Typical Design Calculations of Pier
Typical Design Calculations of Pier
Typical Design Calculations of Pier
INTRODUCTION :
The type of pier is Wall type pier.
The pier is designed based on the critical load combinations as stipulated under IRC:6.
DATA :
1. SUPER STRUCTURE
C/C Distance between pier 8400 mm
C/C Distance between expansion joint 8400 mm
Overall length of deck slab 8300 mm
Carriageway Width 7500 mm
Overall Width of Deck. 7500 mm
Height of Superstructure 700 mm
Width of Crash Barrier 0 mm
Height of Crash Barrier 0 mm
Width of Foot Path 0 mm
Width of Hand rails 0 mm
Height of Hand rails 0 mm
Thickness of Wearing coat Average 65 mm
Thickness of Deck Slab 700 mm
Radius of Curvature 0.000 m
2. SUBSTRUCTURE
Formation RL +104.200
Level
7500
0 3750 3750 0
Pier Cap Top RL +103.500
Pier Cap Top RL +103.500 0
250
500
Pier Cap CG. RL +103.250
0
RL +103.000 7500
Pier Cap
Bottom
7500 0 6000 6500
Pier CG. RL +100.000
GL RL +100.000
Foundation top RL +97.000 3000
F.C.G. RL +96.250
1500
F.Bottom RL +95.500 150
0 4700 4700 0
9400
9700
TRANSVERSE VIEW OF PIER SECTION
1200
650
275 275
1200
0 0
1800 1200 1800
0 4800 0
4800
5100
LONGITUDINAL VIEW OF PIER SECTION
3.750 3.750
14.06 t/m
RA = 14.06*(9.2-0.05*2)*0.5+0*0+0.5*0*0+0+0*0.5 64.0 T
say 90.477 T
1) Crash Barrier
2) Wearing coat
Span-1 = 8.400 m
Load
S.No. Reaction due to Dead load
kN
1 Slab 950.00
2 Precast plan 0.00
3 Crash Barrier 200.00
4 Hand rails 0.00
5 Wearing Coat 75.00
6 Footpath live load 0.00
PERMANENT LOADS 1150.00
SURFACING LOADS 75.00
2. From Substructure
L B D V LOAD
S.No. Dead Load due to Nos
m m m m³ kN
1 Pedestal 0 0.000 0.000 0.000 0.000 0.000
1 7.500 1.200 0.500 4.500 112.500
2 Pier Cap
1 7.500 1.200 0.000 0.000 0.000
3 Pier Stem 1 7.500 1.200 6.000 42.390 1059.750
4 Foundation 1 9.400 4.800 1.500 67.680 1692.000
5 Soil below ground 1 9.400 4.800 3.000 135.360 2707.200
EFFECT OF ECCENTRICITY
Eccentricity in Longitudinal Direction
275 275
650
1200
0 0
TION CONDITION) SUMMARY OF FORCES AND MOMENTS AT BEARING LEVEL (CONSTRUCTION CONDITION)
Vertical Longitudinal Transverse Longitudinal Transverse
S.No. Description Force Force Force Moment Moment
kN kN kN kNm kNm
3 FOOTPATH LIVE LOAD 0.00 0.00 0.00 0.00 0.00
4 WEARING SURFACE 75.00 0.00 0.00 20.63 0.00
STRUCTION CONDITION)
VARRIABLE LOAD
1. CARRIAGEWAY LOADING
Impact Factor
For Class A 4.5 = 1.313
I.F. = 1 +
6+L
70R loading I.F. = = 1.250
Load Load * IF
S.No. Reaction due to Live Load
kN kN
SPAN 1
1 CLASS - A (ALL FWD) 1108.00 1454.25
2 CLASS - A (1L FWD + 1L BWD) 1108.00 1454.25
3 CLASS - 70R 1000.00 1250.00
4 Footpath live load 0.00 0.00
SPAN 2
1 CLASS - A (ALL FWD) 0.00 0.00
2 CLASS - A (1L FWD + 1L BWD) 0.00 0.00
3 CLASS - 70R 0.00 0.00
4 Footpath live load 0.00 0.00
DESIGN LIVE LOAD 1108.0kN 1454.3kN
RL +105.400
1200
RL +104.200
1.90
2.15
RL +103.500 8.40
RL +103.500 9.90
RL +103.250
RL +100.000
RL +100.000
RL +97.000
RL +95.500
650
275 275
1200
0 0
CLASS - A (ALL FWD)
Live load moment (SPAN 1) 399.92 kNm
Live load moment (SPAN 2) 0.00 kNm
Longitudinal eccentric LL moment 399.92 kNm
CLASS - 70R
Live load moment (SPAN 1) 343.75 kNm
Live load moment (SPAN 2) 0.00 kNm
Longitudinal eccentric LL moment 343.75 kNm
500 500
0.655 m
7.500 m
Total load = 1000.00 kN
Impact factor = 1.250
Moment due to 70R = 818.8 kNm
2L Class A Loading
3.750 m ₠
3.500 m
0.45 0.4
1.8 1.7 1.8 0 0
277 277 277 277 0 0
0.250
7.500 m
Total load = 1108.00 kN
Impact Factor = 1.313
Moment due to 3 lane Class A loading = 363.6 kNm
2. EFFECT OF BRAKING
No of lanes = 2
(IRC:6 - 2014, Cl 211.2, Page 37)
1. 20 % of Ist Train Load. + 10% of succeding Train Loads for Single or a Two Lane Bridge.
