DESIGN OF PIERIVRCL INFRASTRUCTURES ANDPROJECTS LIMITEDDESIGN OF
PIER UNDER AQUEDUCT AT KM.
0.3342.200+203.6260.040+201.426m0.0400.400+201.386m0.4000.750+200.986m4.4390.051.100+200.236m5.3390.750+199.136m2.5891.1004.4395.339MFL
+198.6471.4891.000GL
+197.647m1.1002.000+196.547m1.1002.0000.9000.900+195.647m1.2004.800CROSS
SECTION OF THE
PIER4.3500.2003.7500.0750.7+203.6260.3500.04+201.426+201.386200.986+200.236+199.136GL
+197.6471.2001.1000.900+196.547+195.6474.800LONGITUDINAL SECTION OF
PIER1.8001.2001.8001.8004.8001.2001.8004.800Clear span of
trough=8.800mEffective span of trough=9.4mOverall length of
slab=10.000mDepth of slab=0.350mThickness of the wearing
coat=0.04mDiameter of the pier at top=1.200mDiameter of pier at
bottom=1.200mWidth of abutment1.200mWidth of pier cap=1.200mLength
of pier cap=4.550mWidth of trough slab=4.350mWidth of clear
trough=3.650mWidth of foundation offset=1.800mDepth of Water in the
trough=2.200mFree board=0.000mHeight of side walls=2.200mWidth of
side wall=0.350mClear cover for pier and pier
cap=40.000mm491.0714285714Main reinforcement provided for pier
cap25.000mm113.143reinforcement for
stirrups12.000mm78.5714285714Distribution
steel10.000mm113.1428571429Hanger bars12.000mmEffective depth for
the pier cap=0.75 + 1.1 - 40/1000 - 25/1000 -25/ 2000(steel
provided in two rows)=1.7725mHalf of the effective depth=1.7725 /
2=0.886m0.849m1.200m0.175Side of square inscribed in a
circle=SQRT(0.6 + 0.6)=0.849mHalf of the side of a
square=0.425mDistance from the outremost point of circle to side of
the square=0.6 - 0.425=0.175Clear span for LL=1.675 +
0.175=1.850mEffective span for LL=1.85 + 0.886=2.736mDESIGN OF PIER
CAP4.5500.7501.1001.6751.2001.675Self wt of the pier capWt of major
rectangular portion=0.75 x 1.2 x 4.55 x 2.5=10.238tWt of triangular
portion=1/2 x 1.1 x 1.675 x 1.2 x 2.5 x 2=5.528tWt of minor
rectangular Portion=1.2 x 1.1 x 1.2 x 2.5=3.96tTotal
load=19.726tWeight of trough slab:-Reaction from side walls from
staad out put=178.12t356.24Load due to self weight of cantelever
portionWt. triangular portion=1/2 x 1.1 x 1.675 x 1.2 x
2.5=2.764tWt. major rectangular portion=0.75 x (1.675 + 0.6) x 1.2
x 2.5=5.119t/mWt. minor rectangular portion=0.6 x 1.1 x 1.2 x
2.5=1.98t/m9.863t/mMax. B.M at face of the supportBM due to
LL=(178.12) x (2.736 - 0.1 - 0.175 )=438.353t-mBM due to DL=9.863 x
2.736/2=13.493t-mTotal Load=451.846t-mDESIGN CONSTANTSFor M25 grade
concrete and
Fe415Fck=25N/mm2sst=190N/mm2scbc=8.5N/mm2m=10.980k=0.329j=0.89Q=1.244Max
required depth of pier cap=(4518.46 X 10^6/(1.244 X
1200))^0.5=1740mmMax depth provided=1772.5mmHENCE SAFEArea of stel
required=4518.46 x 10^6/(190 x 0.89 x 1772.5)=15075.113mm2No of 25
mm dia bars required=31.000No'sArea of steel
provided=15223.214mm2HENCE SAFECheck for shearCritical plane occurs
at distance of d/2 from the face of the
support=1.675-1.7725/2=0.789mTotal depth of section at critical
section=(1.1 x 0.789 / 1.675) + 0.75=1.268mShear force at d/2 from
faceDue to dead load=19.726 x 1.268/2=12.506tDue to live
load=178.12=178.12tTotal=190.626tNominal shear stresstv=1906.26 x
10^3=19062601772.5 x 12002127000=0.896N/mm2Area of steel
provided=15223.2mm2% of steel provided=15223.2x 100=0.716%1850 x
1200Permissible shear stress =0.31 + ((0.36-0.31) / (0.75 - 0.5) x
0.216)=0.3531N/mm2Hence shear reinforcement is to be providedShear
force carried by concrete=1772.5 x 1200 x 0.3531=751043.7NVs =
