8/10/2019 77623202-Crack-Width.xls

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Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment.

Material parameters

Grade of concrete = M 45Characteristic strength of concrete f ck = 45 N/mm

Grade of steel = Fe 415

Yield stress of steel f y = 415 N/mm2

Max. Permissible stresses in concrete in compresssion (Bending) = 14.5 N/mm 2

Max. Permissible stresses for steel in flexural tension = 165 N/mm 2

Modular ratio m = 6.44

1.5 x m = 9.66

Member forces

Axial load on pile = 100.2 T = P = 100200 kg

Moment on the pile = 1 T.m = M y = 100000 kg.cm

Moment on the pile = 150.2 T.m = M z = 15020000 kg.cm

Resultant Moment on Pile = 150.20 T.m = M Res = 15020333 kg.cm

Check for eccentricityEccentricity = M / P = e = 149.90 cm

Limit of eccentricity for the entire cross section to be in compression > 16.3 cm (0.125 x D)Geometrical parameters used in the evaluation of crack width of the pile

Diameter of Pile = 1300 mm = D = 130 cm

Distance between centre of the section to the outer most fibre R = 65 cm

No of longitudinal rebars N b = 60 Nos

Diameter of longitudinal rebars f rebar = 25 mm

Area of the longitudinal reinforcment A st = 294.52 cm2

Clear cover to reinforcement c = 7.5 cm

Effective cover = clear cover + cg of the rebar d c = 9.55 cm

Diameter of thin shell of reinforcement D shell = 110.9 cmDistance between centre of section to cg of main steel (inner radius) i r = 55.5 cm

Effective depth of pile cross section d eff = 120.5 cm

Secondary parameters used in the evaluation of crack width of the pile

Cos a = -0.259

Cos b = -0.303

Sin a = 0.966Sin b = 0.953

a = 1.8325 radiansb = 1.8790 radians

Sin 4 a = 0.866Sin 2 a = -0.500Sin 2 b = -0.578

Determination of neutral axis

Thickness of thin shell of reinforcement t shell = 0.845 cm

Assuming Neutral axis depth Coefficient N = 0.4000

Depth of Neutral axis (N x d eff ) dn = 48.18 cm

Expressions for evaluating f s1 from P

Total compression in concrete above neutral axis, C c C c = 1862 f s1Total compression in steel above neutral axis, C s C s = 532 f s1

Total tension in steel below neutral axis, T s Ts = 1058 f s1Expressions for evaluating f s2 from M

Moment of compression in concrete about the centre line of section MCc = 83703 f s2Moment of compression in steel about the centre line of section MCs = 25207 f s2

Ast / (2 p r)

cl no.8.3.4 ofIS: 4651-part 4

Assuming that the steel bars are equivalent to a thin shell of the same cross sectional area

r

D5.0NdCos

b

a

D5.0D5.0Nd

Cos

R ab

d

RNd

N A

cbc

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8/10/2019 77623202-Crack-Width.xls

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Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment.

Moment of tension in steel about the centre line of section MTs = 41746 f s2

Net axial stresses on the pile section C axial = 1337 f s1Net bending stresses on the pile section Cben = 150655 f s2Evaluation of extreme fibre stress in concrete

Evaluation of extreme fibre stress in concrete by first condition of equilibrium, i.e, P = 0

Axial Load, P = (C c + C s - T s) x f s1 = 75 kg/cm2

Evaluation of extreme fibre stress in concrete by second condition of equilibrium, i.e, M = 0

Moment, M = (M Cc + M Cs + M Ts ) x f s2 = 100 kg/cm2

Evaluation of internal forces & moments on cross section of pile

Total compression in concrete above neutral axis C c = 139578 kg

Total compression in steel above neutral axis C s = 39888 kg

Total tension in steel below neutral axis T s = 79269 kg

Moment of compression in concrete about the centre l ine of section M Cc = 8345164 kg.cm

Moment of compression in steel about the centre line of section M Cs = 2513108 kg.cm

Moment of tension in steel about the centre line of section M Ts = 4162050 kg.cmEvaluation of distance of centroid of tensile steel from centre of cross section of the pile

cg = 28.12 cm

Evaluation of extreme fibre stress in concrete

The mean value of f s1 & f s2 has been adopted as the final extreme fibre stress in concrete

f s1 = 75 kg/cm2

f s2 = 100 kg/cm2

Maximum compressive stress, = 87 kg/cm 2

The distance of the centroid of tension steel from neutral axis has been evaluated as under

= 44.94 cm

The tensile stress at the centroid of tensile steel is evaluated as under = 524 kg/cm 2

< 1682 kg/cm 3 Safe= 7 kips/inch 2

= 81.82 cm

Determination of crack width of concrete on tensile face of pile

= 0.103 mm

= 1.82

= 103.08 cm 2

= 15.98 sq.inches

Summary

Actual Crack width = 0.004041 inches

= 0.10 mm

Permissible Crack width < 0.30 mm ( Refer Cl 8.3.4 of IS: 4651 (Part-4) - 1989 ) Hence safeConclusion

f s1 = P/C axial

f s2 = M/C ben

The distance from neutral axis to extreme fibre (h 2), where crack width is calculated has been evaluated as under

The distance of centroid of tensile steel, which is in the form of an arc of a circle, from the centre of the cross section of the pile has beenevaluated.

As the actual crack width is less than the permitted crack width, the design is safe in Limit state of serviceability.

A =

The crack width of the pile has been evaluated by the following Gerely - Lutz Equation, given in ACI 318R-95 Commentary of Buildingcode requirements for structural concrete published by the American Concrete Institute.

Effective tension area of concrete surrounding the flexural tension reinforcement and having the samecentroid, as that reinforcement, divided by the total number of bars in the pile

0.5 x (74.95 + 99.7)

(65 + 28.12 - 48.18)n1 dcgRh

n

1cbcst d

hm

n2 dR2h

1000

Ad076.0cw

3cst

)h( AxisNeutralfromsteeltensionof centroidof cetanDis

)h( AxisNeutralfromfibretensionextremeof cetanDis

1

2

bN

d2d2D A

ffp

)radians(sin

r cgb

b

cbc

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