2. 20 % of Ist Train Load. + 10% of succeding Train Loads + 5 % of Loads on the lanes exceeding two
Since 2 lane is governing in transverse eccentric moment, only 2 lane loading has been considered
a) 1 lane of 70R
Total load of 70R wheeled vehicle = 1000.00 kN
Braking Force = 0.20 x 1000 = 200.00 kN
Horizontal force on pier = 200.00 kN
b) 2 lane of Class A
Ist Train Load 0.20 x 554 = 110.80 kN
Succeding Train Loads 0.05 x 554 27.70 kN
Braking Force = 138.50 kN
RL +104.200
0
RL +104.200
0.35
RL +103.500 0.85
RL +103.500 6.85
8.35
RL +103.000
RL +100.000
RL +100.000
RL +97.000
RL +95.500
650
275 275
1200
0 0
Average height exposed surface of pier stem above Bed level = 3.500 m
Average height in meters of the exposed surface above Bed level = 4.200 m
Vz Pz
H
(m/s) (kN/m²)
4.200 27.800 0.463
RL +105.700
1.500
RL +104.200
0.700 2.20
2.70
RL +103.500 8.70
RL +103.500 10.20
RL +103.000
#REF!
RL +100.000
RL +97.000
RL +95.500
d or t = 7500 mm
LONGITUDINAL DIRECTION
Average height exposed surface of pier above Bed level = 3.500 m
Exposed area of substructure(Transverse), A1 = b x H = 1.200h.m²
Gust factor G = 2
( IRC:6-2014,CL: 209.3.3 Page 31)
Thickness to breadth ratio t / b = 6.250
(IRC:6-2014 , Table:6, page 33)
Height to breadth ratio H / B = 2.917
(IRC:6-2014 , Table:5, page 29)
Drag coefficient CD = 0.900
(IRC:6-2014 CL 209.4, PAGE 33)
The transverse wind Force (FT in N) shall be taken as acting at the centroids of the
appropriate areas and horizontally and shall be estimated from the following eqn
(IRC:6-2014 ,CL 209.3.3,PAGE 31)
The Transverse Wind Force FT = PZ X A1 x G x CD
(IRC:6-2014 CL 209.3.3, PAGE 31)
FT = 0.939 x 1.200 x 2 x 0.900 = 2.03h kN
7500
1mm
6.500 m
Horizontal force in kN required to be applied at the centre of mass of superstructure for one mm
deflection at the top of the pier/abutment along the considered direction of horizontal force.
T = 2 x D = 0.016 sec
1000 x F
Ah = 0.119
The horizontal seismic force acting at the centers of mass, which are to be resisted by the structure as a whole,
shall be computed as follows.
(IRC:6 - 2014, Cl 219.5.1, Page 53)
The Forces on various members of bridge structure (i.e.,Ah) are to be divided by Response Reduction Factor
given in table 8 before combining with other forces as per load combination Given in table 1
(Page 56,Cl 219.5.5,IRC:6-2014).
