TCC11 Element Design.xls of Slab and Beam

SOLID SLABS

v 3.5 on CD © 2003-2005 TCC

INPUT

Location 1st Floor, Span H-J

M kNm/m

15.12

fck N/mm²

32

γc =

1.50

δ

1.00

fyk N/mm²

500

γs =

1.15

span mm

5000

gk

7.50

h mm

250

qk

2.50

Bar Ø mm

8

Steel class

A

mm

35

to this steel

Usage

Office

mm

10

Section location

END SPAN

brittle partitions?

YES

OUTPUT

1st Floor, Span H-J

.

d = 250 - 35 - 8/2 = 211.0 mm

3.1.7 (3)

x = [211 - √(211² - 4000/0.85 x 15.12 x 1.5/32)]/0.8 = 5.0 mm

5.5 (4)

(x/d) limit = 0.600

x/d actual = 0.024 < 0.600 ok

Fig 3.5

z = 211 - 0.4 x 5.0 = 209.0 > 0.95d = 200.5 mm

.

As = 15.12E6/500/200.5 x 1.15 = 173 < As min = 208 mm²/m

9.2.1.1 (1)

As min = 1.57 x 211 = 208 mm²/m

As def = 173 mm²/m

Provide H8 @ 225

= 223 mm²/m

Table A1.1 EN1990

0.3 (Office)

QP udl = 7.5 + 0.3 x 2.5 = 8.25 kN/m², n = 7.5 x 1.35 + 2.5 x 1.5 = 13.88

QP M = 15.12 x 8.25/13.88 = 8.99 kNm

201.7 N/mm²

7.4.2 (2)

Modification factor = 310/201.7 = 1.500(max)

Table 7.4

Permissible L/d = 1.500 x 425.72 = 638.58

Actual L/d = 5000/211 = 23.70 ok

.

Section design to Eurocode 2 (BS EN 1992-1) Originated from TCC11.xls, kN/m2 kN/m2 cover, C_nom Δc_dev

ψ

₂

=

σ

s =

RECTANGULAR BEAMS

Originated from TCC11.xls, v 3.5 on CD © 2003-2005 TCC

INPUT

Location 1st Floor, Span 1

Beam type

END SPAN

M kNm

370.0

fck

32

N/mm² γc =

1.50

δ

0.85

fyk

500

N/mm² γs =

1.15

span mm

8000

Steel class

A

10

h mm

500

REBAR Ø COVER to main bars

b mm

300

Tension

32

42

gk kN/m

25.80

Comp'n

20

35

qk kN/m

20.00

Side

--

42

0.6

Shopping

brittle partitions?

YES

OUTPUT

1st Floor, Span 1

.

Effective depth,

d = 500 - 42 - 32/2 = 442.0 mm

Neutral axis,

x = [442-√(442² -2E6x370x1.5/0.85/300/32)]/0.8 = 248.0 mm

(x/d) limit = 0.450 x/d actual = 0.561 > 0.450, x = 198.9 mm

Lever arm,

z = 442 - 0.4 x 198.9 = 362.4 mm

d2 = 35 + 20/2 = 45 mm

Gross fsc = 434.8 N/mm² from strain diagram

Net fsc = 434.8 - 0.85 x 32 /1.5 = 416.6 N/mm²

Excess M = 370 - 313.7 = 56.3 kNm

Compession steel,

As2 = 56.3E6 /416.6 /(442 - 45) = 340 mm²

PROVIDE 2H20 COMPRESSION STEEL = 628 mm²

Steel stress,

fyd = 434.8 N/mm² from strain diagram

r = 280 N/mm²

Tension steel,

As = 313.7E6/362.4/434.8 + 340.2 x 416.6/434.8 = 2317 mm²

9.2.1.1 (1)

As min = 1.3 x 300 x 500 = 208 mm²

7.3.2 (1)

As crack = 400 x 0.86 x 3.024 x 68.1/500 = 142 mm²

.

7.4.2

As def = 2350 mm²

PROVIDE 3H32 TENSION STEEL = 2413 mm²

DEFLECTION

QP M =370 x 37.8 /64.8 = 253.8 kNm

σs = 280 N/mm²

7.4.2 (2)

Modification factor = 310 /280.0 = 1.107

Permissible L/d = 1.107 x 0.875 x 18.899 = 18.30

Actual L/d = 8000 /442 = 18.10 ok

.

