x2 x1
0 0 0
1 2 1.414214
Chart Title
2 4 2
3 6 2.44949 12
4 8 2.828427
10
5 10 3.162278
6 12 3.464102 8
7 14 3.741657
8 16 4 6
9 18 4.242641
10 20 4.472136 4
11 22 4.690416
2
0
0 5 10 15
Horizontal force due to water currents
As per cl. 210.2 of
�= 〖 52 ��^2 〗∕ 1000 IRC 6:2017
where
P Intensity of pressure in t/m2
V Velocity of current at the point where pressure intensity is calculated in m/s
K constant depend upon shape of pier
Square of velocity at height 'X' from point of deepest scour
�^2=(2𝑉 ̅^2 𝑋)/�
𝑉 ̅ Maximun mean velocity in m/s
H height b/w free surface of water and point of deepest scour in m
Pier intented to be inclined at θ to the direction of current shall be designed for a
current direction inclined at (20±θ) degree to the length of pier
Horizontal force due to water currents on suface of constant width b
�= 〖 52 �� ^2 �� 〗∕ 1000
Effect of cross current shall not be less than static force due to difference
of head of 250mm b/w the opposite face of pier
cl. 210.7 not clear
𝑉 ̅ Maximun mean velocity 20 m/s
H height b/w free surface of water and 10 m
point of deepest scour
Type of Pier shape Piers with traingular cut and ease waters,
the angle included b/w the faces being
30o or less
K1 Constant 0.5
b Width 2m
P1 Pressure at free surface of water 20.8 t/m2
X1 height b/w free surface and pier bottom 9m
P2 Pressure at pier bottom 0.208 t/m2
F1 Horizontal force due to water currents 189.072 t
acting at 6 m above
M1 Moment at Pier bottom 1128.816 t-m pier bottom
Type of Pier shape
Square Ended Piers
K2 Constant 1.5
b Width 5.3 m
P3 Pressure at pile cap top 0.624 t/m2
X1 Depth of pile cap expose 1m
D Depth of pile cap 1.5 m
P4 Pressure at pile cap bottom 0 t/m2
F3 Horizontal force due to water currents 1.65 t
act at 1.17m above
M2 Moment at Pile bottom 1414.35 t-m pile cap bottom
Type of Pier shape
Pile foundation
K3 Constant 1.25
N No. of pile in row 2
b Eqivalent Width 4.8 m
P5 Pressure at pile top 0 t/m2
X1 Depth of pile expose 0m
F4 Horizontal force per pile 0t acting at 0 m below
pile cap bottom
Hydrodynamic forces on bridge pier and foundations
As per cl. 4.8 of IRC
�= 𝐶_𝑒 𝛼_ℎ � SP 114
Ce Coefficient depend on ratio of height of submerged portion of
pier (H) to radius of enveloping cyclinder R e
αh Design seismic coefficient
W Weight of water of the enveloping cyclinder
Chart Title
10 15 20 25
Pier shape K
Square Ended Piers 1.5
Circular Piers or piers with semi- circular ends 0.66
Piers with traingular cut and ease waters, the angle included b/w the faces
0.5 being 30 o or less
Piers with traingular cut and ease waters, the angle included b/w the faces
0.5 being more than 30 o
Piers with traingular cut and ease waters, the angle included b/w the faces
0.7 being less than 60 o
Piers with traingular cut and ease waters, the angle included b/w the faces
0.7 being more than 60 o
Piers with traingular cut and ease waters, the angle included b/w the faces
0.9 being less than 60 o
Piers with cut and ease waters of equilateral arcs of circles 0.45
Piers with arcs of cut and ease waters intersecting at 90 o 0.5
Pile foundation 1.25
Maximum velocity of water current shall be assumed √2 times maximum mean velocity of current
F Horizontal force due to water currents 208 t
acting at 2H/3 from point o
deepest scour
Line of action of force above pier bottom 5.970 m
Line of action of force above pile cap bott 1.166667 m
Line of action of force below pile cap bott 0m
H/Re Ce C1 C2 C3 C4
1 0.39 0.1 0.41 0.025 0.9345
2 0.575 0.2 0.673 0.093 0.8712
3 0.675 0.3 0.832 0.184 0.8103
4 0.73 0.4 0.922 0.289 0.7515
0.5 0.97 0.403 0.6945
0.6 0.99 0.521 0.639
0.8 0.999 0.76 0.532
1 1 1 0.4286
C1H C3F = Resultant Pressure on C1H
H C2Pb C4H
Scour Level
�_𝑏=1.2 �∕�
6.67 m
acting at 2H/3 from point of
deepest scour
