check if the column is slender: 3.8.1.3

lx = 19.0 > 15

ly = 19.0 > 15

\ The column is slender.

Check slenderness limit: 3.8.1.7

Lo = 6.000 m < 60 dia' = 18.000 m

\ Slenderness limit not exceeded.

Initial moments:The initial end moments about the X-X axis: M1 = Smaller initial end moment = 0.0 kNm M2 = Larger initial end moment = 10.0 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 10 - +

= 6.000 kNm

=Mi2 0.4 M2.

= 0.4 10

= 4.000 kNm

\ Mi 0.4M2 = 6.0 kNm

SheetJob Number

Job Title

Client



The initial end moments about the Y-Y axis: M1 = Smaller initial end moment = 0.0 kNm M2 = Larger initial end moment = 10.0 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 10 - +

= 6.000 kNm

=Mi2 0.4 M2.

= 0.4 10

= 4.000 kNm

\ Mi 0.4M2 = 6.0 kNm

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

=Nuz 0.4444 fcu Ac 0.95 fy Asc. . . . + = 0.4444 25000 .07069 0.95 460000 .0003 +

= 916.466 kN

Maximum allowable stress and strain:

Allowable compression stress in steel

=fsc 0.95 fy.

= 0.95 460

= 437.000 MPa

Allowable tensile stress in steel

=fst 0.95 fy.

= 0.95 460

= 437.000 MPa

Allowable tensile strain in steel

=eyfstEs

=438.1

200000

= 0.0022

SheetJob Number

Job Title

Client



Allowable compressive strain in concrete

ec = 0.0035

For bending about the X-X axis:Balanced neutral axis depth

=xbaldia dcx

1ey

cstrain

-

+

=.3 .041

1.00219.0035

-

+

= 0.1593 mm

Nbal calculated from basic principles using x = xbal = 368.3 kN

=KNuz N

Nuz Nbal -

-

=756.77 20

756.77 368.34 -

-

= 1.897

=a1

2000lexdia

2.

=1

20005.7.3

2

= 0.1805

Therefore:

=Madd N a K dia. . .

= 20 .1805 1 .3

= 1.083

For bending about the Y-Y axis:Balanced neutral axis depth

SheetJob Number

Job Title

Client



=xbaldia dc

1ey

cstrain

-

+

=.3 .041

1.00219.0035

-

+

= 0.1593 mm

Nbal calculated from basic principles using x = xbal = 368.3 kN

=KNuz N

Nuz Nbal -

-

=756.77 20

756.77 368.34 -

-

= 1.897

=a1

2000leydia

2.

=1

20005.7.3

2

= 0.1805

Therefore:

=Madd N a K dia. . .

= 20 .1805 1 .3

= 1.083

Design ultimate load and moment:Design axial load: Pu = 20.0 kN

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

M2 = 10.0 kNm

(b) 3.8.3.2

=M Mi Madd + = 6 1.083 +

= 7.083 kNm

(c) 3.8.3.2

SheetJob Number

Job Title

Client



=M M1Madd

2 +

= 01.083

2 +

= 0.5415 kNm

(d) 3.8.3.2

=M emin N.

= .015 20

= 0.3000 kNm

Thus 3.8.3.2

M = 10.0 kNm

Moment distribution along the height of the column for bending about the X-X: At the top, Mx = 10.0 kNm Near mid-height, Mx = 7.1 kNm At the bottom, Mx = 0.0 kNm

Madd/2=0.5 kNm

Mxa

dd/2

=1.1

kN

m

Mxtop=10.0 kNm

Moments about X-X axis( kNm)

Initial Additional Design

Mx=10.0 kNmMxmin=0.3 kNm

+ =

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

M2 = 10.0 kNm

(b) 3.8.3.2

=M Mi Madd + = 6 1.083 +

= 7.083 kNm

(c) 3.8.3.2

SheetJob Number

Job Title

Client



=M M1Madd

2 +

= 01.083

2 +

= 0.5415 kNm

(d) 3.8.3.2

=M emin N.

= .015 20

= 0.3000 kNm

Thus 3.8.3.2

M = 10.0 kNm

Moment distribution along the height of the column for bending about the Y-Y: At the top, My = 10.0 kNm Near mid-height, My = 7.1 kNm At the bottom, My = 0.3 kNm

Madd/2=0.5 kNm

Mya

dd/2

=1.1

kN

m

Mytop=10.0 kNm

Moments about Y-Y axis( kNm)

Initial Additional Design

My=10.0 kNmMymin=0.3 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 therefore added vectoriallyto obtain the final design moment:

=M' Mx2 My2 +

= 10 2 102 +

= 14.142

SheetJob Number

Job Title

Client



Design axial load: Pu = 20.0

For bending about the design axis:

Column design chart

Mom

ent m

ax =

141

.5kN

m @

315

kN

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

200 400 600 800

100012001400160018002000220024002600

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 Loa

d (k

N)

Bending Moment (kNm)

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

From the design chart, Asc = 299 = 0.42%

Column design chart

Mom

ent m

ax =

141

.5kN

m @

315

kN

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

200 400 600 800

100012001400160018002000220024002600

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 Loa

d (k

N)

Bending Moment (kNm)

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

Design chart for bending about any axis:

SheetJob Number

Job Title

Client



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 (mm)

1X-XY-Y 20.0

0.0 0.0

10.0 10.0

6.0 6.0

1.1 1.1

X-XTop

10.0 10.0 14.1

299 (0.42%)

prokon - circular column

Documents