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Chapter 7 Design of Piled Foundations
7.0 NOT A TION
a Deflection due to slenderness of a circular pile av Distance
of shear plane fro m nearest support ax Deflection due to
slenderness producing additional moment about x-axis ay Deflection
due to slenderness producing additional moment about y-axis A c Net
area of concrete in a p ile cross-section Ap Cross-sectional area
of pile (m2) A s Surface area of pile in contact with soil Av Total
area of link bars perpendicular to longitudinal bars Asc Total area
of steel reinforcement in a pile A51 Area of tensile reinforcement
in pile cap Asv Area of steel effective in resisting shear in a
pile A sx Area of tensile steel in a pile section resisting moment
about b-axis A sy Area of tensile steel in a pile section resisting
moment about h-axis b Width of reinforced concrete section b
Overall dimension of rectangular pile section b' Effective depth of
tensile reinforcement in b direction B Width or diameter of pile B
Overall width of a group of piles c Soil cohesion for a stratum
(kN/m2) CH Horizontal load-carrying capacity of a single pile Cv
Vertical load-carrying capacity of a single pile d Effective depth
to tensile re inforcement in a concrete section D Depth of a group
of piles below ground Dr Relative density ex Eccentricity of
combined unfactored vertical load on pile cap in x-direction ey
Eccentricity of combined unfactored vertical load on pile cap in
y-direction e11x Eccentricity in x-direction of combined unfactored
horizontal load Hy ehy Eccentricity in y-direction of combined
unfactored horizontal load Hx Er Stress-strain modulus of pile
material {kN/m2) Es Stress-strain modulus of soil (kN/m2) fc Stress
in concrete due to prestress aJone f s Skin resistance at soil/pile
interface f1 Maximum design principal tensile stress in concrete /y
Characteristic yield strength of steel reinforcement /ci Cube
strength of concrete at transfer of prestress
293
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294 Reinforced Concrete
[cp Average concrete stress in a prestressed concrete section
after losses feu Characteristic cube strength of concrete at 28
days [pc Average tensile stress in steel tendons after all losses
[pu Characteristic ultimate strength of steel tendons [yv
Characteristic yield strength of shear reinforcement h Overall
depth of pile cap h Overall dimension of a rectangular pile h
Overall diameter of a circular pile h' Effective depth of tensile
reinforcement in a rectangular pile in h-direction H Unfactored
horizontal load on a single circular pile H x Unfactored combined
horizontal loads on pile cap in x-direction H.v Unfactored combined
horizontal loads on pile cap in y-direction Hpx Unfactored
horizontal load on a single pile in x-direction Hpy Unfactored
horizontal load on a single pile in y-direction H.m Ultimate
horizontal load on pile cap in x-direction H_.u Ultimate horizontal
load on pile cap in y-direction Hpxu Ultimate horizontal load on a
single pile in x-direction H pyu Ultimate horizontal load on a
single pile in y-direction lr Moment of inertia of pile (m4) 1:
Polar moment of inertia of a group of piles about z-axis through CG
fx x Moment of inertia of a group of piles about x-x axis through
CG of group f.v.v Moment of inertia of a group of piles about y-y
axis through CG of group k, Modulus of subgrade reaction of soil
(kN/m3) K, Coefficient of friction K, Factor used to determine
transmission length of prestressing wires or
strand lc Effective length of pile for calculation of
slenderness ratio 10 Unsupported length of pile / 1 Transmission
length of prestressing wires or strands L Depth of penetration of
pile L Overall length of a group of piles Lb Average depth of pile
in ground m Modular ratio Esl Ec mv Coefficient of volume
compressibility (m2 /kN) M Factored bending moment in a circular
pile section M0 Moment to produce zero stress at tension fibre of a
prestressed section
with 0.8/cp (average uniform prestress) Mp Unfactored bending
moment in a single circular pile M x Unfactored combined moment on
pile cap about x-axis M .v Unfactored combined moment on pile cap
about y-axis
M~ Modified bending moment about x-axis to account for biaxial
bending M.~ Modified bending moment about y-axis to account for
biaxial bending M; Unfactored moment about x-axis due to eccentric
surcharge on pile cap
M.~ Unfactored moment about y-axis due to eccentric surcharge on
pile cap Mpx Unfactored bending moment in a single pile about
x-axis due to Hpy Mp.v Unfactored bending moment in a single pile
about y-axis due to Hpx Mxx Unfactored combined moment on pile
group about x-axis M yy Unfactored combined moment on pile group
about y-axis
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Mp.ru Mpyu Madd.x
Madd _v n
N N Nq Nu Ny N~ N~ Nu, Nbal p Px
p Pa Pu Ppu P si
ii qc qu qcs R R;H R;v s
Sv T Ta Tu u v
Design of Piled Foundations 295
Ultimate bending moment in pile about x-axis Ultimate bending
moment in pile about y-axis Additional bending moment in pile about
x-axis due to slenderness Additional bending moment in pile about
y-axis due to slenderness Slenderness ratio in a prestressed pile
Statistical average of SPT number for a soil stratum Combined
vertical load on pile cap - unfactored Soil bearing capacity
coefficient as per Terzaghi Ultimate vertical load on a circular
pile Soil bearing capacity coefficient as per Terzaghi Adjusted
bearing capacity factor for cohesion Adjusted bearing capacity
factor for Ll 8 > 1 Design ultimate capacity of a concrete
section subjected to axial load only Design axial load capacity of
a balanced section ( = 0.25 fcubd) Percentage of tensile
reinforcement in a circular pile Percentage of tensile
reinforcement in a pile section to resist bending about x-axis
Percentage of tensile reinforcement in a pile section to resist
bending about y-axis Total vertical load on a group of piles
Allowable unfactored vertical load on pile Ultimate axial
compressive load on pile End-bearing resistance of pile Skin
friction resistance of pile Effective vertical stress at pile point
Statistical average of cone resistance of soil in a stratum (kN/m2)
Unconfined compressive strength (kN/m2) Side friction resistance in
a cone penetrometer Number of piles in a group Initial estimate of
number of piles based on total horizontal load Initial estimate of
number of piles based on total vertical load Spacing of nodes in
pile for finite element analysis Spacing of links used as shear
reinforcement Unfactored torsion on a group of piles Allowable
unfactored tension load on pile Ultimate axial tensile load on pile
Perimeter at punching shear plane in a pile cap Shear stress in
concrete in pile cap Design concrete shear stress in concrete Shear
stress in concrete for shear due to bending about x-axis Shear
stress in concrete for shear due to bending about y-axis Modified
design shear stress to take into account axial compression Design
shear stress in concrete for shear due to bending about x-axis
Design shear stress in concrete for shear due to bending about
y-axis Ultimate shear force in a circular pile section Shear
resistance of a concrete section Shear resistance of uncrackcd
prestressed section Shear resistance of cracked prestressed
section
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296 Reinforced Concrete
W Weight of pile (kN) z Depth of lever arm
a Coefficient for calculation of skin resistance of a pile f3
Factor for computation of effective length of a pile j3 Factor for
conversion of biaxial bending moment into uniaxial bending y Unit
weight of soil (kN/m3) 0 Angle of friction between soil and
concrete J.l. Poisson's ratio Angle of internal friction Nominal
diameter of tendon in prestressed concrete section
7.1 VERTICAL LOAD - SINGLE PILE CAPACITY
Ft. = Applioo load
1 . t Psi 11 tPsi
1 . tSkin friction 1 t
Ppu= End b~aring SK 711 Single pile capacity.
P u = P pu + "LPs; - W Tu = 'LPs; + W
where Pu = ultimate compressive load on pile Tu = ultimate
tensile load on pile
'LP,; = skin friction resistance P pu = end-bearing
resistance
W = weight of pile
First method for point resistance
(see Reference 6, page 602)
where Ap = cross-sectional area of pile (m2) N = statistical
average of the SPT number in a zone of about 88
above to 38 below the pile point
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Design of Piled Foundations 297
B = width or diameter of pile Lb = average depth of pile in the
ground
Second metlwd for poinJ resistance Ppu = Apqc (see Reference 6,
page 602) where Ap = cross-sectional area of pile (m2)
qc = statistical average of cone point resistance in a zone of
about 88 above to 38 below pile point (kN/m2)
Third metlwd for poinJ resistance (see Reference 6, page
598)
where Ap = cross-sectional area of pile (m2) c = cohesion or
undrained shear strength Su = qu/2 kN/m2
qu = unconfined compressive strength q = effective vertical
stress at pile point N~ = adjusted bearing capacity factor for
cohesion (see Fig. 7.2) N~ = bearing capacity factor adjusted for
Ll b > 1 dependent on
initial angle of shearing resistance (see Fig. 7.2). (See
Reference 8. page 600.)
L = depth of penetration B = width or diameter of pile
Ll B should be greater than Lei B as obtained from Fig. 7.2 for
the value of .
Note: Find point resistance by more than one method if soil test
data allow and take the lowest for a conservative estimate.
Determination of skin resistance LPs; = LAsfs
where As == pile perimeter x pile length over which Is acts (m2)
Is = skin resistance (kN/m2)
First method of skin resistance Is= 2N kN/m2 Is= N kN/m2
for large volume displacement piles for small volume
displacement piles
where N = statistical average blow count in stratum for
S.fYf.
Second metlwd of skin resistDnce Is= 0.005qckN/m2
where Qc = cone penetration resistance (kN/m2).
Third method of skin resistance for small volume displacement
piles
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298 Reinforced Concrete
fs = l.5qc5 to 2.0qcs for large volume displacement piles where
qcs = side friction resistance in cone penetrometer.