Δc_dev ψ2 =

Section design to Eurocode 2 (BS EN 1992-1)

SIMPLE TEE & L BEAMS

Originated from TCC11.xls, v 3.5 on CD © 2003-2005 TCC

INPUT

Location 1st Floor, Span 3 to 4

M kNm

271.2

Beam type

SUPPORT

δ

1.00

fck

32

N/mm² γc =

1.50

span mm

7500

fyk

500

N/mm² γs =

1.15

h mm

425

Steel class

A

10

bw mm

325

REBAR Ø COVER bf mm

775

Tension

16

40

hf mm

125

Comp'n

12

40

gk kN/m

32.40

Side

--

40

qk kN/m

25.00

ψ2 =

0.6

Shopping

brittle partitions?

YES

OUTPUT

1st Floor, Span 3 to 4

Effective depth,

d = 425 - 40 - 16/2 = 377 mm

Neutral axis,

x = [377-√(377² -2E6x271.2x1.5/0.85/325/32)]/0.8 = 69.0 mm

(x/d) limit = 0.600x/d actual = 0.183 ok

Lever arm,

z = 377 - 0.4 x 69.0 = 349.4 mm

Tension steel,

As = 271.2E6 /349.4 /434.8 = 1785 mm²

9.1.1.1 (1)

As min = 1.3 x 483.0 x 377 = 286 mm²

7.3.2 (1)

As crack = 661.1 x 0.67 x 3.024 x 107.8 /500 = 288 mm²

.

PROVIDE 9H16 TENSION STEEL = 1810 mm²

.

.

σs = 274 N/mm²

7.4.2 (2)

.

.

.

.

.

.

.

σs = 274 N/mm²

.

.

.

.

Δc_dev

Originated from TCC11.xls, v 3.5 on CD © 2003-2005 TCC

INPUT

Location 1st Floor, Span 2 at 2E

fck N/mm²

30

γc =

1.50

d bw

fywk N/mm²

500

γs =

1.15

440

300

Main Steel Link Ø Legs Side cover n

Ø

25

10

2

30

258.0

64.8

No

2

mm No mm kN/m

OUTPUT

1st Floor, Span 2 at 2E

6.2.2 (1)

982 mm² = 0.744%

20.0 N/mm²

equation (6.6)

0.6(1 - 30/250) = 0.528 .

2.50

equation (6.9)

1 x 300 x 396.0 x 0.528 x 20.0 /2.90 /1000 = 432.6 kN

ok

6.2.1 (8)

258 - 64.8 x 0.44 = 229.5 kN

6.2.2 (1)

k = 1 + √(200 /440) = 1.674 .

equation (6.2)

0.12 x 1.674 cube root(0.744 x 30) = 74.7 kN

.

9.2.2 (5)

0.08 x 300 /500 x √30 = 0.263 mm

equation (6.9)

0.5 x 300 /500 x 1.15 x 0.528 x 20.0 = 3.643 mm

ok

equation (6.7)

229.5E3 /(396.0 x 434.8 x 2.50) = 0.533 > 0.263

9.2.2 (6)

330 mm

330 mm

9.2.2 (8)

ok

PROVIDE 2 legs T10 @ 275

Provide for distance of 825 mm from support face

then nominal links = 2 legs T10 @ 325

BEAM SHEAR

VEd kN at face

A

_sL

=

f

_cd

=

ν

=

cotθ =

V

_Rd,max

=

V

_Ed

@ d =

V

_Rd,c

=

A

sw

/s

(min)

=

A

_sw

/s

(max)

=

A

_sw

/s =

s

_max,L

=

s

_max,T

=

Section design to Eurocode 2 (BS EN 1992-1)

COLUMN DESIGN

Originated from TCC11.xls, v 3.5 on CD © 2003-2005 TCC

INPUT

Location

Column 2E

35

N/mm²

2507

kN

500

N/mm²

27.0

kNm Main bar Ø

20

mm height, h

300

mm Link Ø

8

mm breadth, b

325

mm

1.50

concrete

25

mm

1.15

steel

CALCULATIONS

43

mm

19.8

N/mm²

d =

257

mm

434.8

N/mm²

from iteration, neutral axis depth, x =

374.7

mm

dc = 299.7

mm

1932.1

kN

Steel comp strain =

0.00258

Steel tens strain = -0.00092

434.8

N/mm²

(Comp. stress in reinf.)

415 net

-183.3

N/mm²

(Tensile stress in reinf.)

