TCC14 Crack Width - 2002-2005

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Project Spreadsheets to EC2

Client Point No 2 in concourse beam Made by Date Page

Location Grid line 1 rmw 7-Nov-14 202

FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004 Checked Revision Job No

Originated from TCC14.xls v3.1 on CD 2002-2005 BCA for RCC RECTANGULAR chg - FB625

LEGEND

INPUTck= 40 MPa rea o tens on stee , s= 8500

yk= 500 MPa = 940 mm= 500 mm rea o compress on stee , s2= 1000 mm

h= 1000 mm d2= 60 mmQP moment, M= 2093 KNm Maxmum tension bar spacing, S= 100 mm

Age at cracking = 28 days ax tens on ar a, eq= 25 mm

Cement type = N (S, N, or R) Short term or long term ? L (S or L)reep actor, = 2.6 Cover to As, c= 38 mm

CALCULATIONS

modulus of elasticity of concrete = 22[(fck+8)/10].

Ecm= 35.2 GPa

moduli of elasticity of steel Es= 200.0 GPa

Modular ratio e= 20.44

mean concrete strength at cracking fcm,t= 48.00 MPa

mean concrete tensile strength fct,eff= 3.51 MPa

uncracked neutral axis depth

[bh/2+(e-1)(Asd+As2d2)]/[bh+(e-1)(As+As2)] xu= 593.71 mm

uncracked 2nd

moment of area

bh/12+bh(h/2-x)+(e-1)[As(d-x)+As2(x-d2)] Iu= 71413 mm 10

cracking moment = fctI/(h-x) Mcr= 616.74 kNm

< 2093 kNm section is CRACKED

fully cracked neutral axis depth

(-Ase-As2(e-1)+[{Ase+As2(e-1)}+2b{Ased+As2d2(e-1)}])/b xc= 512.10 mm

concrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)] c= 18.425 MPa

stress in tension steel = ce(d-x)/x s= 314.7 MPa

effective tension area = min[2.5(h-d), (h-x)/3, h/2]b - A s Ac,eff= 66500 mm2

As /Ac,eff p,eff= 0.1278

max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)] sr,max= 160.8 mm

average strain for crack width calculation sm-cm= 1375.3 strain

CALCULATED CRACK WIDTH Wk= 0.221 mm

The Concrete Centre

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Client Point No 2 in concourse beam

Location Grid line 2

FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004

Originated from TCC14.xls v3.1 on CD 2002-2005 BCA for RCC CO

LEGEND

INPUT

ck= 35 MPa rea o ens

yk= 500 MPa

w= 300 mm rea o compress o

= 450 mm

f= 2170 mm axmum ens on ar

f= 125 mm ax ens onmomen , M= 114.2 KNm Short term o

Age at cracking = 14 days Co

Cement type = R (S, N, or R)reep ac or, = 2.0

CALCULATIONS modulus of elasticity of concrete = 22[(fck+8)/10].

moduli of elasticity of steel

Modular ratio

mean concrete strength at cracking

mean concrete tensile strength


[bwh/2+(bf-bw)hf/2+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)]

uncracked 2n

moment of area

bwh/12+bwh(h/2-x)+(bf-bw)hf/12+(bf-bw)hf(x-hf/2)+(e-1)[As(d-x)+As2(x-d2)]

cracking moment = fctI/(h-x)

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< 114.2 kNm

fully cracked x (within flange)

concrete stress (x within flange)

stress in tension steel = ce(d-x)/x

effective tension area = min[2.5(h-d), (h-x)/3, h/2]bw- A

s

As /Ac,eff

max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)]

average strain for crack width calculation

CALCULATED CRACK WIDTH

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Made by Date Page

rmw 7-Nov-14 33

TEE IN Checked Revision Job No

PRESSION chg - FB625

n s ee , As= 1473= 399.5 mm

n s ee , As2= 236

2= 33 mm spac ng, = 87 mm

ar a, eq= 25 mm

r long term ? L (S or L)

er to As, c= 38 mm

Ecm= 34.1 GPa

Es= 200.0 GPa

e= 17.61

fcm,t= 39.58 MPa

fct,eff= 2.95 MPa

xu= 138.21 mm

Iu= 6653 mm 10

Mcr= 63.05 kNm

The Concrete Centre

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section is CRACKED

xc= 85.53 mm

c= 3.234 MPa

s= 209.0 MPa

Ac,eff= 34974 mm2

p,eff= 0.0421

sr,max= 230.1 mm

sm-cm= 800.8 strain

Wk= 0.184 mm

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Table 3.1

Table 3.1 & equation (3.4)

Table 3.1

OPERATING INSTRUCTIONS

ENTER DATA INBLUE CELLSONLY.RED MESSAGESINDICATE ENTRY ERRORS.