Fourth nutlwd of skin resisllmce fs = ac + 0.5 ij K5 tano (see
Reference 8, page 603) where c = average cohesion or Su of stratum
(kN/m2)
ij = effective vertical stress (kN/m2) () = angle of friction
between soil and pile
Ks = coefficient of friction Dr = relative density of sand.
Table 7.1 Values of K, (Reference 8, page 603).
Pile type K5 for low Dr K5 for high Dr
Steel Concrete Wood
20 0.754> 0.674>
(See Reference 7, page 136.)
0.5 1.0 1.5
Table 7.2 Values of a (Reference 7, page 126) .
Soil condition
1.0 2.0 4.0
Values of oc
DIB c =50 c = 100 c= 150 c =200 c= 250
Sands or sandy gravel 40 0.9 0.65 0.4 0.4 0.4 Soft clays or
silts 10 0.35 0.30 0.25 0.2 0.2 overlying stiff to very > 20
0.75 0.70 0.63 0.55 0.5 stiff cohesive soil
Stiff to very stiff 10 0.9 0.7 0.3 0.2 0.2 cohesive soils
without >40 1.0 0.9 0.3 0.3 0.3 overlying strata
The units of c are kN/m2
Note: Find skin resistance by more than one method if soil test
data allow and take an average.
p = Pu a 2.5
Tu T =-a 2.5
where P8 = allowable pile load in compression T3 = allowable
pile load in tension
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- --- - --- -- ..
Design of Piled Foundations 299
7.2 HORIZONTAL LOAD- SINGLE PILE CAPACITY
Method I Cohesive soils
k sB = 1.3(EsB4)fi (~) Etlr 1 - f.L
as per Vesic, 1961 (see Reference 6). where k5 = modulus of
subgrade reaction (kN/m3)
B = width or diameter of pile (m) E5 = stress- strain modulus of
soil (kN/m2) Er = stress-strain modulus of pile material (kN/m2) Ir
= moment of inertia of pile (m4) !l = Poisson's ratio of soil
Es may be obtained by the following methods:
(1) Triaxial tests. (2) Borehole pressuremeter tests. (3) Es =
650N (kN/m2)
N = SPT number of blows. ( 4) Es = 3 (1 - 2!!)/ mv where mv =
coefficient of volume compress-
ibility (m2/kN).
Method 2 Cohesive soils
k s = 240qu kN/m3
where qu = unconfined compression strength (kN/m2).
Cohesionkss soils
ks = 80 fC2qNq + C, (0.5 y BNy)] kN/m3 as per Vesic (see
Reference 8, page 631 and page 323, equation 9-8). where c, = c2 =
1.0 for square piJes
C1 = 1.3 to 1. 7 for circular piles c2 = 2.0 to 4.4 for circular
piles q = effective stress (kN/m2) y = unit weight of soil B =
width or diameter of pile
N,1 and Ny may be obtained from the following table (Hansen
equations) - see Reference 8, page 137, Table 4- 4:
Finite ekment model of vertical pik Spring stiffness = SBk5
kN/m
where S = node spacing not greater than B B = width or diameter
of pile (m) k, = modulus of subgrade reaction (kN/m3)
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300 Reinforced Concrete
Table 7.3 Values of N4 and Ny (Reference 8, page 137).
Rotation about X Z axis
Translations about x and y axis
Translations
......._Rotation about a-
(degrees)
0 5
lO 15 20 25 30 35 40 45 50
Nq
l.O 1.6 2.5 3.9 6.4
10.7 18.4 33.3 64.2
134.9 319.0
Ny
0 0.1 0.4 1.2 2.9 6.8
15.1 33.9 79.5
200.8 568.5
SK 7/2 Two-dimensional model of pile in soil (degrees of freedom
-top and bottom of pile).
Note: For horizontal loads which are not constant and are
reversible or repetitive, the top 1.58 of pile may be assumed
unsupported by soil.
Boundary conditions (I) Free head pile Translations x, y
Rotation z Translations y Rotation z (2) Fixed head pile
Translations x, y Rotation z Translations y Rotation z
Material type
Free at top Free at top Restrained :at bottom Free at bottom
Free at top Rigid at top Restrained at bottom Free at bottom
For sustained horizontal load due to dead load, water pressure,
earth
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Design of Piled Foundations 301
pressure, etc., use short-term Young's modulus of concrete for
bending moment computations but long-term Young's modulus of
concrete for pile head deformation.
For short-term horizontal loads due to wind, earthquake, crane
surge, etc., use short-term Young's modulus of concrete for bending
moment and deflection computations.
Software Use any fully validated software which has a suite for
analysis of 2-D plane frame with sprung boundaries.
Member type For rectangular pile usc minimum width Bin all
computations involving B. A cracked section moment of inertia may
be used for reinforced concrete piles based on Section 2 .1.
7.3 PILE GROUP EFFECTS
7.3.1 Spacing of piles
S?:. 2B S?:. 3B
for end-bearing piles for friction piles
where S = spacing of piles B = least width or diameter of
pile.
Note: Piles carrying horizontal load should not be spaced at
less than 3B.
7 .3.2 Pile group capacity
Ultimate group capacity :::;; group friction capacity + group
end-bearing capacity
Ultimate group friction capacity = 2D( B + L )c~
SK 7/3 Group of piles - plan of overall dimensions of group.
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302 Reinforced Concrete
0 ~.,.,... I Frict1on
where c = average cohesion of clay = average Su = average
qu/2
SK 714 Elevation of group of piles showing group capacity.
CY = coefficient (from Section 7.1, Table 7.2) D = depth of pile
group below ground B = overall width of group L = overall length of
group.
Ultimate group end-bearing capacity= BL (N~ + qN~) where c =
cohesion or undrained shear strength Su = quf2 at bottom of
pile group qu = unconfined compressive strength q = effective
stress at bottom of pile group N~ = bearing capacity factor (see
Fig. 7.2) N; = bearing capacity factor (see Fig. 7.2)
Note: Total vertical load on a group of piles should not exceed
the group capacity. Individual pile loads inside the group will be
limited by the single pile capacity. Piles carrying horizontal load
and spaced at 38 or more need not be checked for group effects due
to horizontal load.
ultimate group capacity + ultimate group end-bearing capacity
Allowable group capacity =-------~"----'--"------
2.5
7.4 ANALYSIS OF PILE LOADS AND PILE CAPS
7.4.1 Rigid pile cap
N = combined vertical load on pile cap - unfactored Mx =
combined moment about x-x - unfactored My= combined moment about y
- y - unfactored
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Design of Piled Foundations 303
SK 7/5 Loads and eccentricity on pile cap.
SK 7/6 Plan view of loads and eccentricity on pile cap.
X
y e.
Hx . M. -.~. 1 Hy! e~uc
. .
y
"'In - 0
ey
X
Hx = combined horizontal load on pile cap- unfactored in x- x
direction Hy = combined horizontal load on pile cap- unfactored in
y - y direction ex= eccentricity of N from CG of pile group in x- x
direction ey = eccentricity of N from CG of pile group in y-y
direction
ehx = eccentricity of Hy from CG of pile group in x-x direction
eh.v = eccentricity of Hx from CG of pile group in y-y
direction
h = depth of pile cap.
Loads on pile group
P = vertical load on pile group = N + weight of pile cap +
weight of backfill on pile cap + surcharge
on backfill Mxx = moment about x-x on pile group
= Mx + Ney + Hyh + M: Myy = moment about y-y on pile group
= My + Nex + Hxh + M:
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304 Reinforced Concrete
X
y !JC.G. of pile goop
----
:-- ---+ f~ ,__ .
v y, . .
X 1---,: 1"---~ f-- X y
y' '
x' xr ' x2 Xl X4 i
y
-~ i ! xs
~ Y,
R:Total - ~x' x= Ff
number of piles
- ~ y = R x: andy' arc orthogonal dtstanccs of each pile from
corner pile
SK 717 Typical pile foundation showing CG of group and
co-ordinates of piles.
SK 7/8 Group of piles subject to horizontal loads and
torsion.
where M: and M; are moments with respect to CG of pile group due
to eccentric surcharge on backfill or pile cap.
T = torsion on pile group = H,ehy + H_.ehx
fxx = l:y2 about x-x axis passing through CG of pile group lyy =
U about y-y axis passing through CG of pile group
f l = f xx + f yy
R = number of piles in group.
Vertical load on a pile = (!_) ( M xxY) ( M,vyx) R fxx l yy
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Design of Piled Foundations 305
(H2 + H 2)! T(x2 + y 2)f Horizontal load on any pile = resultant
of x Y and - ----
R f z
Sign convention Vertical loads: Torsion on pile group:
Moments on pile group:
downwards positive clockwise positive
clockwise positive
+ve M xx produces compression in piles which have +ve y
ordinates.
+ve M.v.v produces compression in piles which have +ve X
ordinates.
Hx is positive in direction of increasing x in positive
direction.
Hy is positive in direction of increasing y in positive
direction.
Eccentricities arc +ve for +vex and +ve for +ve y.
Bending moments in pile cap
SK 7/9 Critical sections for bending moment in a pile cap.
Take sections X- X or Y- Y through pile cap at faces of columns
or base plates. Find pile reactions due to combined and load
factored basic load cases. Consider all upward and downward
loadings across sections X-X and Y- Y. Find bending mo ments across
section . Find horizontal load on each pile by using the following
expressions:
H = Hxu pxu R
Hyu Hpyu = R where R is number of piles in pile cap. Find
bending moments in pile Mpxu corresponding to Hpyu and M pyu
corresponding to Hpxu assuming an end fixity to pile cap following
the method in Section 7.2. Hxu and Hyu are combined factored
ultimate horizontal loads.
