Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment Material !arameters Grade of concrete f c)
Characteristic strength of concrete Grade of steel
=
M "#
=
45 mm2
=
Fe "1#
Yield stress of steel
f -
=
415 mm2
Max. Permissible stresses in concrete in compresssion !ending"
σ cbc
=
1"# mm2
=
1$5 mm2
Max. Permissible stresses for steel in flex#ral tension Mod#lar ratio
m
=
$.44
1.5 x m
=
%.$$
=
P
=
1((2(( )g
cl no.6.+.4 of 89: 4$51part 4
Member forces &xial load on pile
=
100$ '
Moment on the pile
=
1 '.m
=
M-
=
1((((( )g.cm
Moment on the pile
=
1#0$ '.m
=
M;
=
15(2(((( )g.cm
*es#ltant Moment on Pile
=
15(.2( '. '.m
=
M*es
=
15(2(+++ )g )g.cm
=
e
=
14%.%( cm
1$.+ cm
0
=
1+( cm
* b
=
$5 cm
=
)0 os
0iameter of longit#dinal rebars
f rebar
=
$# mm
&rea of the longit#dinal reinforcment
&st
=
2%4.52 cm2
c dc
=
*# cm
=
%.55 cm
Assuming that the steel bars are equivalent to a thin shell of the same cross sectional area 0shell 0iameter of thin shell of reinforcement =
11(.% cm
Check for eccentricit% ,ccentricit-
=
MP
/imit of eccentricit- for the entire cross section to be in compression 'eometrical !arameters used in the e(aluation of crack width of the !ile 0iameter of Pile
=
1300 mm
=
0istance beteen centre of the section to the o#ter most fibre o of longit#dinal rebars
Clear co3er to reinforcement ,ffecti3e co3er = clear co3er cg of the rebar
ir
=
55.5 cm
deff
=
12(.5 cm
Cos a
=
(.25%
Cos b
=
(.+(+
9in a
=
(.%$$
9in b
=
(.%5+
a b
=
1.6+25 radians
=
1.67%( radians
9in 4a
=
(.6$$
9in 2a
=
(.5((
9in 2b
=
(.576
0istance beteen centre of section to cg of main steel inner radi#s" ,ffecti3e depth of pile cross section +econdar% !arameters used in the e(aluation of crack width of the !ile
(
Nd −0 . 5 × D 0. 5 × D
= Cos α = Cos β =
)
( Nd −0 . 5× D ) r
Nd R θ R
N
α
dθ
β
A
Determination of neutral axis tshell
=
&ss#ming e#tral axis depth Coefficient
=
0epth of e#tral e#tral axis x deff "
dn
=
46.16 cm
'otal compression in concrete abo3e ne#tral axis< Cc
Cc
=
16$2 f s1
'otal compression in steel abo3e ne#tral axis< Cs
Cs
=
5+2 f s1
'otal tension in st eel belo ne#tral axis< 's
/s
=
1(56 f s1
'hic)ness of thin shell of reinforcement
&st 2 p r"
(.645 cm (.4(((
,x!ressions for e(aluatin- fs1 from .P
,x!ressions for e(aluatin- fs$ from .M 1 of 2
(.125 x 0"
Determination of Crack width for 1300mm dia Pile subjected to Axial Load & Moment Moment of compression in concrete abo#t the centre line of section
MCc
=
Moment of compression in steel abo#t the centre line of section
MCs
=
6+7(+ f s2 252(7 f s2
Moment of tension in steel abo#t the centre line of section
M's
=
4174$ f s2
et axial stresses on the pile section
Caxial
=
1++7 f s1
et bending stresses on the pile section
Cben
=
15($55 f s2
,(aluation of extreme fibre stress in concrete Evaluation of extreme fibre stress in concrete by first condition of equilibrium, i.e, >P = ( &xial /oad< P = Cc Cs 's" x f s1
f s1 = PCaxial
75 )gcm2
=
Evaluation of extreme fibre stress in concrete by second condition of equilibrium, i.e, >M = ( Moment< M = MCc MCs M's" x f s2
f s2 = MCben
=
'otal compression in concrete abo3e ne#tral axis
Cc
=
1+%576 )g
'otal compression in steel abo3e ne#tral axis
Cs
=
+%666 )g
'otal tension in steel belo ne#tral axis
's
=
7%2$% )g
Moment of compression in concrete abo#t the centre line of section
MCc
=
6+451$4 )g.cm
Moment of compression in steel abo#t the centre line of section
MCs
=
251+1(6 )g.cm
Moment of tension in steel abo#t the centre line of section
M's
=
41$2(5( )g.cm
1(( )gcm2
,(aluation of internal forces & moments on cross section of !ile
,(aluation of distance of centroid of tensile steel from centre of cross section of the !ile 'he distance of centroid of tensile steel< hich is in the form of an arc of a circle< from the centre of the cross section of the pile has been e3al#ated. sin β cg = r × cg = 26.12 cm β radians
(
)
,(aluation of extreme fibre stress in concrete 'he mean 3al#e of f s1 ? f s2 has been adopted as the f inal extreme fibre stress in concrete
Maxim#m compressi3e stress<
σ cbc
(.5 x 74.%5 %%.7"
f s1
=
75 )gcm2
f s2
=
1(( )gcm2
=
* k-cm$
'he distance of the centroid of tension steel from ne#tral axis has been e3al#ated as #nder
h1 = R + cg − d n
$5 26.12 46.16"
=
44.%4 cm
'he tensile stress at the centroid of tensile steel is e3al#ated as #nder σ st =
m ×σ cbc× h1
=
524 )gcm2
dn
1$62 )gcm+
+afe
= 7 )ipsinch2 'he distance from ne#tral axis to extreme fibre h2"< here crac) idth is calc#lated has been e3al#ated as #nder
(
)
h2 = 2× R − d n
=
61.62 cm
Determination of crack width of concrete on tensile face of !il e 'he crac) idth of the pile has been e3al#ated b- the folloing Gerel- /#t; ,#ation< gi3en in &C8 +16*%5 Commentar- of !#ilding code re#irements for str#ct#ral concrete p#blished b- the &merican Concrete 8nstit#te.
cw = γ = & =
0. 076
3 d c × A × γ ×σ st ×√
=
(.1(+ mm
1000
Dis tan ce of extreme tension fibre from Neutral Axis ( h 2 )
=
1.62
Dis tan ce of centroid of tension steel from Neutral Axis ( h1 )
,ffecti3e tension area of concrete s#rro#nding the flex#ral tension reinforcement and ha3ing t he same centroid< as that reinforcement< di3ided b- the total n#mber of bars in the pile
