TCC53 Column Design - 2002-2008

Project

Spreadsheets to EC2

Client

Advisory Group

Location

The Concrete Centre Made by

Column D2

RMW

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT TWO AXES TO EN 1992-1 : 2004 Originated from TCC53.xls v 3.4 on CD

Checked

Date

Page

30-Nov-14 Revision

Job No

-

© 2002-2008 TCC

279

FB625

MATERIALS fck fyk

32 500

φ

2.2

h b with and

550 550 3 3

γs γc

1.15 1.5

Cover to link, Cnom dg

70 20

mm

φef Steel class . .

1.21 B

Δc,dev

10

mm

N/mm² N/mm²

SECTION mm mm

mm

Y

bars per 550 face

Y

bars per 550 face

ie. 550 x 550 columns with 8 bars Remote

RESTRAINTS Y-AXIS Z-AXIS

Y-AXIS Z-AXIS

Top Condition

Condition

Braced ?

7500 7500

F F

F F

Y Y

L (mm)

L0 (mm)

h0 (mm)

7000 7325

5792 6027

275

Asc %

Link Ø

3.32 2.13 1.30 0.83 0.53 0.30

10 8 8 8 8 8

BAR ARRANGEMENTS Bar Ø B 40 B 32 B 25 B 20 B 16 B 12 LOADCASES 1 2 3 4 5 6 DESIGN MOMENTS 1 2 3 4 5 6

CONNECTING BEAMS/SLABS

Storey height (mm)

AXIAL

Btm

175 181 185 187 189 191

500 500 175 175 500 500 500 500 70%

L (m)

end (F) or (P)

8 F 6 F 5 F 5 F 8 F 6 F 5 F 5 F of uncracked stiffness Col below? Y Checks

ok ok ok ok ok ok

8822 7621 6789 6319 6019 5786

BTM MOMENTS (kNm)

N (kN)

m0y

m0z

m0y

m0z

1800 1700 1500 1000 600 900

19.5 29.9 50.0 80.0 120.0 130.0

2.5 2.5 2.5 2.5 2.5 2.5

14.0

2.3

Y AXIS

h (mm)

Top West 300 Top East 300 Top North 3500 Top South 3500 Bottom West 300 Bottom East 300 Bottom North 300 Bottom South 300 Beam stiffnesses are Column above? Y BAR CENTRES (mm) 550 Face 550 Face Nuz (kN) 175 181 185 187 189 191

TOP MOMENTS (kNm)

b (mm)

8.0

Z AXIS

Moments m 0 at top and bottom of column (from analysis) are combined to find m 0e . The moment due to imperfections (e 1 N) and the second order moment (M 2 ) are then added to obtain M Ed In the table below.

Critical

Biaxial Check

MEd y

MRd y

MEd z

MRd z

axis

Equation (5.39)

REBAR

40.0 49.3 66.4 90.9 126.6 139.9

391.2 382.4 362.3 296.3 224.8 279.6

21.8 20.7 24.1 13.2 8.9 12.1

391.2 382.4 362.3 296.3 224.8 279.6

Z Z Z Z Z Z

0.104 0.128 0.195 0.324 0.602 0.523

8 B12 8 B12 8 B12 8 B12 8 B12 8 B12

SEE CHARTS ON NEXT SHEET

The Concrete Centre

Spreadsheets to EC2

Project

Client Advisory Group Location Column D2

Made by

RMW

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT TWO AXES TO EN 1992-1 : 2004

Originated from TCC53.xls v 3.4 on CD

Checked

Page

280

30-Nov-14 Revision

-

© 2002-2008 TCC

N:M interaction chart for MEd Y

Date

Job No

FB625

550 x 550 column (h x b), fck = 32, 70 mm cover

10000 9000

AXIAL LOAD NEd (kN)

8000 8B40

7000 6000

8B32

5000

8B25 8B20 8B16

4000

8B12

3000 N bal

2000

1800 1700 1500 1000900 600

1000

0 0

100

200

300

400

500

600

700

800

900

1000

MOMENT MEd Y (kNm) N:M interaction chart for MEd Z

550 x 550 column (h x b), fck = 32, 70 mm cover

10000 9000

AXIAL LOAD NEd (kN)