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306 Reinforced Concrete
HPIW i Hpxu i Hpllu i Hpxu Hpxu
SK 7/10 Additional bending moment in pile cap due to pile
fixity.
AlgebraicaUy add the bending moments in pile cap due to vertical
load and pile fixity moments due to horizontal load to find design
bending moments in pile cap.
7 .4.2 Flexible pile cap
Large pile caps including piled raft foundations should be
modelled as flexible . The modelling will normally be carried out
using either a grillage suite of a computer program or a
general-purpose finite element program. The piles should be
modelled as springs in the vertical direction. The vertical spring
stiffness should be obtained from test results on site. A
parametric study can be carried out using minimum and maximum
stiffness of the pile if there is a large variation.
Grillage model
(1) Divide pile cap into an orthogonal grillage network of
beams. Ensure that piles are located at crossing of orthogonal
beams. Each grillage beam represents a certain width of pile
cap.
(2) Use short-term Young's modulus for concrete material
properties. (3) Full section concrete stiffness properties may be
used for hypothetical
grillage beams (hypothetical width X depth of pile cap). (4)
Piles will be modelled as sprung supports vertically. (5) Vertical
loads on pile cap may be dispersed at 45 up to central depth
of pile cap. (6) Apply at each node with a pile, the moments
given by the following
formulae:
about x-axis
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Design of Piled Foundations 307
SK 7/tt Plan of raft on piles showing idealised grillage
elements - flexible analysis.
Column load may spread onto grill~ ~l~ment
Pil~ Cap/ Raft
SK 7/12 Part section through raft showing details of grillage
idealisation.
M = Hxh Y R abow y-axis
(7) Find horizontal load on each pile by using the following
expressions:
where R is total number of piles in group.
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308 Reinforced Concrete
(8) Find bending moments in pile, Mpx corresponding to Hv.v and
Mp.v corresponding to Hpx assuming an end fixity to pile cap
following method in Section 7 .2. Apply these moments to pile cap
grillage model as nodal loads. The pile head to pile cap connection
may be assumed a'i hinged and then Mv:c and Mp_v will be zero.
(9) Find bending moments in pi1e cap by grillage analysis.
Divide bending moments by width of hypothetical strips of pile cap
representing grillage beams and obtain Mx, M_. and Mx.v in pile cap
per metre width. Apply load factors and combine basic load cases.
Modify these combined moments by Wood- Armer method to find design
bending moments. [11.121
(10) Combine basic load cases at serviceability limit state to
find reactions at pile nodes. Compare maximum reaction with pile
capacity.
Finite-element model
SK 7/13 Typical finite element modelling of a circular raft on
piles.
(1) Create a finite element model of pile cap using either
4-noded or 8-noded plate bending elements. The elements may only
have three degrees of freedom at each node viz z. ex and Ely. The
piles will be represented by vertical springs.
Piles will come at nodes in finite element model. Between two
piles' nodes there should be a minimum of one plate node without
pile.
(2) Use short-term Young's modulus for concrete material
properties. (3) Full section concrete section properties may be
used in the analysis. (4) Vertical loads on pile cap may be
dispersed at 45 up to central depth
of pile cap. These loads may be applied as nodal loads or
uniformly distributed loads on plate elements depending on software
used.
(5) Apply at each node with a pile, the moments given by the
following formulae.
M = Hxh .v R
about x-axis
about y-axis
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Design of Piled Foundations 309
(6) Find horizontal load on each pile by using the following
expressions: Hx H.,
Hpx = R and Hp_v = R where R is total number of piles in
group.
(7) Find bending moments in pile, Mpx corresponding to Hp_v a nd
Mpy corresponding to Hpx , assuming an e nd fixity to pile cap
following method in Section 7.2. Apply these moments as nodal loads
in finite e lement model at nodes with piles. These moments will be
zero in the case of a hinged connection of pile to pile cap.
(8) Carry out analysis using a validated general-purpose finite
e lement software . Apply load factors to combine basic load cases.
Modify the combined Mx, M., and Mxv using the Wood - Armer method
to find design bending moments.lll.l2]
(9) Combine basic load cases at serviceability limit state to
find reactions at pile nodes. Compare maximum reaction with rated
pile capacity.
7.5 LOAD COMBINATIONS
Applied loads on pile cap will be combined using the following
principles.
7 .5.1 Pile load calculations
LCI: l.ODL + 1.0/L + l.OEP + l.OCL v + l.OCLH LC2 : l.ODL + l
.OEP + l.OCLV + 1.0CLH + l.OWL (or l.OEL) LC3: l.ODL + 1.0/L +
l.OEP + l.OWL (or l.OEL) LC4 : l.OL + l.OWL (or l.OEL) where DL =
dead load
I L = imposed load EP = earth pressure and water pressure
CL V = crane vertical loads CLH = crane horizo ntal loads
WL = wind load EL = earthquake load.
7 .5.2 Bending moment and shear calculations in pile cap or
piles
LC5 : 1.4DL + 1.6/L + 1.4EP LC6: 1.2DL + 1.2/L + l.2EP + 1.2WL
(or 1.2EL) LC1 : 1.4DL + 1.4WL (or 1.4EL) + 1.4EP LC8 : l.ODL +
1.4WL (or 1.4EL) + 1.4EP (if adverse) LC9: 1.4DL + 1.4CLV + 1.4CLH
+ 1.4EP LC10: 1.4DL + 1.6CL V + 1.4EP LC11 : l.4DL + 1.6CLH + 1.4EP
LC12: 1.2DL + 1.2CLV + 1.2CLH + 1.2EP + 1.2WL (or 1.2EL)
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310 Reinforced Concrete
7.6 STEP-BY-STEP DESIGN PROCEDURE FOR PILED FOUNDATIONS
Step 1 Select type of pile The type of pile will depend on the
following principal factors:
Environmental issues like noise, vibration. Location of
structure. Type of structure. Ground conditions. Durability
requirements. Programme duration. Cost.
The commonly available types of piles can be broadly classified
as below.
Large-displacement piles (driven)
Precast concrete. Prestressed concrete. Steel tube with closed
end. Steel tube tiJied with concrete.
S11Ulll-displacement piles (driven)
Precast concrete tube with open end. Prestressed concrete tube
with open end. Steel H-section. Screw pile.
Non-disphlcement piles
Bored and cast-in-situ concrete pile. Steel tube in bored hole
tilled with concrete. Steel or precast section in drilled hole.
Step 2 Determine vertical capacity of single pile Follow Section
7 .1.
Step 3 Determine horizontal capacity of single pile Follow
Section 7 .2.
Nou: Horizontal capacity of a single pile is limited by maximum
deflection of pile cap that structure can accommodate and also by
pile structural capacity.
Step 4 Deurmine approxi11Ulle number of piles and spacing p
R;v = Cv
-
H R;H = CH
Design of Piled Foundations 311
R; = R;v or R;H, whichever is greater
where R; :;: approximate number of piles P = total vertical load
on pile cap - unfactored
Cv = rated working load capacity of pile - vertical load CH =
rated working load capacity of pile - horizontal load H = total
horizontal load on pile cap - unfactored
= (H; + H;)4 Spacing of piles should be according to Section
7.3. To minimise the cost of pile cap , the spacing should be kept
close to minimum allowed. Larger spacing increases the pile group
capacity and pile group moment capacity .
SK 7/14 Determination of approximate number of piles.
X
(1} Select a group of piles with approximate number of piles=
R;. (2) Find CG of pile group and locate orthogonal axes x- x and
y-y
through the CG. (3) Find CG of group of piles on left of axis y
- y and right of axis y-y. (4) Find the x-axis distance between
these two CGs and call it Sx (5) Similarly, find Sv about y-axis.
(6) Find M .. IP = ey and MyfP = ex, where Mx and My are total
combined
applied moments on pile cap about x- x and y - y respectively.
(7) Find exiSx and e_) S_v (8) Find Ex and E.v from Fig. 7.1.
1.1 R;v (9) R = -- ~ RiH ExEv
where R = number of piles in group for checking pile load.
Not$: The factor 1.1 is introduced to cater for additional
vertical loads from self-weight of pile cap, surcharge on pile
caps, backfilHng, etc.
Revise the number of piles in group from R; toR.
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312 Reinforced Concrete
Step 5 Determine size of pile cap Allow 1.58 from centre of pile
to edge of pile cap . Depth of pile cap is governed by the
following:
Shrinking and swelling of clay. Frost attacks. Holding down bolt
assemblies for columns. Water table and soluble sulphates. Pile
anchorage. Punching shear capacity of pile cap .
Step 6 Carry out load combination Follow Section 7.5.
Step 7 Check pile group effects Follow Section 7 .3.
Step 8 Carry out analysis of pile cap Follow Section 7 .4.
Step 9 Determine cover to reinforcement From the soils
investigations report , find the concentration of sulphates
expressed as so). Find, from Table 17 of BS8004: 1986121, the
appropriate type of concrete.
Table 7.4 Minimum cover to reinforcement for class of
exposure.
Class of Total S03 Minimum cover Minimum cover exposure
percentage on blinding (mm) elsewhere (mm)
I < 0.2 35 75 2 0.2 to 0.5 40 80 3 0.5 to l.O 50 90 4 1.0 to
2.0 60 100 5 > 2.0 60 100
Note: Concrete in 'class of exposure 5' needs protective
membrane, or coating. The uneven heads of piles normally
necessitate a minimum 75 mm cover over blinding for pile caps. The
concrete piles will have minimum cover as specified elsewhere.