V-(tv x bd)=1906260 - 751043.7=1155216.3NProvide 12 mm dia 4 legged
stirrupsSpacing Sv=(175 x 113.143 x 4 x 1772.5) /
1155216.3120mmAdopt Spacing of120 mmAs per article 26.5.1.5 of IS :
456 - 2000, maximum spacing of shearreinforcement is( I )
0.75d=0.75 x 1850=1387.5mm( ii ) 300 mm whichever is less.Hence
provide a spacing of=300mmHence provide12 mm dia @ 120 mm c/c
4-legged stirrupsDead load due to super structure:-Dead Load due to
superstructure=356.24t/mMOMENT DUE TO WIND FORCE:-As per clause
212.2 of IRC:6 - 2000CASE (I) DRAIN FULL CONDITIONAs per clause
212.3 of IRC :6 - 2000Height of side wall=2.2mExposed height over
trough bottom=0.35 + 0.04 + 2.2 + 0.05+0.35+0.7=3.69mCenter of
gravity of exposed area=3.69 x 3.69 / 23.69=1.845mCenter of gravity
of exposed area acts at a elevation of=200.986 +
1.845=202.831Height above FSL200.986 - 198.647 + 1.845=4.184mHeight
above base of pier202.831 - 196.547=6.284mWind pressure for a
height 4.184m=63.92Kg/m2Wind force at a height of 4.184m=10 x 3.69
x 63.92 / 1000=2.359tMoment due to wind force at top of foundation
of pier=2.359 x 6.284=14.824t-mMoment due to wind force at bottom
of foundation of pier=2.359 x 7.184=16.947t-mCASE (II) DRAIN EMPTY
CONDITIONCenter of gravity of exposed area acts at a elevation
of=202.831mHeight above CBL200.986 - 197.647 + 1.845=5.184mWind
pressure for a height 5.184m=68.92Kg/m2- + 1.845=6.284mWind force
at a height of 5.184m=10 x 3.69 x 68.92 / 1000=2.543t6.284=6.284mAs
per clause 212.3 of IRC :6 - 2000Wind pressure for a height
6.284m=0Kg/m2Area of super structure acted up on by wind pressure
(on each span)3.69 x=0m2Total wind force on deck slab0 / 1000 x x
3.69=0tThis force acts at center of area of pressure from top of
foundationMoment due to wind force at top of foundation of
pierMoment due to wind force at top of foundation of pier=2.543 x
6.284=15.98t-mMoment due to wind force at bottom of foundation of
pier=2.543 x 7.882t-m=18.269t-mCondition:- I canal full
conditionMoment due to wind force at top of
foundation=14.824t-mMoment due to wind force at bottom of
foundation=16.947t-mCondition:- II canal empty conditionMoment due
to wind force at top of foundation=15.98t-mMoment due to wind force
at bottom of foundation=18.269t-mCASE(2)As per clause212.6 of IRC:
6 - 2000The wind force as calculated should not be les than that
obtained by 450 Kg/m on the trough10 x 0.450=4.5tThis force acts at
center of the slabTherefore lever arm from top of foundation of
pier4.439 + 1.845=6.284mMoment due to wind force at top of
foundation4.5 x 6.284=28.278t-mThere fore lever arm at bottom of
foundation5.339 + 1.845=7.184mMoment due to wind force at bottom of
foundation4.5 x 7.184=32.328t-mCASE(3)As per clause 212.7 of
IRC-6-2000, Wind load on pier considered is=240Kg/m2Span on which
wind load acts=10mLateral wind force=10 x 3.69 x 240 /
1000=8.856tMoment at base of the pier8.856 x 6.284=55.651t-mMoment
at bottom of foundation8.856 x 7.184=63.622t-mTHE MAXIMUM OF THE
ABOVE THREE CASES IS CONSIDERED FOR DESIGNMoment due to wind force
at top of foundation=55.651t-mMoment due to wind force at bottom of
foundation=63.622t-mMOMENT DUE TO WATER CURRENTS:-CONDITION I: (IN
DRAIN FLOW DIRECTION)CASE: IAs per clause 213.2 of IRC:6 -
2000Force due to water currents in direction of drain flow is given
byV=1.414 x vv=Velocity of flow in drain=1.5m/secV=2.121m/secMax
velocity at the base of the pier=2 x 2.121 /