-163 net

from M, As =

994

mm²

from N, As =

994

mm²

OUTPUT

OK

Column 2E

Requires 994mm² T&B:-

PROVIDE 12T20

(ie 4T20 T&B - 1257mm² T&B - 3.87% o/a, @80 c/c.)

Links : -

PROVIDE T8 @ 300

see clause 9.5.2 (4)

19.8 N/mm²

Notes Compression +ve SYMMETRICAL RECTANGULAR COLUMN DESIGN

MOMENTS ABOUT X AXIS ONLY

f_ck

Axial load, N_Ed f_yk

Moment, M_Ed

γ_c =

cover (to link) γs =

from M

_ED

_{As = [M -}

_αη

_f

ck

.b.d

c

(h/2 - d

c

/2)] / [(h/2-d

2

).(

σ

sc

+

σ

st

).

γ

c

]

from N

_Ed

A

_s

= (N -

αη

f

_ck

.b.d

_c

) / [(

σ

_sc

-

σ

_st

).

γ

_c

]

A_sc = A_st = A_s d_c = min(h, λx)

d

₂

=

αη

f

_ck

/

γ

_c

=

f

_yk

/

γ

_s

=

αη

f

_cu

.b.d

_c

/

γ

_c

=

σ

_sc

=

σ

_st

=

Stresses in N/mm2 - - - Neutral axis 2 Stress diagram 5 7 9 12 Strain diagram

Indirect Supports

Originated from TCC11.xls, v 3.5 on CD © 2003-2005 TCC

INPUT

Location

1st Floor, Beam 7D-E

500

N/mm²

1.15

300

mm

450

mm

225

mm Link Ø =

10

300

mm

127.0

kN from secondary

OUTPUT

1st Floor, Beam 7D-E

a = Min(300/2 + 300/3, 300/2) = 150 mm

d = Min(450/3 + 225/2, 450/2) = 225 mm

500 /1.15 = 434.78 N/mm²

1000 x 127 /434.78 = 292 mm²

PROVIDE 4 additional T10 legs within 2a

(and within d,if needed)

314 mm²

fywk γs = h1 h2 bw1 bw2 VEd

f

yd

=

Extra A

sw

=

A

sw,prov

=

a

150

d

225

fyd

434.78

Asw

292.1

No

4

Asw,prov

(and within d,if needed)

OPERATING INSTRUCTIONS

ENTER DATA IN BLUE CELLS ONLY.

RED MESSAGES INDICATE ENTRY ERRORS. COPY OUTPUT SECTION & PASTE WHERE YOU WANT.

NATIONAL ANNEX VALUES

Originated from TCC11.xls,

EC2 Ref Function Value TABLE A1.1 EN1990

EN 1990 1.35 dead load factor A 0.7 0.5 0.3

EN 1990 1.5 imposed load factor B 0.7 0.5 0.3

Table 2.2 1.5 concrete C 0.7 0.7 0.6

Table 2.2 1.15 steel D 0.7 0.7 0.6

3.1.6 (1)P 0.85 strength factor - flexure E 1 0.9 0.8

3.1.6 (1)P 1.00 strength factor - shear F 0.7 0.7 0.6

5.5(4) 0.4 redistribution factor G 0.7 0.5 0.3

- = - 1 H 0 0 0

- = - 0.6 - = - J 0.6 0.5 0

- = - 0 =

-- = -- 0.4 redistribution factor TABLE 7.1N

- = - 1 X0, XC1 0.4

- = - 0.6 - = - XC2 to XC4 0.4

- = - 0 - = - XD1 to XS3 0.3

- = - 0.7 redistribution factor TABLE 7.4N

- = - 0.8 redistribution factor 0 0

6.2.2 (1) 0.18 basic shear stress 1 1

- = - 0.04 2 1.3

6.2.3(2) 1 2.5 3 1.5

6.2.3(3) 1 4 1.2

8.2(2) 1 min bar spacing 5 0.4

- = - 5 - = - Max 310/σs 1.5

9.2.1.1 (1) Equn (9.1) 0.26 min steel

- = - Equn (9.1) 0 =

-9.2.1.1(3) 4% max steel

9.2.2(5) 0.08

9.2.2(6) 0.75 x d

9.2.2 (8) 600 max trans link spacing

9.3.1.1 (3) 400 250

- = - - = - 3 2

9.5.2 (1) 12 min column bar dia

9.5.2 (2) 0.2% min column steel 0.1

9.5.2(3) 4.0% max column steel

9.5.3(3) 20 400 ψ₀ ψ₁ ψ₂ γ_G γ_Q γ_c γ_s α_cc α_cc k1 k2 a a(b+c/ecu2) k2 b k2 c k3 k4 a a(b+c/ecu2) k4 b k4 c k5 k6 CRd,c vmin x k3/2fck1/2