Step 10 Calculate area of reinforcement in pile cap M = bending
moment as found in Step 8 at ultimate limit state
M K = --2 s 0.156 fcubd where feu = concrete characte ristic
cube strength at 28 days
-
Design of Piled Foundations 313
b = width of section over which moment acts d = effective depth
to tension reinforcement.
If K is greater than 0.156, increase depth of pile cap.
M Ast = - - -
0.87/yz
z = d[ 0.5 + J ( 0.25 - 0~9) J ~ 0.95d Distribute this area of
reinforcement uniformly across the section.
Note: The effective depth to tension reinforcement will be
different in the two orthogonal directions.
Step 11 Check shear stress in pile cap
SK 7/15 Critical section for checking shear stress in pile
cap.
cap (~ffective depth = d)
Enhanc~mmt of shear stress is allowed i f ay:ralSd
The critical section for checking shear stress in a pile cap is
cjl/5 into the pile. All piles with centres outside this line
should be considered for calculating shear across this section in
pile cap. For shear enhancement, av is from face of column to t his
critical section. No enhancement of shear stress is allowed if av
is greater than 1.5d. Where pile spacing is more than 3cjl then
enhancement of shear should be applied only on strips of width
3cjl. The rest of the section will be limited to uncnhanced shear
stress.
IP V=-~ v Bd c or enhanced vc1 if applicable
where IP = sum of all pile reactions at ultimate loading on left
of section
8 = width of pile cap at critical section
-
314 Reinforced Concrete
Pil~ with dia!Tl4Zter
d = average effective depth at critical section
Vel = Vc (~) ::; 0.8y feu or 5 N/mm2 For rectangular piles the
critical section may be considered at face of pile.
"-----+-Vc ~-4~ --GT--~~~J-.~2d a;
a-+----1- Vc
SK 7116 Diagram showing zones of enhanced shear stress on
critical section.
The value of ve1 can be found from Figs 11.2 to 11.5 depending
on percentage of tensile reinforcement and feu
Shear capacity of section should be greater than or equal to
applied shear. Ultimate limit state analysis results should be used
for checking shear capacity.
Step 12 Check punching shear stress in pile cap
M II
No check necessary if. pile spacing is less than 3 +
Pllnching shear perimeter around loaded area ' Check V
-
Design of Piled Foundations 315
When the spacing of piles is greater than 3 times the diameter
of a pile then the punching shear plane for column should be
considered . For rectanguJar piles the plane can be considered at
face of pile. The stress on this punching shear plane should not
exceed vc depending on the percentage of tensile reinforcement in
pile cap.
Check of punching shear stress is also requjred at perimeter at
face of column or pile. This shear stress should not exceed 0.8\/
feu or 5 N/mm2
Punching perimeter
SK 7118 Further perimeters for punching shear checks in a pile
cap.
The punching shear planes for piles will depend on location of
pile with respect to edge of pile cap . Find the perimeter U at
punching shear plane.
p v=-:sv Ud c
where P = ultimate vertical column load or ultimate vertical
pile reaction vc =design concrete shear stress obtained from Figs
11.2 to 11.5.
Percentage area of tensiJe reinforcement for computation of
design concrete shear stress will be average percentage across
punching shear planes.
Step 13 Check area of reinforcement in pik Effective length of
pile, lc = ~10 where 10 = unsupported length of pile (piles which
are not subjected to
horizontal load may be assumed fully supported by ground from
ground level; piles subjected to horizontal load may be assumed
supported by ground at a depth of l .5b below ground level where b
is width of pile or diameter of pile)
-
316 Reinforced Concrete
h t_
~ = 1.2 = 1.6
Rectangular piles
-pM y y ..
. -+--f-
for piles with head fixed to pile cap for piles with head free
to rotate.
L.-~- ._. Asc_/2 I. y .I SK 7119 Typical section through a
rectangular pile.
(A) If lelb ~ 10, then treat piles as a short column. (i) Pile
with no moment
N = 0.4/cubh + 0. 75AsJy Check N ~ applied direct load on pile.
(ii) Pile subjected to uniaxial moment Find e = MIN and then elh.
Find N I bh and select appropriate table from Tables 11.8 to 11 .17
depending on feu and k = dlh. From appropriate table find p which
satisfies value of Nlbh for given elh. Find A sc = pbhl l OO. Put A
scl2 on each face of pile equidistant from axis of moment.
Note: The moment M in pile is due to horizontal load as obtained
in Step 3 following Section 7.2. (iii) Pile subjected to biaxial
moment Assuming diameter of reinforcement and finding cover from
Step 9, find h' and b' . Find Mxl h ' and M_.lb' . If Mxlh ' >
Mylb', then
M~ = Mx + ~Mv (h') . b'
If M . .fb' > Mxlh', then
M~ = M., + ~Mx (b') . . h'
-
Design of Piled Foundations 317
Find Nlfcubh. The values of~ are given in the table below.
Table 7.5 Values of~ for biaxial bending of pile.
0 1.00
0.1 0.88
0.2 0.77
0.3 0.65
0.4 0.53
0.5 0.42
~0.6 0.30
Design as uniaxial bending with N and M~ or M~ whichever is more
promi-nent. Find Asc in manner described in (ii) for pile subjected
to uniaxial moment.
(B) If lelb > 10, then treat pile as a slender column.
1 (/ )2 ax= 2000 ~ hK
ay = 2~ (iYbK Select A sc
N - N K = uz s 1 Nuz- Nbal
Nuz = 0.45fcuAc + 0.87/yAsc Nbal = 0.25fcubh A c = bh- A sc
Maddx = Nax M addy= Nay
Combine these additional moments with moments obtained from
analysis as in Step 3 following Section 7.2. Design pile subjected
to biaxial bending as described previously.
Circular piles
SK 7120 Typical section through a circular pile.
h Usc m inimum six bars
-
318 Reinforced Concrete
X
(A) If lclh ::: 10, then treat pile as a short column. (i) Pile
with no moment Assume size of reinforcement and at least six
bars.
Ac = 0.25rrh2 - Asc
N = 0.4/cuAc + 0.75Asc/y Check N ~ applied vertical load o n
pile. (ii) Pile with moment Find e = MIN and the e!R, where 2R =h.
Find N/11 2 and select appropriate table from Tables 11.18 to 11.27
corresponding to feu and k = h51 h. Find p from appropriate table
which satisfies N/h 2 for given value of e!R . Find Asc =
p1tR21100. Use at least six bars.
(B) If lclh > 10, then treat pile as a slender column .
[2
a = 2~11 K (assume K = 1 conservatively) M add = Na
Combine this additional moment with moment obtained by analysis
in Step 3 following Section 7 .2. Design pile with moment as
described in (ii) above.
Step 14 Check stresses in prestressed concrete piles
X
v
y
+ X y
y X SK 7/21 Typical section of a prctcnsioned prestressed
pile.
Stresses may be checked at the serviceability limit state only
as per BS8110: Part 1, Section 4.1 11
Permissible maximum compressive fibre stress in concrete =
0.4/cu
Assume pile as Class 3 member with a limiting crack width of 0.1
mm.
-
Design of Piled Foundations 319
Hypothetical flexural tensile stress in concrete = 4.1 N/mm2 for
Grade 40
= 4.8 N/mm2 for Grade 50 and above
Depth factors to modify tensile stress are shown in the
following table.
Depth (mm)
Up to 400 500 600
N = direct service load on pile
Factor
1.0 0.95 0.9
M:rx = bending moment as obtained from Step 3 about axis x-x M
yy = bending moment as obtained from Step 3 about axis y-y.
Assume the pile section is uncraeked.
Find A~ = area of concrete I= = moment of inertia about x- x
axis fyy = moment of inertia about y-y axis P = residual prestress
after all losses.
Maximum compressive stress in concrete = (~) + (MxY) A c lxx +
(~:)
( P A+c: N\ _ (M/~) Maximum tensile stress in concrete = - ) ~ -
(~:)
m = modular ratio fs = strand stress prior to release fc =
stress in concrete due to prestress alone.
( ) . . (lOOmfc:) 1 Loss due to elastiC shortenmg = --- % Is
(2) Loss due to relaxation of steel - refer to strand
manufacturer's brochure.
(3) Loss due to creep of concrete - follow clause 4.8.5 of BS
8110: Part 1.(1 ]
(4) Loss due to shrinkage o f concrete - follow clause 4.8.4 of
BS8110: Part L l1l
Note: Prestressed piles designed as fixed to pile cap must
extend into pile cap by
-
320 Reinforced Concrete
a minimum distance equal to transmission length given by the
following equation:
K, 11 == Y/cu (mm) where feu = concrete cube strength at 28
days
K1 = 600 for plain or indented wire == 400 for crimped wire =
240 for 7-wire standard or super strand = 360 for 7-wire drawn
strand
0.6h and/or MpyuiNu > 0.6b Find Vx = Hpyufbh' and Vy =
Hpxulhb' Find Px = lOOAsxlbh' and P.v = lOOAs_vfhb' Find Vex and
Vcy corresponding to Px and P.v from Figs 11.2 to 11.5.
-
Design of Piled Foundations 321
If this check fails, provide shear reinforcement in the form of
links.
I
Nu
Enhancement of design
Enhancement of design concrete shear stress
=0-6 NuHxub/MyuAc Hxub/Myu~ 10 concrete stress= 06 N"u Hyu h/
MxuAc
Hyuh/ Mxu~ 10 SK 7124 Shear stress enhancement due to presence
of axial load. SK 7/23 Shear stress enhancement due to
presence of axial load.