3=2.999m/secK=0.66Pressure due to water currents at FSDP=52 x 0.66
x 2.121=154.393Kg/m2Pressure due to water currents at drain bed
level=52 x 0.66
x2.999=308.674Kg/m21.20.4894.4391.2198.6472.58911.2197.6471.2Pressure
due to water currents at FSD=154.393Kg/m2Pressure due to water
currents at bottom of drain=308.674Kg/m2Area of pier profile
immersed in water1.2 x 1=1.2m2Total pressure due to water
currents.(154.393 + 308.674) / 2 x 1/1000 x 1.2=0.278tlever
arm(154.393 x 2 + 308.674)1=0.444m(154.393 + 308.674)3Depth of pier
from bottom level of drain to top level of foundation=1.1mMoment
due to water currents at top of foundation0.278 x (0.444 +
1.1)=0.4292t-mDepth of pier from canal bed level to bottom level of
foundation=2mMoment due to water currents at bottom of
foundation0.278 x (0.444 + 2)=0.6794t-mCASE ( II ) (A)Force
parrllel to the length of the pier :-Due to the cross currents as
per para 213.5 of IRC - 6 - 1966P =52 x K x V2K =0.66V = 20.5 x V x
cos(A)Maximum variation in the direction of currents=20Pressure at
FSL=52 x K x V2 x cos20=52 x 0.66 x 2.121 x cos
(20)=145.082Kg/m2Max velocity at the base of the pier=2 x 2.121 /
3=2.999m/secPressure at canal bed level=290.059Kg/m2Length of the
pier=1.2mHeight of water column=1mArea on which water pressure
acts=1.2m2lever arm(145.082 x 2 + 290.059)1=0.444m(145.082 +
290.059)3Total force=0.261tMoment due to this force at the top
foundation of the pier=0.261 x ( 0.444 + 1.1)=0.403t-mMoment due to
this force at the bottom of foundation concrete=0.261 x ( 0.444 +
2)=0.638t-mCASE ( II ) (B)Force perpendicular to the length of the
pier :-Due to the cross currents as per para 213.5 of IRC - 6 -
1966P =52 x K x V2K =1.5V = 20.5 x V x sin(A)Maximum variation in
the direction of currents=20Pressure at FSL=52 x K x V2=52 x 1.5 x
2.121 x sin 20=120.013Kg/m2Pressure at canal bed
level=80.006Kg/m2Length of the pier=1.2mHeight of water
column=1mArea on which water pressure acts=1.2m2lever arm(120.013 x
2 + 80.006)1=0.533m(120.013 + 80.006)3Total force=0.12tMoment due
to this force at the top foundation of the pier=0.12 x ( 0.533 +
1.1)=0.196t-mMoment due to this force at the bottom of foundation
concrete=0.12 x ( 0.533 + 2)=0.304t-mMaximum moments of both the
cases are considered for the designMoment at the base of the
pier=0.403t-mMoment at the base of the
foundation0.638t-mconcreteCONDITION II: (IN CANAL FLOW
DIRECTION)Water force in road way direction due to 250mm difference
in water levels between theopposite forces of the pier.Depth of
flow in drain=1mLength of pier immersed in water=1.2mDepth of pier
from CBL to the top of foundation1.1mMoment at top of
foundationM11/2 x (1) x (1 /3 + 1.1) x 1.2=0.86t-mM21/2 x (1.25) x
(1.25 / 3 + 1.1) x 1.2=1.422t-mM2-M1=0.562t-mMoment at bottom of
foundationM11/2 x ( 1) x (1 /3 + 2) x 1.2=1.4t-mM21/2 x (1.25) x
(1.25 /3 + 2) x 1.2=2.266t-mM1-M2=0.866t-mDRAIN FULL CONDITION:-(I)
TOTAL MOMENTS IN CANAL FLOW DIRECTIONTOP OF FOUNDATIONBOTTOM OF
FOUNDATIONCASE(I)CASE(I)Water currents0.5620.866Total
moments0.5620.866(II) TOTAL MOMENTS IN DRAIN FLOW DIRECTIONTOP OF
FOUNDATIONBOTTOM OF FOUNDATIONCASE(I)CASE(I)Wind
force55.65163.622Water currents0.4290.679Total
moments56.08064.301DRAIN EMPTY CONDITION:-(II) TOTAL MOMENTS IN
DRAIN FLOW DIRECTIONTOP OF FOUNDATIONBOTTOM OF
FOUNDATIONCASE(I)CASE(I)Wind force55.65163.622Total
moments55.6563.622SELF WEIGHT OF PIER:Weight of
bracket=19.726tWeight of circular pier=( 22/7) / 4 x (1.2) x 2.589