8000 8B40

7000 8B32

6000 8B25 8B20 8B16

5000

8B12

4000

3000 N bal

2000

1800 1700 1500

1000

1000 900 600

0 0

100

200

300

400

500

MOMENT MEd Z (kNm)

600

700

800

900

1000

Project

Spreadsheets to EC2

Client Location

Advisory Group Column D2

The Concrete Centre Made by

RMW

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT TWO AXES TO EN 1992-1 : 2004

Originated from TCC53.xls v 3.4 on CD

TYPICAL CALCULATION

for loadcase 1

Checked

Date

Page

30-Nov-14 Revision

281 Job No

-

© 2002-2008 TCC

FB625

550 x 550 column with 8 B12 bars

About Y axis Column is braced 7325

SLENDERNESS Clear height, L

mm

About Z axis Column is braced 7000

Rotational stiffness, k 1

Max[0.1, EI/l cols /∑(κEI/l beams )]

1.189

0.854

Rotational stiffness, k 2

0.854

5.8.3.2(3)

(κ=2 braced, or 4 unbraced)

0.595

Effective length, l 0 Exp (5.15) braced or (5.16) unbraced Radius of gyration, i including reinforcement

6027

mm

5792

5.8.3.2(3)

159.0

mm

159.0

5.8.3.2(1)

Slenderness ratio, λ

l 0 /i

37.9

36.4

Reinforcement ratio, ω

A s ∙f yd /(A c ∙f cd )

0.072

0.072

5.8.3.1

Relative normal force, n

N Ed /(A c ∙f cd )

0.328

0.328

5.8.3.1

Limiting slenderness, λ lim

Exp (5.13N)

72.7

78.8

Slenderness condition N Ed = BUCKLING

λ > λ lim ?

Short

Short

At maximum MOR, n bal

from charts

0.418

0.418

5.8.8.3(3)

Axial correction factor, K r

(n u - n)/(n u - n bal )

1.138

1.138

Eqn (5.36)

Creep adjust factor, β

0.257

0.267

5.8.8.3(4)

Creep effect factor, K φ

0.35 + f ck /200 - λ / 150 1 + β∙φ ef ≤ 1

1.311

1.323

Eqn (5.37)

Basic curvature, 1/r 0

f yd /(0.45d.E s )

0.0104

/mm

0.0104

5.8.8.3(1)

Curvature, 1/r

K r ∙K φ ∙1/r 0

0.01547

/mm

0.01561

Eqn (5.34)

Curvature distribution, c

9.870

5.8.8.2(4)

Deflection, e 2

8 if M 0 costant, otherwise π² (1/r)∙l 0 ² /c

0.0569

mm

0.0531

5.8.8.2(3)

Second order moment, M 2

N Ed ∙e 2 if short, otherwise 0

0.00

kNm

0.00

Eqn (5.33)

0.0037

Eqn (5.1) Eqn (5.2)

1800

kN

9.870

IMPERFECTIONS Inclination, θ i

0.0038

Imperfection M, M imp

Min[1,Max(⅔, 2/√l)]∙θ 0 θ i ∙N Ed ∙l 0 /2

20.50

kNm

19.26

MOMENTS First order end M, M 01

lesser of end moments

14.00

kNm

2.30

First order end M, M 02

greater of end moments

19.50

kNm

2.50

Equivalent end M, M 0e

0.6M 02 + 0.4M 01

7.80

kNm

1.00

Eqn (5.32)

Minimum moment, M min

Max(20, h/30)∙N Ed

36.00

kNm

0.00

6.1(4)

Final design M, M Ed

Max[M min ,max(M 02 +M 2 /2,M 0e +M 2 )+ M imp ]

40.00

kNm

21.76

Eqn (5.33)

BIAXIAL CHECK Section MOR, M Rd

from charts, with NEd = 1800

391.16

kNm

391.16

Relative force, n

N Ed /(A c ∙f cd + A s ∙f yd ) =

0.303

Exponent, a

If{n