Feq. =
Seismic force to be resisted Ah x (Dead Load +Appropriate Live Load)
R
Lever arms
#########
#########
#########
#########
#########
#########
6.850
6.500
######### 6.250 8.350
3.000 8.000
######### 7.750
4.500
#########
#########
#########
3750
7500
3750
1200
Ast = 58905mm²
Ac = 1072068mm²
Ag = 1562746mm²
Ixx = 4.4E+13mm4
Iyy = 1.1E+12mm4
Zxx = 1.2E+10 mm³
Zyy = 1.8E+9 mm³
rxx = 5306 mm
ryy = 831 mm
ey = 429 = 0.023
heq 18381
ex = 183 = 0.063
beq 2880
BI AXIALBENDING
(Eq 8.3, Page 75,IRC:112-2011)
Design value of axial force NEd = 7292.00 kN
Gross area of the C/S Ac = 1562746mm²
Area of longitudinal R/F Ast = 42194mm²
Design axial resistance of section
NRd = Ac * fcd + As * fyd
1562746 x 11.17 + 42194 x 434.78 = 35795.94 kN
1000
MEd = MoEd + M2
M2 = NEd * e2
1/r = Kr * Kφ * (1/ro)
Kφ = 1+ βɸeff ≥ 1
Kr = (nu-n)/(nu-nbal.) ≤ 1
1 / ro = εyd = 0.002174 = 5.33E-07
0.45 * d 0.450 x 9056
n = 0.204
nbal. = 0.400
nu = 1 + As * fyd = 1 + 58905 x 434.78 = 3.139
Ac * fcd 1072068 x 11.17
β = 0.35 + fck λ
-
200 150
φeff. = = 1
Kr = (nu-n)/(nu-nbal.) ≤ 1 = = 1.000
Kφ = 1 + βφeff ≥ 1 = 1.000 + 0.463 x 1.000 = 1.463
1/r = = 7.80E-07
le = = 14950 mm
c = 10 * π2 = 98.70
e2 = (1/r) * (le2 / c ) = 1.767
MEd = MoEd + M2
MEd = 3127.80 + 12.885 = 3140.69 kNm
α = 2
Moment resistance in the x - direction
MRdx = NRd x ex = 35795.94 x 183 = 6545.46 kNm
Design moments
MEdx = 1333.38 kNm
MEdy 3127.80 kNm
α α
Medx Medx
+ ≤ 1
MRdx MRdx
2 2
1333.38 3127.80 = 0.083
+
6545.46 15354.18
SAFE
Bi-Axial Column
Design Loads
Pu = 7292 kN
Mux = 1339 KN-m
Muy = 3129 KN-m
Col Data
b= 1200 mm
D= 7500 mm
d' = 50 mm
d'/D = 0.05
d'/b = 0.05
Material Grades
fck = 25
fy = 500
Design Constants
Steel % pt = 0.655
pt/fck = 0.022
Pu/fck*b*D = 0.03
Mux/fck*b*D2 = 0.05
Muy/fck*D*b2 = 0.05
Puz = 142810 kN
Mux1 = 101250 KN-m
Muy1 = 16200 KN-m
Pu/Puz = 0.050
Mux/Mux1 = 0.010
Muy/Muy1 = 0.190
αn = 1
Steel Percentage OK
CALCULATION OF HORIZONTAL REINFORCEMENT :
(IRC 112 : 2011, Cl. 16.3.2 )
Area of horizontal reinforcement is the greater of
1 As = 0.25 x Area of vertical reinforcement
= 0.25 x 58905 = 14726mm²
OR
2 As = 0.001 x Gross Area of Concrete
= 0.001 x 9600000 = 9600mm²
Load Pu 7292 KN
Design Load P 5104 KN
Zx 51.84
Zx 145.80
Footing Size OK
2 Slab Design
lx 3.000
ly 1.800
Spacing c/c in mm
Area of Steel
10# 12# 16# 20#
1728 sqmm 45 c/c 65 c/c 116 c/c 182 c/c
1728 sqmm 45 c/c 65 c/c 116 c/c 182 c/c
Minimum Ast required across x direcion
Minimum Ast required across y direcion
Vu1 1197 KN
ζv 0.173 MPa
ζc 0.287 MPa
Vc1 1983 KN
Vu1 777 KN
ζv 0.040 MPa
ζc 0.287 MPa
Vc1 5578 KN
7500
##
B= 4.80 meters
1500 mm
1000 mm
SRB SRB
a 0.8744 a 0.8744
b -4.3500 b -4.3500
c 0.3468 c 0.1249
-p 0.0811 -p 0.0289
Ast 1167 Ast 416