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RCC14 Crack Width

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Project

Spreadsheets to BS 8110etc The Concrete Centre


Client
Advisory Group Made by Date Page
Location
Grid line 1 RC 16-May-2023 34
Crack Width Calculations to BS8110: 2005/ BS8007:1987 Checked Revision Job No
Originated from RCC14.xls v 4.0on CD © 2006 TCC chg - R68

CRACK WIDTH CALCULATIONS - FLEXURE -

INPUT
fcu= 45 N/mm 2
fy= 500 N/mm 2
Area of reinforcement " As " = 1005 mm 2
b= 1000 mm
h= 325 mm
d= 285 mm
Minimum cover to tension reinforcement " CO " = 30 mm
Maxmum bar spacing " S " = 200 mm
Bar dia " DIA " = 20 mm
" acr " =(((S/2)^2+(CO+DIA/2)^2)^(1/2)-DIA/2) as default or enter other value = 97.70 mm
"acr " is distance from the point considered to the surface of the nearest longitudinal bar
Applied service moment " Ms "= 112.0 KNm

CALCULATIONS
moduli of elasticity of concrete " Ec" = (1/2)*(20+0.2*fcu) = 14.5 KN/mm 2
moduli of elasticity of steel " Es " = 200.0 KN/mm 2
Modular ratio " a " = (Es/Ec) = 13.79
" r " = As/bd = 0.004
depth to neutral axis, "x" = (-a.r +((a.r)2 + 2.a.r)0.5.d = 76 mm

" Z " = d-(x/3) = 260


Reinforcement stress " fs " = Ms/(As*Z) = 429 N/mm 2
Concrete stress " fc " = (fs*As)/(0.5*b*x) = 11.34 N/mm 2
Strain at soffit of concrete beam/slab " e1 " = (fs/Es)*(h-x)/(d-x) = 0.002557
Strain due to stiffening effect of concrete between cracks " e2 " =
e2 = b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.2 mm Used
e2 = 1.5.b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.1 mm n/a
e2 = 0.000492
Average strain for calculation of crack width " em "= e1-e2 = 0.002065

Calculated crack width, " w " = 3.acr.em/(1+2.(acr-c)/(h-x))


CALCULATED CRACK WIDTH, 'w' = 0.39 mm

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