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Below

x is within flange 0 Within

Below

7.3.2 (3) Within

7.3.4 (2)

Equations (7.11) & (7.14)

Equation (7.9)

Equation (7.8) 1

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a b c

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-150 263604.55 25099852 90.5519 bx^2/2 - bx^2 - x[(bf-bw)hf + (ae-1)As'

-1085 29854.548 10490477 85.5292 bf.x^2/2 - bf.x^2 - x[(ae-1)As' + ae.As]

f z m

33.657 200.57774 5.9594776 3.75527

3.23423 M/[bfx(d-x/3)/2+(

e-1)A

s2(x-d

2)/x(d-d

2)]

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+ ae.As] + (bf-bw)hf^2/2 + (ae-1)As'd' + ae.As.d = 0

+ (ae-1)As'd' + ae.As.d = 0

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Client Point No 2 in concourse beam

Location Grid line 2

FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004 TEE IN

Originated from TCC14.xls v3.1 on CD 2002-2005 BCA for RCC TENSION

LEGEND

INPUT

ck= 35 MPa rea o ens on s ee , s=

yk= 500 MPa =

w= 300 mm rea o compress on s ee , s2=h= 450 mm d2=

f= 1222 mm axmum ens on ar spac ng, =

f= 125 mm ax ens on ar a, eq=

QP moment, M= 147 KNm Short term or long term ?

Age at cracking = 14 days Cover to As, c=

Cement type = R (S, N, or R)Creep factor, = 2.0

CALCULATIONS modulus of elasticity of concrete = 22[(fck+8)/10].

Ecm=

moduli of elasticity of steel Es=

Modular ratio e=

mean concrete strength at cracking fcm,t=

mean concrete tensile strength fct,eff=


[bwh/2+(bf-bw)hf(h-hf/2)+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)] xu=

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uncracked 2nd

moment of area

bwh/12+bwh(h/2-x)+(bf-bw)hf/12+(bf-bw)hf(h-x-hf/2)+(e-1)[As(d-x)+As2(x-d2)] Iu=

cracking moment = fctI/(h-x) Mcr=

< 147 kNm section is

fully cracked neutral axis depth

(-Ase-As2(e-1)+[{Ase+As2(e-1)}+2b{Ased+As2d2(e-1)}])/bw xc=

concrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)] c=

stress in tension steel = ce(d-x)/x s=

height of tension zone = min[2.5(h-d), (h-x)/3, h/2] hc,eff=

effective tension area Ac,eff=

As /Ac,eff p,eff=

max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)] sr,max=

average strain for crack width calculation sm-cm=

CALCULATED CRACK WIDTH Wk=

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Made by Date Page

rmw 7-Nov-14 33

Checked Revision Job No

chg - FB625

1000

417 mm

23634 mm

87.4 mm

10 mm

L (S or L)

28 mm

34.1 GPa Table 3.1

200.0 GPa

17.61

39.58 MPa Table 3.1 & equation (3.4)

2.95 MPa Table 3.1

303.18 mm '=

The Concrete Centre OPERATING INSTRUCTIONS

ENTER DATA INBLUE CELLSONLY.RED MESSAGESINDICATE ENTRY ERRORS.

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4572 mm 10

92.01 kNm

CRACKED

162.73 mm

14.638 MPa

402.7 MPa s > 0.8fyk

82.50 mm

99815 mm2

7.3.2 (3)

0.0100 7.3.4 (2)

264.9 mm Equations (7.11) & (7.14)

1319.6 strain Equation (7.9)

0.350 mm Equation (7.8) 1

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0.0019 = 0.0080

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National Annex valuesEC2 Ref Function Value

7.2 (2) k1 0.6 stress limit - concrete

7.2 (3) k2 0.45 linear creep limit

7.2 (5) k3 0.8 stress limit - steel

7.3.4 (3) k3 3.4 Equation (7.11) factor

7.3.4 (3) k4 0.425 Equation (7.11) factor

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Notes

Disclaimer

Status of spreadsheet

First public release

Revision history TCC14

Date Version

28-Feb-07 TCC14 v3.1

28-Jun-06 TCC14 v3.0

3-Feb-05 TCC14 v1.0

30-Apr-03 RCCen14 4

26-Mar-03 RCCen14 3

21-Dec-01 RCCen14 2

31-Aug-01 RCCen14 1

All advice or information fr

those who will evaluate the

application. No liability (inis accepted by the BCA, TC

software and publications a

are in possession of the late

This spreadsheet should

Spreadsheets: v3' available

607777 or +44 (0)1276 60714

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Notes

Crack Width

Action Size(kB)Correction to calculation of Aceffand cracked x for rectangular

sections. Default cement type changed to 'R'.919

v3 release. Page nos, User Guide and registration details amended. 918

Tee sections added. RE-BADGED 924

Correction to use of equation (7.14). 258

Updatd to November 2002 draft. 258

Updated to final draft. 266

First issue for in-house comment 266

This spreadsheet is shareware. It may be distributed freely, but maynot be used for commercial purposes until the user has registered

with the TCC via The Concrete Bookshop.

om the British Cement Association and/or The Concrete Centre is intended for

significance and limitations of its contents and take responsibility for its use and

luding that for negligence) for any loss resulting from such advice or informationC or their subcontractors, suppliers or advisors. Users should note that all TCC

re subject to revision from time to time and should therefore ensure that they

st version.

e used in compliance with the accompanying publication 'User Guide RC

from The Concrete Bookshop, www.concretebookshop.com, Tel +44 (0)700 4

0

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Notes

P 20

TCC14 Crack Width - 2002-2005

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