TCC14 Crack Width - 2002-2005
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Transcript of 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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Project Spreadsheets to EC2
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
uncracked neutral axis depth
[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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Project Spreadsheets to EC2
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=
uncracked neutral axis depth
[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