x 2.57.323t27.049Weight of displaced water due to pier (with 100%
buoyancy)(22/7)/4 x 1.2 x 1 x 1=1.131tSelf weight of pier with
(100% buoyancy)=19.726 + 7.323 - 1.13125.918tDirect loads at top of
foundation (when drain is full)Case(i)=25.918 +
356.24=382.158tDirect loads at top of foundation (when drain is
empty)Case(ii)=27.049 + 356.24=383.289tSELF WEIGHT OF
FOUNDATIONWeight of foundation=79.758tincluding top soilWeight of
foundation considering 100% Buoyancyincluding top
soil=43.912tDirect loads at bottom of foundationDirect loads at
bottom of foundation (when drain is full)Case(i)=382.158 +
43.912=426.07tDirect loads at bottom of foundation (when drain is
empty)Case(ii)=383.289 + 79.758=463.047tSECTIONAL PROPERTIES:-At
the base of the pierArea (a)=(22/7)/4 x(1.2)=1.131m2Section
modulus:Zxx = Zyy=PI x 1.2 / 32=0.17m3At the base of the
foundationArea=3.147 x 4.8 / 4=18.127m2Section modulusZxx=3.147 x
4.8 / 32=10.857m3Zyy=3.147 x 4.8 / 32=10.857m3CONDITION - ISTRESSES
AT TOP OF FOUNDATION (CONCRETE)(when drain is
full)Case(I)=382.1580.56256.0801.1310.170.17=337.8943.306329.884Max=671.084t/m2Min=4.704t/m2STRESSES
AT BOTTOM OF FOUNDATION (SOIL)(when drain is
full)Case(I)=426.070.86664.30118.12710.85710.857=23.5050.085.923Max=29.508t/m2Min=17.502t/m2CONDITION
- IISTRESSES AT TOP OF FOUNDATION (CONCRETE)(when drain is
empty)Case(I)=383.28955.6511.1310.17=338.894327.359Max=666.253t/m2Min=11.535t/m2STRESSES
AT BOTTOM OF FOUNDATION (SOIL)(when drain is
empty)Case(I)=463.04763.62218.12710.857=25.5455.86Max=31.405t/m2Min=19.685t/m2STRESS
TABLECONDITION(I)TOP OF FOUNDATIONBOTTOM OF
FOUNDATIONMAXMINMAXMINCASE(I)671.0844.70429.50817.502CONDITION(II)CASE(I)666.25311.53531.40519.685Calculated
direct compressive stress = 382.158 /
1.131=337.894t/m2sco(cal)Permissible direct
stress=800t/m2scoPermissible direct stress x
1.33=1064t/m2scoCalculated bending compressive stress=(0.562 /
0.17) + (56.0802 / 0.17)=333.189t/m2sc(cal)Permissible bending
compressive stresses=1000t/m2scPermissible bending compressive
stress x1.33=1330t/m2sc337.894+333.189=0.5684524mm2HENCE
SAFETransverse reinforcement:-(a)Diameter of transverse reinforcing
bar is the largest of the following(i) 1/4 th of the dia of
longitudinal bar=20/4=5mm(ii) or8mmHence provide 8 mm dia
bars(b)Spacing of transverse reinforcement is the least
of(i)Minimum spacing=300mm(ii)Least lateral dimension of the
member=1.2 x 1000=1200mm(iii)12 times the dia of longitudinal
bar=12 x 20=240mmHence provide a pitch of 240 mmCHECK FOR
PERMISSIBLE STRESSES IN STEEL AND CONCRETEArea of steel
providedAst=4712.389mm2Radius of the pierR=600mmClear cover
provided=40mmDia of steel provided=20mmRadius excluding
coverr=550mmMaximum axial load=3821.580KNMoment acting on the
column about X- axis=5.620KN - mHence eccentricity about X-axisex =
5.62 / 3821.580.001mMoment acting on the column about Y-
axis=560.802KN - mHence eccentricity about Y-axisey = 560.802 /
3821.580.147mResultant Eccentricity, e =ex2 + ey2=0.147mResutant
Moment, M=P x e=3821.58 x 0.147=561.772kN-mModular
ratiom=10.980mc=1.5 x 10.98=16.470Assume the thickness of
equivalent steel shell placed at a radius of r be ZZ
=4712.389=1.364mm2 p re =561.772=147mm3821.580n = kdThe value of k
may be assumed between 0.4 - 0.7, smaller value for larger
eccentricityd =1200 - 40 - 40 - 10 - 10=1100mmAssume
K=0.7007.215n=770mma1 ==73.541cosa1=0.283a2
==72.017sina1=0.959cosa1=0.283sin2a1=0.543sina2=0.951sin4a1=-0.912cosa2=0.309sin2a2=0.587C1