Note: v,. ... and vc_v may be enhancecl by using the following
formulae due to presence of an axial load Nu:
HpyuhiMpxu and Hpxub!Mpyu should be less than or equal to
1.0.
Shear reinforcement bSv( V - v~) Asv = -~-____:~
0.87/yv
where A sv = total area of legs in direction of shear b = width
of section perpendicular to direction of shear
Sv = spacing of links {yv s 460N/mm2 for links.
Circular piles
Nu = ultimate vertical load with Hpu Hpu = combined ultimate
horizontal load Mpu = moment in pile due to Hpu
-
322 Reinforced Concrete
A_ 2:: bxSv(Vx -Vex> ""'SVX - 087 Jyv
Asvy ~ by5v(Vy-Vty) 087Jyv
Asv(aYUof link)
Sv
Sv
No shear check is necessary if"
SK 7/25 Shear reinforcement in a rectangular pile.
SK 7/26 Shear reinforcement in a circular pile.
Mpu1Nu s 0.60h and Hpu/0.75Acs0.8Vfc:uS5N/mm2
where A c: = 0.25nh2
Shear check is necessary if' M pu/ Nu > 0.60h
Shear stress, v = Hpuf0.75Ac
p = 100A5/ 1.5Ac assuming 50% of bars effectively in tension
where A s = total area of steel in pile.
-
Design of Piled Foundations 323
Find vc corresponding top from Figs 11.2 to 11.5. The shear
stress vc may be enhanced by using the following formula due to
presence of an axial load Nu:
0.6NuHpuh , 1 2 v~ = Vc + ::5 0.8 vfcu ::5 SN/mm AcMpu
H puhl M pu should be less than or equal to 1.0.
If v > v~. then use shear reinforcement.
where Av = total area of link bars perpendicular to longitudinal
bars, i.e. the two legs of hoop reinforcement
fY" = characteristic yield strength of link reinforcement S =
spacing of links.
Find z/ R from appropriate table from Tables 11.18 to 11.27
corresponding to feu hsfh, p , NIR2 and e/R. Check H pu ::5 V5 +
Vc
The total shear resistance for inclined links = Vs = l0.87 f yA
sv (cos~+ sin ~cot~) (z/S)] where Asv = total area of link bars
i.e. the two legs of hoop reinforcement.
~ may be taken as 45 when ~ is angle of inclination of link.
Step 16 Check shear capacity of prestressed pile
b
h d Spiral link .r~in~ccment
Aps to find Vc
SECTION
SK 7127 Typical section and elevation of a prestressed concrete
pile.
Vco = 0.67bh(f~ + 0.8fcpft)! ( 0.55fpe) M 0 V Vcr = 1 - -- vcbd
+ -- ~ O.lbdVfcu fpu M
j r
ELEVATION
Spiral link
Vc = V co or Vcr as the case may be (kN) resistance
design ultimate shear
-
324 Reinforced Concrete
h
Vco = shear resistance of section uncracked (kN) Vcr = shear
resistance of section cracked (kN)
f, = maximum design principal stress at the centroidal axis =
0.24'1/ feu fcp = design compressive stress at centroidal axis of
concrete section due
to prestress alone
fpe = design effective prestress in tendons after all losses~
0.6fpu fpu = characteristic ultimate strength of tendons
vc = design concrete shear strength from Figs 11.2 to 11.5 where
percent-age of steel reinforcement should include tendons plus any
ordinary untensioned longitudinal steel reinforcement in tensile
zone of section
d = effective depth to centroid of reinforcing steel in tension
zone where reinforcing steel should include tendons and any
untensioned reinforcement
feu = characteristic cube concrete strength at 28 days M 0 =
moment to produce zero stress at tension fibre with 0.8fcp on
section.
b
.I ~t~ssmg strands
l.Jc.1tformly. prestr~sed t.hiform Prest~ss ptle sectton
:OSfcp
+
-1, Stress due to M0 M0 = ZJc = 08Zfcp
SK 7/18 Stress diagram for a symmetrical rectangular prestressed
pile due to M,,.
If Hpu < 0.5 Vc, no shear reinforcement is required. If
Hpu;::: 0.5Vc, then provide shear reinforcement as follows. Shear
reinforcement If horizontal shear on pile , Hpu is less than or
equal to ( Vc + 0.4bd) then, A,v 0.4b -=---
Sv 0.87fyv
lf horizontal shear on pile, Hpu is more than ( Vc + 0.4bd)
then,
-
Design of Piled Foundations 325
Note: For biaxial bending and shear, check requirement for shear
reinforcement for each direction of bending separately, but allow
for contribution of concrete shear resistance V< in one
direction of loading only for calculation of shear reinforcement.
(See Step 7 of Section 4.3.1.)
Step 17 Check minimum reinforcenuml in RC pile For rectangular
and circular piles, lOOAsciAc ~ 0.4.
Step 18 Check minimum prestress in prestressed pile
Find slenderness ratio of pile = n = ~ where b = minimum width
of pile
l = total length of prestressed pile at commencement of
driving.
Minimum prestress after losses = 60n psi or = 0.4n N/mm2
If diesel hammer is used,
minimum prestress in concrete= 5 N/mm2
Step 19 Maximum reinforcement in pile lOOA scl Ac :s 6
Step 20 Containment of reinforcement in pile Minimum dia . of
links = 0.25 x largest bar ~ 6 mm Maximum spacing of links = 12 x
smallest dia. of bar
Step 21 Links in. prestressed piles At top and bottom 38 length
of pile , provide 0.6% of volume of pile in volume of link.
Step 22 Minimum tension reinforcement in pile cap As~ 0.0013bh
in both directions
Step 23 Curtailment of bars in pile cap A minimum anchorage of
12 times diameter of bar should be provided at ends by bending bar
up vertically. Additionally check that full tension anchorage bond
length is provided from cri tical section for bending in a pile cap
where design for flexure and requirement for flexural steel in
tension is determined. In finding anchorage bond length beyond that
section, actual area of steel provided may be taken into
account.
Step 24 Spacing of bars in pile cap Clear spacing of bars should
not exceed 3d or 750 mrn.
-
326 Reinforced Concrete
h
L = Tension Anchorage Bond Length
Percentage of reinforcement, IOOAsfbd (%)
1 or over 0.75 0.5 0.3
Les~ than 0.3
SK 7/29 Typical section through a pile cap.
Maximum clear spacing of bars in pile cap (mm)
160 210 320 530
3d or 750
Note: This will deem to satisfy a crack width limitation of 0.3
mm.
Step 25 Early thermal cracking See Chapter 3.
Step 26 Assessment of crack width in flexure See Chapter 3.
Step 27 Connections See Chapter 10 for connection of pile to
pile cap and column to pile cap.
7.7 WORKED EXAMPLE
Example 7.1 Pile cap for an internal column of a building Size
of column = 800 mm x 800 mm Spacing of column = 8 m x 8 m on
plan
-
Design of Piled Foundations 327
Unfactored column loads
Dead Imposed Wind
Vertical load, N (kN) Horizontal shear, Hx (kN) Horizontal
shear, Hy ( kN) Moment, Mx (kNm) Moment, My (kNm)
1610 28
112
Geotechnical information (see SK 7130) Stratum 1 Average
thickness of layer= 1.5 m
1480 18
72
156 112 448 624
Classification: very loose yellow brown to brownish grey sandy
silt.
Average N = 3 (SPT) c = 11.3 kN/m2 = 40 y = 26kN/m3
Stratum 2 Average thickness of layer= 9 m Classification: soft
to medium bluish-grey clayey silt.
Average N = 5 (SPT) c = 20.2 kN/m2 = so y = 24kN/m3
Ysat = 27 kN/m3
Stratum 3 Average thickness of layer = 2 m
Classification : stiff to very stiff bluish-grey silty clay.
Average N = 14 (SPT} c = 60kN/m2 = 60
Ysat = 26 kN/m3
Stratum 4 Average thickness of layer = 7 m
Classification: dense to very dense mottled brown sandy
silt.
Average N = 24 (SPT) c = 13.8 kN/m2 = 31
Ysat = 27kN/m3
-
3~ Reinforced Concrete
~ -----------------------------::::> ~ "'
VERY LOOSE YELLOW BROWN SANOY SILT N=3 ~
------------------------------
SOFT TO MED IUM BLUiSH-GREY CLAYEY SILT N=S AVERAGE
~ STIFF TO VEQY STIFF BLUISH-GREY ~ SILTY CLAY N-14 ~VERAGE "'
::;;----------------------------
_,
::E: ::::> JENSE TO VERY OENSE MOTTLED BROWN ~ SANOY SILT N
24 AVERAGE .....
VI
VERY S"IFF TO HARO S:LTY CLAY N=31 AVERAGE
:r ....
0. w O CJ'I
a: I.Ul!J 0>- u. < O
0 0 0 01
0 0 0
""
0 0 0
~
SK 7/30 Average ground condition soil strata.
-
Design of Piled Foundations 329
Stratum 5 Average thickness of layer= 15m
Classification: very stiff to hard silty clay.
Average N = 31 (SPT) c = 71.5 KN/m2 =S"
Ysat = 28kN/m3
Water table at 3.0m below ground level.
Step 1 Select type of pile Considering all the factors as
described in Step 1 of Section 7.6 it 1s decided to use a
non-displacement pile. Choose 600mm diameter bored and cast-in-situ
concrete pile.
Step 2 Determine vertical capacity of pile Follow Section
7.1.
First method of point resistance
Assume pile to go into Stratum 5 and stop at 8.0 m within
Strlllum 5.
