Column Checkhjdksahdkjasbcnxz mcbkewdfic,mnxzc,m nzxmnv iklds;akd;lask;ldksa lcm...

8/12/2019 Column Checkhjdksahdkjasbcnxz mcbkewdfic,mnxzc,m nzxmnv iklds;akd;lask;ldksa lcm zxlmcx.,zvhfuhvkcxhnvl

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Calcs by Checked by Date

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

C11Rectangular column design

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Rectangular column design by PROKON . (RecCol Ver W2.4.01 - 01 Apr 2008)

Design code : BS8110 - 1997

General design parameters:Given: h = 350 mm b = 350 mm d'x = 50 mm d'y = 50 mm Lo = 8.000 m fcu = 25 MPa fy = 460 MPa

Column design chart (X-X)

M o m e n

t m a x =

4 6 2 . 2 k N m

@ 6

4 6 k N

-3000-2500-2000-1500-1000

-500

50010001500200025003000350040004500

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. 0 4 0

. 0 6 0

. 0 8 0

. 0 1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

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2 2 0

2 4 0

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2 8 0

3 0 0

3 2 0

3 4 0

3 6 0

3 8 0

4 0 0

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4 4 0

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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 =

4 6 2 . 2 k N m

@ 6

4 6 k N

-3000-2500

-2000-1500-1000

-500

50010001500200025003000350040004500

2 0

. 0 4 0

. 0 6 0

. 0 8 0

. 0 1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

2 4 0

2 6 0

2 8 0

3 0 0

3 2 0

3 4 0

3 6 0

3 8 0

4 0 0

4 2 0

4 4 0

4 6 0

4 8 0

5 0 0

A x i a l

l o a d

( k N )


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

Design chart for bending about the Y-Y axis:

Therefore: Ac = b h = 122500.00 mm h' = h - d'x = 300 mm b' = b - d'y = 300 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.

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 co lumn s lenderness:End fixity and bracing for bending about the X-X axis: At the top end: Condition 2 (partially fixed). At the bottom end: Condition 2 (partially fixed). The column is braced.

x = 0.85 Table 3.21


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End fixity and bracing for bending about the Y-Y axis: At the top end: Condition 2 (partially fixed). At the bottom end: Condition 2 (partially fixed). The column is unbraced.

y = 1.50 Table 3.22

Effective column height: lex = x Lo = 6.800 m ley = y Lo = 12.000 m

Check if the column is slender: 3.8.1.3 lex/h = 19.4 > 15 ley/b = 34.3 > 10

The column is slender.

Check slenderness limit: 3.8.1.7 Lo = 8.000 m < 60 b' = 21.000 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 = 0.0 kNm

The initial moment near mid-height of the column : 3.8.3.2 Mi = -0.4M1 + 0.6M2 0.4M2 = 0.0 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 : 3.8.3.7 Mi = -0.4M1 + 0.6M2 0.4M2 = 0.0 kNm

Deflection induced moments: 3.8.3.1Design ultimate capacity of section under axial load only: Nuz = 0.45 fcu Ac + 0.95 fy Asc = 1865.3 kN

Maximum allowable stress and strain: Allowable compression stress in steel, fsc = 0.95 fy = 438.1 MPa Allowable tensile stress in steel, fst = 0.95 fy = 438.1 MPa Allowable tensile strain in steel, ey = fst/Es = 0.0022 m/m Allowable compressive strain in concrete, ec = 0.004m/m

For bending about the X-X axis: Balanced neutral axis depth, xbal = ec/(ec+es) h' =184.5 mm Nbal = 0.44 b fcu xbal + At/2 (fsd-fs) = 649.0 kN K = (Nuz - N) / (Nuz - Nbal) = 1.000 1.0 a = (1/2000) (lex/h) = 0.189

Madd = N a K h = 33.0 kNm

For bending about the Y-Y axis: Balanced neutral axis depth, xb = ec/(ec+es) b' =184.5 mm Nbal = 0.44 h fcu xbal + At/2 (fsd-fs) = 649.0 kN K = (Nuz - N) / (Nuz - Nbal) = 1.000 1.0 a = (1/2000) (ley/b) = 0.588

Madd = N a K b = 102.9 kNm


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Design ultimate load and moment:Design axial load: P u = 500.0 kN

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

(a) M2 = 0.0 kNm (b) Mi + Madd = 33.0 kNm (c) M1 + Madd/2 = 16.5 kNm (d) emin N = 8.8 kNm

Mx = 16.5 kNm

Moment distribution along the height of the column for bending about the X-X: At the top, Mx = 16.5 kNm Near mid-height, Mx = 33.0 kNm At the bottom, Mx = 16.5 kNm

Mxadd/2=16.5 kNm

Mxadd/2=16.5 kNm

M x a

d d = 3

3 . 0 k N m

Mxtop=0.0 kNm

Mxbot=0.0 kNm

Moments about X-X axis( kNm)

Initial Additional Design

Mx=33.0 kNmMxmin=8.8 kNm

+ =

For bending about the Y-Y axis, the maximum design moment is the greatest of: 3.8.3.7 (a) M2 + Madd = 102.9 kNm (b) emin N = 8.8 kNm

My = 102.9 kNm

Moment distribution along the height of the column for bending about the Y-Y: At the top, My = 102.9 kNm Near mid-height, My = 0.0 kNm At the bottom, My = 102.9 kNm

Myadd=102.9 kNm

Myadd=102.9 kNm

Mytop=0.0 kNm

Mybot=0.0 kNm

Moments about Y-Y axis( kNm)

Initial Additional Design

My=102.9 kNmMymin=8.8 kNm

+ =


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Check for miminum eccentricity: 3.8.2.4 For bi-axial bending, it is only necessary to ensure that the eccentricity excceeds the minimum about one axis at a time.

For the worst effect, apply the minimum eccentricity about the minor axis: Mmin = 8.8 kNm about the Y-Y axis.

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

Column design chart (Y-Y)

M o m e n

t m a x =

4 6 2 . 2 k N m

@ 6 4 6 k N

-3000-2500-2000-1500-1000

-500

5001000150020002500300035004000

4500

2 0

. 0 4 0

. 0 6 0

. 0 8 0

. 0 1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

2 4 0

2 6 0

2 8 0

3 0 0

3 2 0

3 4 0

3 6 0

3 8 0

4 0 0

4 2 0

4 4 0

4 6 0

4 8 0

5 0 0

A x i a l

l o a d

( k N )


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

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 500.0

0.00.0

0.00.0

0.00.0

33.0102.9

Y-YTop

16.5102.9 116.2

500 (0.41%)1112 (0.91%)

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