=2 x 600C'/(1+0.283) x
[0.959/3+3.14-1.284/2x0.283-0.283/4x0.543]=290841.979C'M1
=2x600C'/(1+0.283) x [(3.14 - 1.284)/8 -0.912/32+0.283/3 x
0.959]=96534846.1943944C'C2 =2 x 550x1.364(16.47-1)x
C'/(600+550x0.309) x (0.951 + (3.14 -1.257) x 0.309)=25415.365C'M2
=2 x 550 x 1.364(16.47 - 1) c' / (600 + 550x0.309) x ((3.14 -
1.257)/2+0.587/4))=9924049.01701734C'T =T =2 x 550 x 1.364 x 10.98
x c' / (600 + 550x0.309) x (0.951-1.257 x 0.309)=6620.629C'M3 =2 x
550x1.364x10.98/(600+550x0.309) x (1.257 / 2
-0.587/4)=3118128.255C'Equating the sum of internal forces to the
external forcesC1 + C2 - T = P290841.979C' + 25415.365C' -
6620.629C' = 3821580309636.715C'=3821580C'=12.342N/MM2Equating the
sum of internal moments to the external momentM1 + M2 + M3 =
M7.215109577023.466412C'=561772000N-MMC'=5.127N/MM2Adopt C'=1/2 x
(12.342 + 5.127)=8.735N/MM2HENCE OKt=10.98 x 8.735/770 x (1100 -
770)=41.104N/MM2HENCE OKDESIGN OF PIER FOOTING:-Maximum load coming
on to the foting=3832.89KNMax. Moment=636.22Kn - mDiameter of the
pier=1.200mThickness of the footing at the face of
support=0.9mThickness of footing at edge=0.3Footing
offset=1.8mDiamter of footing=4.8mReinforcement
provided=25mm491.719Distribution reinforcement=16mm201.408Clear
cover provided=75mmheight of soil above footing (at face of
support)=1.2mheight of soil above footing (at edge of
support)=1.8mAverage height of soil (above sloped portion)=1.5mArea
of footingArea of major circular portion=3.147 x 4.8 /
4=18.096m2Thickness of footing for major portion=0.3Average
diameter of the sloped portion of footing=(2.2 + 4.8) / 2=3.5mArea
of footing=3.147 x 3.5 / 4=9.621m2Thickness of footing in sloped
portion=0.6mWeight of major rectangular portion of footing=18.096 x
0.3 x 25=135.72KNWeight of footing in sloped portion=9.621 x 0.6 x
25=144.315KNTotal weight of footing=135.72 + 144.315=280.035KNArea
of soil above footing=3.147 (2.2 - 1.2) / 4=2.67m2height of soil
above footing (at face of support)=1.2mWeight of soil=2.67 x 1.2 x
21=67.284KNArea of soil above sloped portion=14.294m2Average height
of soil (above sloped portion)=1.5mWeight of soil above
footing=14.294 x 1.5 x 21=450.261KNTotal weight of soil=67.284 +
450.261=517.545KNTotal weight footing + soil=280.035 +
517.545=797.58KN79.758weight of footing + soil + pier=797.58 +
3832.89=4630.4743.912Exposed area of footing in plan=3.142 x 4.8 /
4=18.096m2Section modulus of footing=3.142 x 4.8 /321=10.857m3P
max.=4630.47+636.2218.09610.857=314.484Kn/m2P
min.=4630.47_636.2218.09610.857=197.284Kn/m21.2001.3000.5000.5001.3000.60.90.31.8001.8002.2004.800197.284314.484Stresses
at foundation levelMaximum stress intensity=314.484KN/m2Minimum
stress intensity=197.284KN/m2Intensity of stress at the face of the
pier=197.284 + ( 1.8 + 1.2) x (314.484 -
197.284)/4.8=270.534KN/m2B.M at sloped portion=R=2.4r=1.1=270.534 x
3.142 / 20 (2.4 - 1.1) x (3 x 2.4 - 2 x 2.4 x 1.1 - 2 x
1.1)=529.237Kn - mThere fore BM at the face of
support=732.79Effective depth required=732.79 x 10^61.244 X
10^3=767.502mmEffective depth provided=0.9 - 75 / 1000 - 25
/2000=0.813mHence safeRequired area of steel=732.79 x 10^6 / (190 x
0.89 x 0.813x1000)=5330.223mm2Required spacing of 25 mm dia
bars=491.719 x 1000 / 5330.223=90mm c/c(REQUIRED)Provided spacing
of 25 mm dia bars=90mm c/c(PROVIDED)Area of steel
provided=5464mm2Hence safeMin area of steel required=0.12 x 1000 x
813100=975.6