Lb = average length of pile = (1.5 + 9 + 2 + 7 + 8) m = 27.5 m
0.62
Ap = cross-sectional area of pile = 1t x 4 = 0.283 m2
B = 0.60 m N = statistical average of SPT in a zone of about 88
above to 38 below
pile point = 31
27.5 P pu = 0.283 X 38 X 31 X 0.6 = 15280 kN
~ 380N(Ap) = 380 X 31.0 X 0.283 = 3334 kN
Second method of point resistance Ppu = Ap(N~c + qN;,) Ap =
0.283m2
c = 71.5 kN/m2
Yw = 10kN/m3
q = effective vertical stress at pile point = 1.5 X 26 + 1.5 X
24 + 7.5 X 27 + 2 X 26 + 7 X 27 + 8 X 27
- (27.5 - 3) X 10 = 489.5 kN/m2
-
330 Reinforced Concrete
0 0 "' !'-
"'
STRATUM 1
Water Table ..
STRATUM 2
STRATUM 3
STRATUM 4
STRATUM 5
-
-
-
-
-
6=26KN/m
~=24KN/m
~ a50 t=27KN/m' !'-
6sot =26KN/m
0 8 650 t=27KN/m' !'-
0 8 650 t=27KN/m' (X)
L = 27.5m B = 0.6011l"
L/8 = 46 =SO From Fig. 7.2,
N~ = 3 N~ = 15 and LJB = 3.5 L Lc - >>-B B
SK 7/31 The pile penetrating different strata.
Ppu = 0.283 ((15 X 71.5) + (3 X 489.5)) = 719kN
-
SK 7132 Condition at bottom of pile.
Determination of skin resismnce '1:P5; = kAJ s
Design of Piled Foundations 331
0 IDO ([) ID
....
0 0 0
-
332 Reinforced Concrete
Stratum 4
A s4 =it X 0.60 X 7 = 13.2m2
/s4 = 24 kN/m2
P si4 = 13.2 X 24 = 316.8 kN
Stratum 5
A ss= :It X 0.60 X 8 = 15.1m2
Iss = 31 kN/m2
Psi5 = 15.1 X 31 X 468.1 kN
'1:P8; = 931.6 kN
Fourth method of skin resistance /s =
-
Design of Piled Foundations 333
q = effective vertical stress at middle of layer = 1.5 X 26 +
1.5 X 24 + 7.5 X 27 + 2 X 26 + 3.5 X 27 - {16- 3) X 10 =
294kN/m2
Is = ~c + 0.5ij Ks tan 0 P si4 = 13.2 [2 X 13.8) + (0.5 X 294 X
2 X 0.43)] = 2033 kN The fourth method of skin resistance is giving
much higher values than the first method and may be ignored from
the point of view of conservatism.
Pu = P pu + P su = 719 + 932 = 1651 kN
Allowable working load on pile = 1651 = 660 kN 2.5
Designed pile is 600 mm diameter bored and cast in-situ concrete
pile with an average length of 27.5 rn to carry a working load of
660 kN. This is a conservative theoretical estimate of single pile
vertical load capacity and must be verified by actual pile tests on
site.
Step 3 Determine horizontal capacity of singk pile See Section
7.2. Assume cohesive soil.
Mellwd 1
Es = 650N where N = SPT No. Es of Stratum 1 = 650 X 3 = 1950
kN/m2 5 of Stratum 2 = 650 x 5 = 3250 kN/m2 5 of Stratum 3 = 650 x
14 = 9100kN/m2 Es of Stratum 4 = 650 X 24 = 15 600 kN/m2 5 of
Stratum 5 = 650 X 31 = 20150 kN/m2
ksB = t.3(s84)ft (~) Erlr 1 - ~
Er = 28 x 106 kN/m2 for pile concrete
k8 ,B = 1672kN/m2 k52B = 2909 kN/m2 k53B = 8875kN/m2 k54B =
15914 kN/m2 ks58 = 20999 kN/m2
X 0.604 = 6.36 X 10-3 m4
k s l = 2787kN/m3 k s2 = 4848 kN/m3 ks3 = 14 792 kN/m3 ks4 = 26
523 kN/m3 k55 = 34998kN/m3
-
334 Reinforced Concrete
g 0>
:.:: ~ UJ
e
8 0 10 ..
"' z 0 ... (.) lJ.J 111
0 ...,
1
2 r-~
4 1--~ 6 ~ 1--6
1--~ 10
1-11
1--12
1-13 ~ 1--15
~ 17 18 -
19 -
20 -
21 1-22 ----23 -24 -~ 26 tn 1-26
~ 30 ~
Method 2
k5 = 240qu kN/m2 = 480ckN/m2
k5 , = 480 X 11.3 = 5424 kN/m3 ks2 = 480 X 20.2 = 9696kN/m3 ks3
= 480 X 60 = 28800kN/m3 k54 = 480 X 13.8 = 6624 kN/m3 kss = 480 X
71.5 = 34320kN/m3
The values given by Method 1 are smaller or softer which will
produce larger deflection and bending moments in pile. For the sake
of conservatism use values given by Method 1.
S = node spacing for finite element analysis = 0.60 m 8 = 0.60m
spring stiffness = SBks kN/m
-
~ ~ :;;
.....
X :::>
~ ex ...
VI
!i tc ex :;;
-7
X :::>
'C ex ...
"'
SK 7/33 Finite element model of pile.
-
Design of Piled Foundations 335
Ignore top l.SB of pile for lateral support from soil. The whole
length of pile need not be modelled.
Stratum 1 Spring stiffness = 0.60 x 0.60 x 27'07
= 1003kN/m
Stratum 2 Spring stiffness = 0.60 x 0.60 x 4848
= 174SkN/m
Stratum 3 Spring stiffness = 0.60 X 0.60 x 14 792
= 5325 kN/m
Stratum 4 Spring stiffness = 0.60 x 0.6 x 26523 = 9548 kN/m
Assume full fixity of pile with pile cap. Apply unit load at top
of pile and find pile stiffness and bending moment and shear in
pile using a two-dimensional computer program.
A = 0.283 m2 I = 6.36 x w-3 m4
ResuUs of computer run Maximum moment = 2.481cNm/kN
Pile top deflection = 0.12 mm/kN
Single pile horizontal stiffness = ~~ = 8333 kN/m Step 4
Determine approximate number of piles and spacing
Maximum vertical load on pile cap = 1610 + 1480 = 3090 kN = P p
3090
R;v = Cv = 660 == 4.7
Assume maximum allowable horizontal displacement of pile cap is
10 mm.
Maximum horizontal load = 28 + 18 + 156 = 202 kN = H
Maximum horizontal load on pile to limit deflection to lOmm =
8333 X 0.010 = 83 kN per pile
H 202 R;H = Cu = 83 = 2.4 R; = greater of R;v and R;H = 4.7
l.lR; == 4.7 X 1.1 = 5.17
Use 6 no. piles.
-
336 Reinforced Concrete
8
10
11
12
13
14
15
16
11
19
20
21
22
23
24
25
2.48
1. 05
.058
0.21
-O.OB
-0.28
-0.42
- 0.51
-0.56
- 0.57
-0.57
-0. 56
-0.52
- 0.48
-0.43
-0.37
-0.31
-0.25
-0. 19
-0.1 4
-0. 11
-0.09
-0.05
-0.02
0
Step 5 Determine size of pile cap B = diameter of pile = 0.6
m
1.58 = 1.5 X 0.6 = 0.9 m
SK 7/34 Bending moment (kNm) due to 1 kN horizontal load at top
of pile.
Allow 0.9 m from centre of pile to edge of pile cap. Assume 0. 9
m depth of pile cap.
-
SK 7/35 Layout of piles under pile cap.
Spacing of piles:::::: 38 2: 3 x 0.6 = l.R rn
Design of Piled Foundations 337
Size of pile cap assumed is 5.4 rn x 3.6 m x 0.9 m.
Step 6 Carry out load combination
Estimation of load on pile LCI = l.ODL + 1.0/L
N = L610 + 1480 = 3090 kN
Hx = 28 + 18 = 46kN H_.., = OkN
MA = OkNm M_. = 112 + 72 = 184kNm
LC3 = l.ODL + 1.0/L + l.OWL
N = 3090kN
Wind in x-x direction
H X = 46 + 156 = 202 kN H_. = OkN
M , = OkNm M,. = 184 + 624 = 808kNm
Wind in y-y direction
H_. = 46kN H . = ll2kN
M .. - = 448kNm Mv = 184kNm
LC4 = l.ODL + l.OWL
-
338 Reinforced Concrete
N = l 610kN
Wind in x - x direction
H,. = 2H + 156 = 184kN H_. = OkN
M_, = OkNm Mv = 112 + 624 = 736 kNm
Wind in y - y direction
II,. = 28kN lfv = 112kN
M.r = 448kNm M_. = 112 kNm
Estimation of loads on piles .for bending moment and sliear
calculations in pile cap
LC5 = 1.4DL + 1.6/L
N = 1.4 X 1610 + l4RO x 1.6 = 4622 kN
H,. = 1.4 X 28 + 1.6 X 18 = 68 kN Hv = OkN
Mx = OkNm M_. = l .4 X 112 + 1.6 X 72 = 272 kNm
LC6 = 1.2DL + 1.2/L + 1.2WL
N = 1.2 X 1610 + 1.2 X 1480 = ::\708 kN
Wind in x - x direction
H,. = l.2 x (28 + 18 + 156) = 242.4 kN H_v = OkN
M_. = OkNm Mv = 1.2 X (112 + 72 + 624) = 969.6kNm Wind in y - y
direction
H, = 1.2 X (28 + 18) = 55.2 kN II,, = 1.2 X 112 = 134.4 kN
M, = 1.2 X 448 = 537.6kNm M_,. = 1.2 x (112 + 72) = 220.8
kNm
LC1 = 1.4DL + 1.4WL
N = 1.4 X 1610 = 2254kN
Wind in x-x direction
H, = l.4 (28 + 156) = 257.6 kN H_. = OkN
-
II T031985 0011425 bTT II
SK 7/35 Layout of piles under pile cap.
