aci 350-06 & aci224r-01 rec sec flexural crack width control rev00 07-sep-2013 1
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Flexural Crack width Calculation for Rectangular RC SlabProject :- Project Designed by:- M. Abu Shady
Building :- Building Checked by:- M. Abu Shady
Element:- Element Date:- 17-Apr-23
Location:- Location M.A.S.
General Input :-
Width b 1000 mm Es 200000
Depth h 300 mm 0.003 mm
cover 50 mm 0.0021 mm420 26587 N/mm2 ACI318 clause 8.5.132 d 244 mm2.9 KN.m d' 56 mm
7.52
Section RFT. No of bars rebar Dia
Top Rft. 8 T 12 Top = 912 mm2 = 125 mm
Bot. Rft. 8 T 12 Bot. = 912 mm2 = 125 mm
Exposure condition Water-retaining structures ACI224R-01,Table 4.1
1- Locate the Neutral axis & Calculate setcion properties:-X-X εc= 0.000019
d'= 56
y= 51.83 N.A. N.A. N.A.
h= 300 d= 244
A εs= 0.000070
Tranformed Section Strain Stressb= 1000
Taking moment of areas @ X-X,
and simplify in form of Quadratic equation (ay2+by+c=0),
Thus, a = 500.00
b= 12808.88 Thus, = 51.83 mm
c = -2007060.08
= 2,250,000,000 mm4 = 300,000 mm2
= 64,639 mm2
= 299,865,909 mm4
2- Check of Concrete & Steel Reinforcement stresses:-= 3.51 ACI 318M-11, Eq 9-10
= 52.61 ACI 318M-11, Eq 9-9
= 0.50 = 0.016 fc'
= 13.98 Ok < f s max = 250.00= 0.033 fy
Ok < f s max= 320N/mm2 allowed for rebar Dia 12 mm used ,According ACI224R-04, Table4.2Ok < f s max= 240N/mm2 allowed for spacing 125 mm used ,According ACI224R-04, Table4.3
3- Calculation of crack width :-
Crack width, = 0.018 mm ACI224R-01, Eq 4-2a
ok Crack Width <= wcr all= 0.100 mm, ACI224R-01,Table 4.1
= 56.000 mm ACI224R-01, 4.2.1
According ACI350-06 &ACI224R-01, Rev0
N/mm2
εc
εy
fy N/mm2 Ec
fc' N/mm2
Ma service
n= Es /Ec =AS mm2
S spacing Top
S spacing Bot.
fc
εs' Cc = 0.5fc*y*bAs Top (n-1)As Top
As Bot. nAs Bot.
T= fs * As
[by+nAs Bot.+ (n-1)As Top]*y = by*y/2 + nAs Bot.*d + (n-1)As Top*d'
(b-b/2) * y2 + (nAs Bot.+ (n-1)As Top) * y + (-nAs Bot.*d - (n-1)As Top*d') = 0
Ig = bh3/12 Ag = b*h
Acr =by+ nAs Bot.+ (n-1)As Top
Icr =by3/12+by*(y/2)2+ nAs Bot.*(d-y)2+ (n-1)As Top*(y-d')2
N/mm2
KN.m
fc a = Ma*y/Icr N/mm2
fs a=Ma(y-d)/(Icr/n) N/mm2 N/mm2 , ACI350-06, Eq 10-4 & 10-5
Where, dc
Page 2 of 6
Flexural Crack width Calculation for Rectangular RC SlabProject :- Project Designed by:- M. Abu Shady
Building :- Building Checked by:- M. Abu Shady
Element:- Element Date:- 17-Apr-23
Location:- Location M.A.S.
According ACI350-06 &ACI224R-01, Rev0
ᵝ = 1.291 mm ACI224R-01, 4.2.1 & ACI350-06, Eq 10-6
A = 14,000 mm2 ACI224R-01, 4.2.2
Rebar AreaDIA (mm)
6 298 51
10 7912 11414 15416 20118 255
20 314
22 38025 49132 804
Element TypeBeamSlab
Area (mm2)
Exposure condition Crack width mmDry air or protective membrane 0.41Humidity, moist air, soil 0.3Deicing chemicals 0.18Seawater and seawater spray, wetting and drying 0.15Water-retaining structures 0.1
Table 4.2—Maximum bar diameter for high bond bars
bar size, mm32 16025 20020 24016 28012 32010 3608 4006 450
Table 4.3—Maximum bar spacing for high bond barsMaximum bar spacing, mm Steel stress, Mpa
Pure flexure Pure tension300250 200 160200 150 200150 125 240100 75 28050 — 320
— 360
ACI224R-01,Table 4.1, reasonable* crack widths,reinforced concrete under service loads
Steel stress, MPa Maximum
References1-ACI350-06 &ACI224R-01,2- Design of Reinforced Concrete by Jack C. McCormac_9th Ed-2013-1118129849_ACI 318-11.pdf pages 43 (Example 2.3), 6.10 Control of Flexural Cracksand excel sheets for chapter 6
3- RCM ACI Builder v 5.3.0.0 by Eng. Hussein Rida
4- Moment of Inertia of Cracked Section Transformed to Concrete
5-Quadratic eq
6- Equivalent Stiffness , Is =Ic/n
for axial force, εc = εc fc/Ec = fs/Es ==> F/(Ac Ec) = F/(As Es) ==> thus As Es = Ac Ec ==> As = Ac * Ec/Es = Ac /n and for moment, εc = εc fc/Ec = fs/Es ==> M*y/(Is Es) = M*y/(Ic Ec) == > Is = Ic Ec/Es = Ic/n
http://www.mediafire.com/download/k42shb458odynac/Sheets_used_in_Design_of_Reinforced_Concrete_by_Jack_C._McCormac_9th_Ed-2013-1118129849_ACI_318-11.rar
http://www.structural-experts.com/showthread.php?tid=742
http://www.concrete.org/technical/ckc/314/314_design_aid_J_1-14_001.pdf
http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html
http://www.bgstructuralengineering.com/BGSMA/BGSMA_Itr/BGSMA_ITR02.htm
http://www.mediafire.com/download/k42shb458odynac/Sheets_used_in_Design_of_Reinforced_Concrete_by_Jack_C._McCormac_9th_Ed-2013-1118129849_ACI_318-11.rar