ACI 350 06 ACI224R 01 Rec Sec Flexural Crack Width Control Rev00 07 Sep 2013

Flexural Crack width Calculation for Rectangular RC

Slab

According ACI350-06 &ACI224R-01, Rev0

Project Building

Project :Building :Element:Location:-

Designed by:- M. Abu Shady Checked by:- M. Abu Shady 15-Nov-13 Date:-

Element Location

M.A.S.

General Input :Width b

1000

mm

Depth h

300

mm

cover

50

fy

420

mm N/mm2

fc'

32

N/mm2

Ma service

2.9

KN.m

Section RFT. Top Rft.

No of bars

N/mm2

Es εc

200000 0.003

mm

εy

0.0021

mm

Ec

26587

N/mm2

d

244

mm

d'

56

mm

n= Es /Ec =

7.52

ACI318 clause 8.5.1

AS mm2

rebar Dia 8 T 12 Top

S spacing Top = 125 mm S spacing Bot. = 125 mm

= 912 mm2

Bot. Rft.

8 T 12 Bot. Exposure condition Water-retaining structures

= 912 mm2

ACI224R-01,Table 4.1

1- Locate the Neutral axis & Calculate setcion properties:X-X

εc= 0.000019

fc

εs'

d'= 56 As Top

(n-1)As Top N.A.

N.A. h= 300

Cc = 0.5fc*y*b

y= 51.83 N.A.

d= 244 As Bot.

nAs Bot.

A Tranformed Section

εs= 0.000070 Strain

T= fs * As Stress

b= 1000 Taking moment of areas @ X-X, [by+nAs Bot.+ (n-1)As Top]*y = by*y/2 + nAs Bot.*d + (n-1)As Top*d' and simplify in form of Quadratic equation (ay2+by+c=0), (b-b/2) * y2 + (nAs Bot.+ (n-1)As Top) * y + (-nAs Bot.*d - (n-1)As Top*d') = 0 Thus, a =

500.00 b= 12808.88 c = -2007060.08

Ig = bh3/12

Ag = b*h

= 2,250,000,000 mm4

Acr =by+ nAs Bot.+ (n-1)As Top

= 51.83 mm

Thus,

= 300,000 mm2

= 64,639 mm2

Icr =by3/12+by*(y/2)2+ nAs Bot.*(d-y)2+ (n-1)As Top*(y-d')2

= 299,865,909 mm4

2- Check of Concrete & Steel Reinforcement stresses:-

fc a = Ma*y/Icr

= 3.51

N/mm2

ACI 318M-11, Eq 9-10

= 52.61

KN.m

ACI 318M-11, Eq 9-9

= 0.50

N/mm2

= 0.016 fc'

2

Ok < f s max = 13.98 = 250.00 N/mm N/mm2 , ACI350-06, Eq 10-4 & 10-5 = 0.033 fy Ok < f s max= 320N/mm2 allowed for rebar Dia 12 mm used ,According ACI224R-04, Table4.2 Ok < f s max= 240N/mm2 allowed for spacing 125 mm used ,According ACI224R-04, Table4.3

fs a=Ma(y-d)/(Icr/n)

3- Calculation of crack width := 0.018 mm

Crack width,

ACI224R-01, Eq 4-2a

ok Crack Width 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

ncrete_by_Jack_C._McCormac_9th_Ed-2013-1118129849_ACI_318-11.rar

s = Ac /n