..
Design of Piled Foundations 337
1800 1800
~7- $ g _y __ - '--=r~-+-m
~ -4- ---4+--f-t: 0 m
Spacing of piles~ 3B ~ 3 x 0.6 = 1.8 m
Size of pile cap assumed is 5.4 m x3.6 m x0.9m.
Step 6 Carry out load combination
Estimation of load on pile LC1 = l.ODL + 1.0/L
N = 1610 + 1480 = 3090 kN Hx = 28 + 18 = 46kN H.v = OkN
Mx = OkNm My = 112 + 72 = 184kNm
LC3 = l.ODL + 1.0/L + l.OWL
N = 3090kN
Wind in x - x direction
Hx = 46 + 156 = 202kN H.v = OkN
Mx = OkNm M,v = 184 + 624 = 808 kNm
Wind in y-y direction
Hx = 46kN H.v = 112kN
Mx = 448kNm My = 184kNm
LC4 = l.ODL + l.OWL
-
340 Reinforced Concrete
c = 71.5 kN/m2 at bottom of group
q = effective stress at bottom of group = 489.5 kN/m2 (see Step
2) N'= 3} N! = 15 for = 8" Group end-bearing capacity = 1 .8 x 3.6
x (15 x 71.5 + 489.5 x 3)
= 16465 kN
Ultimate group capacity = 7996 + 16465 = 24461 kN
24461 Allowable group capacity = -- = 9784 kN
2.5
Allowable group capacity based on single pile capacity
3960kN
Design basis is single pile capacity.
Step 8 Carry out analysis of pile cap
6X660=
Assume that pile cap is rigid. Assume SOO mm backfill on top of
pile cap. Assume a surcharge of 5 kN/m2 on backfill with no
eccentricity. It is always advisable to use the table as
presented.
W = weight of pile cap + weight of backfill on pile cap + weight
of surcharge on backfill
= ).4m X 3.6m X U.Y m X 24kN/m3 + 5.4 X 3.6 X 0.5 m X 20 kN/m3 +
5.4 X 3.6 X 5 kN/m2
= 712kN
Maximum service load on pile without wind = 665 kN
Maximum service load on pile with wind = 771 kN
X y
X
T--'1/--f-;-- - --, - - --r- ~-+--x
4-- ~~- -8- -y
SK 7/37 Calculations of pile group stiffness.
-
Analysis of loads on pile cap.
Load case N Mx My Hx Hy ex e,. ehx eh,- h P or Pu M: M* y Mxx
Myy T
LC1 3090 0 184 46 0 0 0 0 0 0.9 3802 0 0 0 225.4 0 LC3 3090 0
808 202 0 0 0 0 0 0.9 3802 0 0 0 989.8 0 LC3 3090 448 184 46 112 0
0 0 0 0.9 3802 0 0 548.8 225.4 0 LC4 1610 0 736 184 0 0 0 0 0 0.9
2322 0 0 0 901.6 0 LC4 1610 448 112 28 112 0 0 0 0 0.9 2322 0 0
548.8 137.2 0 LCs 4622 0 272 68 0 0 0 0 0 0.9 5619 0 0 0 333.2 0
LCt. 3708 0 969.6 242.4 0 0 0 0 0 0.9 4562 0 0 0 1187.6 0 LCt. 3708
537.6 220.8 55.2 134.4 0 0 0 0 0.9 4562 0 0 658.6 270.5 0 LC1 2254
0 1030.4 257.6 0 0 0 0 0 0.9 3251 0 0 0 1262.2 0 LC1 2254 627.2
156.8 39.2 156.8 0 0 0 0 0.9 3251 0 0 768.3 192.1 0 I~ (I) 60' Mxx
= Mx + Ne1 + Hyh + M: Myy = My + Nex + Hxh + Mi I ~ T = Hxehy +
Hyeh.< P =N+W Pu = N + 1.4W (or l.2W)
~ 0 Q..
6' c :::3 Q.. I .... s :::3 Cll
~ .....
-
Loads on pile.
Load case Por Pu Hx Hy M.u Myy T
LCI 3802 46 225.4 -LC3 3802 202 989.8 -LC3 3802 46 112 548.8
225.4 -LC4 2322 184 901.6 -LC4 2322 28 112 548.8 137.2 -LC5 5619 68
333.2 -LC6 4562 242.4 1187.6 -LC6 4562 55.2 134.4 658.6 270.5 -LC1
3251 257.6 1262.2 -LC7 3251 39.2 156.8 768.3 192.1 -
fxx = ~y2 = 4.86 m2 l yy = u 2 = 12.96m2 l u = lxx + l yy =
17.82m2 P MxxY MyyX Q --+ --+--
max - R lxx f yy P MxxY MyyX
Qmin = R - fxx - l yy H = y(H; + H;)
R R = no. of piles = 6
Mr = bending moment in pile = 2.48H (see Step 3) x = 1.8m y =
0.9m b = horizontal displacement at top of pile = 0.12H mm (see
Step 3)
~ ~ ~. ::I 0' ..,
@ 0.. ('} 0 = (') ...
Cb
Qmax Qmin H or 0
Mp or Mpu b (mm) Hpu
665 602 7.67 19.0 0.9 771 496 33.67 83.5 4.0 767 501 20.18 50.0
2.4 512 262 30.67 76.1 3.7 508 266 19.24 47.7 2.3 983 890 11.33
28.1 1.4 925 595 40.40 100.2 4.8 920 601 24.21 60.0 2.9 717 367
42.93 106.5 5.2 711 373 26.94 66.8 3.2
-
Design of Piled Foundations 343
SK 7138 General arrangement of pile cap and piles. y
SURCHARGE ON BACKFILL
0 0 U'l
0 0 en
Allowable service load on pile without wind = 660 kN OK
Allowable service load on pile with wind = 660 x 1.25 = 825 kN
OK
Bending monunJ and shear force in pile cap
SK 7/39 Critical sections for calculation of bending moment in
pile cap.
2
-
344 Reinforced Concrete
Sections 1-1 and 2- 2 are taken at the face of column. Assume
column size = 800 mm x 800 mm Dead load of pile cap+ surcharge+
backfill = 0.9 x 24 + 0.5 x 20 + 5 = 36.6kN/m2
Applying load factors for different load cases:
1.4 X 36.6 = 51.2 kN/m2 1.2 X 36.6 = 43.9 kN/m2
Ml 1 = bending moment due to dead load of pile cap etc. on
section 1-1 3.6 X 51.2 X 2.32
48 2
= 7.5kNm
3.6 X 43.9 X 2.32 =
2 = 418.0 kNm or
Mn = Bending moment due to dead load of pile cap etc. on section
2-2 5.4 X 51.2 X 1.42 O
2 = 271. kNm
5.4 X 43.9 X 1.42 =
2 = 232.3 kNm or
SK 7/40 Critical sections for shear.
Step 9 Determine cover to reinforcement From soil test reports,
the total S03 is 0.75%. This means it is Class 3 exposure (see
table in Step 9 of Section 7.6). Minimum cover on blinding
concrete= 50 mm Minimum cover elsewhere = 90 mm
Assume 90 mrn cover for pile cap everywhere.
Step 10 Calculate area of reinforcement in pile cap M = bending
moment in pile cap as found in Step 8.
Mll = 2264.9kNm from table in Step 8.
-
Bending moments and shear in pile cap.
Load case Qt Q2 Q;~ Q4 M)t Mh Mit Mh M11 M22 V' 3.' V44
LC5 890 937 983 983 -487.5 -271.0 2752.4 1405 2264.9 1134.0 -
199.1 -298.6 LC6 595 760 925 925 - 418.0 - 232.3 2590.0 1140 2172.0
907.7 - 170.7 -256.0 LC, 844 882 920 676 - 418.0 -232.3 2234.4 1323
1816.4 1090.7 -170.7 -256.0 LC1 367 542 717 717 -487.5 - 271.0
2007.6 813 1520.1 542.0 - 199. 1 -298.6 LC1 657 684 711 427 - 487.5
- 271.0 1593.2 1026 1105.7 755.0 -199.1 - 298.6
Q ., Q2, Q;~ and Q4 are pile reactions Mit = 1.4 (Q;~ + Q4) M22
=0.5 (Qt + Q2 + Q;~) M11 = M]t +Mit
\13:~ = Q;~ + Q4 V44 = Qt + Q2 + Q;~ V33 = V:b + Vj;~ Mit. Mh,
V;\3 and V44 are bending moments and shears in pile cap due to dead
load of pile cap+ surcharge Mil> Mh, V~3 and V44 are bending
moments and shears in pile cap due to pile reaction M 11 , M22,
V;~3 and V44 are combined bending mome nts and shears in pile cap
/5 = 120 mm
-
346 Reinforced Concrete
I ,, II
I I I ,, ,, It It
I I SK 7/41 Moments in pile and pile cap due to pile fixity.
For this load case, pile fixity moment = 19.0 kNm per pile.