cotθmin/max ←max/min strut angle→

α_{cw for V}Rdmax k1 k2 A_s/A_c max ρ_{w,min x fck}1/2_/fyk S_t,max S_t,max

S_{max,slabs, MAIN UD max slab spacing PL}

UD or x h PL

Ø_min A_s,min A_s,max

Disclaimer

Status of spreadsheet

First public release

Date

Version

19-Sep-08 TCC11 v3.5 8-Sep-08 TCC11 v3.4 27-Aug-07 TCC11 v3.3 21-Nov-06 TCC11 v3.2 4-Oct-06 TCC11 v3.1 28-Jun-06 TCC11 v3.0 11-Mar-06 TCC11 v1.3 13-Sep-05 TCC11 v1.2 17-Aug-05 TCC11 v1.1 2-May-05 TCC11 v1.0 15-Dec-03 RCCen11 b 15 25-Mar-03 RCCen11 b 14 21-Dec-01 RCCen11 b 13 20-Dec-01 RCCen11 b 12 14-Dec-01 RCCen11 b 11 12-Sep-01 RCCen11 b 10 18-Jun-01 RCCen11 b 9 12-Jun-01 RCCen11 b 8 3-May-01 RCCen11 b 7

All advice or information from the British Cement Association and/or The Concrete Centre is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the BCA, TCC or their subcontractors, suppliers or advisors. Users should note that all TCC software and publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.

This spreadsheet should be used in compliance with the accompanying publication 'User Guide RC Spreadsheets: v3' available from The Concrete Bookshop, www.concretebookshop.com, Tel +44 (0)700 4 607777 or +44 (0)1276 607140

3-Apr-01 RCCen11 b 6 7-Mar-01 RCCen11 b 5 2-Mar-01 RCCen11 b 4 4-Apr-00 RCCen11 b 3 28-Mar-00 RCCen11 b 2 22-Mar-00 RCCen11 b 1

Action

788 Correction to x limit at TEE~BEAM M8. 787 766 Improvement to L/d calculation. 761 Corrections to text in SLAB!C25, COLUMN!K7 and COLUMN! K11 760 v3 release. Page nos, User Guide and registration details amended. 760 773 Placement setting of controls set to 1. 778 778

RE-BADGED 768

Page added for indirect supports. 479 305 Expression for Asw/S (max) corrected on SHEAR. 311 R Moss comments incorporated. 310 311 312 239 Correction to strain calculation in COLUMN 241 239 evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the BCA, TCC or their subcontractors, suppliers or advisors. Users should note that all TCC software and publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.

This spreadsheet should be used in compliance with the accompanying publication 'User Guide RC Spreadsheets: v3' available from The Concrete Bookshop, www.concretebookshop.com, Tel +44 (0)700 4 607777 or +44 (0)1276 607140

This spreadsheet is shareware. It may be distributed freely, but may not be

used for commercial purposes until the user has registered with the TCC via The

Concrete Bookshop.

Revision history

TCC11 Element Design

Size

(kB)

Covers clarified as C_nom. Improvement to calculation of b_t for flanges in tension.

Correction to ψ₂ for vehicular useage.

Differentiation made between α_cc for flexure (=0.85) and α_cc for shear (=1.00).

Brittle partitions switches highlighted. Use of ψ₂ clarified. Concrete gades 28 and 32 added.

National Annex sheet added and referenced. Updated to November draft.

Variable flange modification factor added in TEE~BEAM, and UPDATED to FINAL DRAFT.

Min main bar spacing to be > bar f and coorection for possible negative square root in calculation of x.

As' changed to As2, d' changed to d2, and net steel stresses used in COLUMNS

Correction to cover warnings & use of d in 310/ss. Also SHEAR:M6 and M15 corrected.

Full SLS moment used for L/d checks 239 SHEAR:D15 & M5 corrected 239 Updated to EC2 second draft. 240 242 238 Updated to EN by RMW - for comment 241 Table 7.5 updated, deflection enhancement correction, gs omitted from

SHEAR., and support tension steel distributed over flange width in TEE~BEAM.

Correction to Tee Beam cracking formulae (tension/compression flanges mixed up)