Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment.
Material parameters
Grade of concrete
fck
Characteristic strength of concrete
Grade of steel
=
M 45
=
45 N/mm2
=
Fe 415
Yield stress of steel
fy
=
415 N/mm2
Max. Permissible stresses in concrete in compresssion (Bending)
σ cbc
=
14.5 N/mm2
=
165 N/mm2
m
=
6.44
1.5 x m
=
9.66
P
My
=
100200 kg
=
=
100000 kg.cm
=
15020000 kg.cm
=
15020333 kg.cm
Max. Permissible stresses for steel in flexural tension
Modular ratio
cl no.8.3.4 of
IS: 4651-part 4
Member forces
Axial load on pile
=
Moment on the pile
=
100.2 T
=
1 T.m
Moment on the pile
=
150.2 T.m
=
Mz
Resultant Moment on Pile
=
150.20 T.m
=
MRes
=
e
Check for eccentricity
Eccentricity
=
M/P
=
149.90 cm
>
16.3 cm
D
=
130 cm
R
Nb
=
65 cm
=
60 Nos
φ rebar
=
25 mm
Area of the longitudinal reinforcment
Ast
=
294.52 cm2
Clear cover to reinforcement
c
dc
=
7.5 cm
=
9.55 cm
Assuming that the steel bars are equivalent to a thin shell of the same cross sectional area
Dshell
Diameter of thin shell of reinforcement
=
110.9 cm
Limit of eccentricity for the entire cross section to be in compression
Geometrical parameters used in the evaluation of crack width of the pile
Diameter of Pile
=
1300 mm
=
Distance between centre of the section to the outer most fibre
No of longitudinal rebars
Diameter of longitudinal rebars
Effective cover = clear cover + cg of the rebar
ir
=
55.5 cm
deff
=
120.5 cm
Cos α
=
-0.259
Cos β
=
-0.303
Sin α
Sin β
=
0.966
=
0.953
α
β
=
1.8325 radians
=
1.8790 radians
Sin 4α
Sin 2α
Sin 2β
=
0.866
=
-0.500
=
-0.578
Distance between centre of section to cg of main steel (inner radius)
Effective depth of pile cross section
Secondary parameters used in the evaluation of crack width of the pile
Cos α =
Cos β =

Nd−0.5×D
0 .5×D

 Nd−0. 5× D 
r
Nd R
θ
R
N
α
dθ
β
A
Determination of neutral axis
Ast / (2 π r)
tshell
=
N
dn
=
=
48.18 cm
Total compression in concrete above neutral axis, Cc
Cc
=
Total compression in steel above neutral axis, Cs
Cs
=
1862 fs1
532 fs1
Total tension in steel below neutral axis, Ts
Ts
=
1058 fs1
Thickness of thin shell of reinforcement
Assuming Neutral axis depth Coefficient
Depth of Neutral axis (N x deff)
0.845 cm
0.4000
Expressions for evaluating fs1 from ∑P
Expressions for evaluating fs2 from ∑M
1 of 2
(0.125 x D)
Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment.
Moment of compression in concrete about the centre line of section
MCc
=
Moment of compression in steel about the centre line of section
MCs
=
83703 fs2
25207 fs2
Moment of tension in steel about the centre line of section
MTs
=
41746 fs2
Net axial stresses on the pile section
Caxial
=
Net bending stresses on the pile section
Cben
=
1337 fs1
150655 fs2
Evaluation 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 = (Cc + Cs - Ts) x fs1
fs1 = P/Caxial
=
75 kg/cm2
Evaluation of extreme fibre stress in concrete by second condition of equilibrium, i.e, ∑M = 0
Moment, M = (MCc + MCs + MTs) x fs2
fs2 = M/Cben
=
100 kg/cm2
Evaluation of internal forces & moments on cross section of pile
Total compression in concrete above neutral axis
Cc
=
139578 kg
Total compression in steel above neutral axis
Cs
=
39888 kg
Total tension in steel below neutral axis
Ts
=
79269 kg
Moment of compression in concrete about the centre line of section
MCc
=
8345164 kg.cm
Moment of compression in steel about the centre line of section
MCs
=
2513108 kg.cm
Moment of tension in steel about the centre line of section
MTs
=
4162050 kg.cm
Evaluation of distance of centroid of tensile steel from centre of cross section of the pile
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
been evaluated.
sinβ
cg = r×
β ra dians
cg
=
28.12 cm
Evaluation of extreme fibre stress in concrete
The mean value of fs1 & fs2 has been adopted as the final extreme fibre stress in concrete
σ cbc
Maximum compressive stress,
0.5 x (74.95 + 99.7)
fs1
=
75 kg/cm2
fs2
=
100 kg/cm2
=
87 kg/cm2
The distance of the centroid of tension steel from neutral axis has been evaluated as under
h1 = R  cg − d n
(65 + 28.12 - 48.18)
=
44.94 cm
The tensile stress at the centroid of tensile steel is evaluated as under
σ st =
m×σ cbc × h1
=
524 kg/cm2
dn
<
1682 kg/cm3
Safe
=
7 kips/inch2
The distance from neutral axis to extreme fibre (h2), where crack width is calculated has been evaluated as under
h2 =  2× R −d n
=
81.82 cm
Determination of crack width of concrete on tensile face of pile
The crack width of the pile has been evaluated by the following Gerely - Lutz Equation, given in ACI 318R-95 Commentary of Building
code requirements for structural concrete published by the American Concrete Institute.
cw =
γ=
A =
0. 076×γ×σ st × 3 d c × A
=
0.103 mm
1000
Dis tan ce of extreme tension fibre from Neutral Axis  h 2 
=
1.82
Dis tan ce of centroid of tension steel from Neutral Axis  h 1 
Effective tension area of concrete surrounding the flexural tension reinforcement and having the same
centroid, as that reinforcement, divided by the total number of bars in the pile
A=
π ×  D− 2× d−φ ×  2×d φ 
Nb
=
=
103.08 cm2
15.98 sq.inches
Summary
Actual Crack width
Permissible Crack width
=
0 inches
=
0.10 mm
<
0.30 mm (Refer Cl 8.3.4 of IS: 4651 (Part-4) - 1989)
Conclusion
As the actual crack width is less than the permitted crack width, the design is safe in Limit state of serviceability.
2 of 2
Hence safe