Pile fixity moment on pile cap is opposite in sign to moment M
11 and may be ignored. Assume 20 mm diameter reinforcement.
dx = 900 - 90 (cover) - 10 (half bar dia.) = 800 mm feu = 30
N/mm2 for concrete in pile cap
K = ~ = 2264.9 X l ~Ji = 0.033 /cubd2 30 X 3600 X 8002
z = d[ 0.5 + J ( 0.25 - 0~9) J = 0.96d =:; 0.95d = 760mm
M 11 2264.9 X lW 2 A = -- = = 7447 mm st 0.87 [yZ 0.87 X 460 X
7fiJ
Assume /y = 460 N/mm2 for HT reinforcement
b = 3.6 m
Area of 20mm dia. bar = 314 mm2 24 x 314 = 7536 mm2
Use 24 no. 20mm diameter bars equally spaced (approximate
spacing 150 mm) in the x-x direction. Mzz = 1134kNm from table in
Step 8.
Ignore the effect of pile fixity moments. Assume 12 mm diameter
reinforcement.
dy = 900 - 90(cover - 20(bar d ia.) - 6(half bar) = 784 mm
-
Design of Piled Foundations 347
K = M 12 = 1134 X l(f = O.Oll fcubd2 30 X 5400 X 7842
z = 0.95d by inspection = 0.95 X 784 = 745 mm
k = Mn = 1134 x 1
-
348 Reinforced Concrete
1.5dx = 1.5 X 800 = 1200 mm
hence no enhancement of shear stress is allowed
V 1766.9 X 103 v =- = = 061N/mm2 bd 3600 X 800 .
p = lOOAs = 100 X 7536 = 0.26% bd 3600 X 800
Vc = 0.425 N/mm2 < 0.61 N/mm2 from Fig. 11.3
400 1200 1100 Ov
SK 7143 Critical shear plane in pile cap.
The cheapest alternative is to bring the outer piles in towards
the centre of pile cap by 20mm in the x-x direction only. This has
very little effect on pile reactions.
av = 1200mm 1.5dx = 1200 mm 2d 2 X 800 av 1200 1.333
Increase grade of concrete from feu= 30N/mm2 to feu= 40N/mm2 in
pile cap.
Vet = 0.47N/mm2 from Figs 11.2 to 11.5
Vc2 = Vc~e~) = 0.47 x 1.333 = 0.63N/mm2 > 0.61N/mm2 OK
V 44 = shear on critical section 4-4 = 2511.4 kN (see table in
Step 8).
av = 1800 - 1200 + 120 - 400 (half column) = 320 mm 1.5dy = 1.5
X 784 = 1176mm > av
-
Design of Piled Foundations 349
2dv 2 X 784 -a-: = 320 = 4'9
= lOOAsc = 100 X 3482 = O OS'Y< p bd 5400 X 784 . 0
(See Step 22 for minimum percentage of reinforcement.) Vet =
0.40N/mm2 for feu = 40N/mm2 vc2 = 0.40 x 4.9 = 1.96N/mm2
V 2511 X toJ Vc = bd = 5400 X 784
= 0.59N/mm2 < 1.96N/mm2 OK
Step 12 Check punching shear stress in pile cap
0 oo (DOl
SK 7144 Critical planes for punching shear of piles in pile cap.
CRITICAL PL ANE FOR PUNCHING SHEAR
U 1 = perimeter of column = 2 (800 + 800) = 3200 mm Since pile
spacing is not greater ~han 3 times diameter of pile, then punching
shear stress at critical perimeter for column need not be
checked.
u2 = perimeter on punching shear critical plane for pile load =
2300 + 2256 = 4556 mm
Ultimate maximum column load, N = 4622 kN
Ultimate maximum pile load, Q = 983 kN from table in Step 8.
-
350 Reinforced Concrete
N 4622 X 103 Column punching shear stress = U
1d = 3200 x 0_5 X (800 + 784)
= 1.82 N/mm2 < 0.8'-/ leu or 5 N/mm2 OK
P . h . f .1 983 X loJ unchmg s ear stress at pen meter o pt e =
600 800 ;tX X
= 0.65 N/mm2 < 0.8'-/ leu OK . . Q 983 X loJ
Ptle punchmg shear stress = U2d = 4556 x 0_5 (SOO + 784)
= 0.27 N/mm2
Minimum ve for Grade 40 N/mm2 concrete = 0 .40 N/mm2 OK
Step 13 Check area of reinforcemenJ in pile Unsupported length
of pile, /0 , is assumed negligible. Assume lclh < 10. The pile
is treated as a short column . From tables in Step 8,
Qmax = 983 kN Qmin = 367 kN
with M = 28.1 kNm with M = 106.5 kNm
Max. shear , Vmax = 42.93kN
Assume minimum cover is 75 mm.
h 600
SK 7/45 Pile reinforcement .
Allowing for links and bar diamete r, assume hs = 420mm.
hs 420 h = 600 = 0.70 = k
leu = 30 N/mm2
~ = 0.029 = 0.095 R 0.3
M 28.1 e = - = - = 0.029 m
N 983
_Q_ma_x = 983 X 103 = 2.73 N/mm2 h 2 600 X 600
-
Design of Piled Foundations 351
From Table 11.19, it is observed that minimum reinforcement may
be used. Use minimum reinforcement. For the second load case,
Qmin = 367 X 1oJ = 1 N/mm2 h2 600 X 600
e -= 1 R
Again use minimum reinforcement.
Step 14 Check stresses in prestressed concrete piles Not
required.
Step 15 Check shear capacity of RC pile No shear check is
necessary if MpuiNu ~0.60h. Mpu 106.5 X 106 -= =290mm Nu 367 X
1oJ
0.60h = 0.60 x 600 = 360 mm No shear check is necessary.
Hpu 42.93 X toJ 0.75Ac = 0.75 X 1t X t/Xf/4
= 0.20N/mm2 < 0.8Yfcu OK
Step 16 Check shear capacity of prestressed pile Not
required.
Step 17 Check minimum reinforcement in RC pile lOOAsc -- ~
0.4
A c
Ac X 0.4 A sc = .....:;__100--
Tt X 30Q2 X 0.4 = 100 = 1131mm2
Use 6 no. 16 mm dia. HT bars (1206 mm2).
Step 18 Check minimum prestress in prestressed pile Not
required.
Step 19 Maximum reinforcement in pile Not required.
-
352 Reinforced Concrete
-
-
Step 20 ConlllinnumJ of reinforcement in pik Minimum dia. of
links= 0.25 x bar dia. = 4mm :::: 6mm
Maximum spacing of links = 12 x smallest dia. of bar = 12 x 16
192mm
Use 6 mm dia. links at 175 mm centres.
Step 21 Links in prestressed piks Not required.
Step 22 Minimum Unsion reinforcement in pile cap
I I
-- $ -I
I ~ - ~ -'r
I I
A s ;:: 0.0013bh in both directions
Minimum reinforcement in the x-x direction = 0.0013 x 3600 x 900
= 4212mm2
Provided 7536mm2 (see Step 10). Minimum reinforcement in the y-y
direction = 0.0013 x 5400 x 900 = 6318mm2
Area of 16 mm dia. bar = 201 mm2 32 X 201 = 6432mm2
Area required = 3842 mm2 from Step 10
Use 32 no. 16mm dia. bars equally spaced (approximate spacing
170 mm) in the y-y direction.
I I
1f -{-(l-
I I
24 - 20
I I
$-I
I rv-I I
32 - 1 6
f--
-
SK 7/4(, Pile cap reinforcement revised to suit minimum
reinforcement.
Step 23 Curtailment of bars in pile cap Minimum anchorage at
ends of bars is 12 X dia. of bar.
12 x 20 = 240mm 12 x 16 = 192mm
Provide a minimum 250 mm bent up length of pile bottom
reinforcement. Check full anchorage bond length of the main tension
bars.
-
Design of Piled Foundations 353
feu = 40N/mm2
Reinforcement used is Type 2 deformed bars. From Table 3.29 of
BS8110: Part 1: 1985,1ll
tension anchorage length = 32 = 32 X 20 = 640 mm
More than 640 mm length of bar is available beyond section 1- 1
in Step 8.
Step 24 Spacing of bars in pile cap . . lOOA. Maxtmum percentage
of retnforcement = p = ----;;;{
_ 100 X 7536 _ 0
- 3600 X 800 - 026 Yo
Maximum allowed clear spacing for p less 0.3% is 3d or 750 mm,
whichever is less. Spacing of bars adopted is 150 mm.
Step 25 Early thermal cracking If it is felt necessary to limit
early thermal cracking of concrete in pile cap then minimum
reinforcement on sides and top of pile cap should be provided based
on method of calculation shown in Chapter 2.
Step 26 Assessment of crack width in flexure Normally the
calculations in Step 24 will deem to satisfy the crock width
limitations of BS8110: Part 1: 198s.tJ
If calculations are necessary to prove the limitations of crack
width due to flexure in pile cap then methods shown in Chapter 3
should be followed.
Step 27 Connection of pile to pile cap From Step 17, 16mm HT
Type 2 deformed bars arc used. From Table 3.29 of BS8110,
full anchorage bond length = 32; 32 x 16 = 512 mm
The bars from the pile will project 600 mm into pile cap. (Sec
general recommendations for design of connections in Chapter
10.)
-
354 Reinforced Concrete
7.8 FIGURES FOR CHAPTER 7
l O
0 9
0 8
E 07
06
0-5
~ I""~
' '-.... ........ ~
......
!'"-r-.. k. 01 02 0 3 04 05 0 '6 07 08 0 ~ 10
e s
1000 8
6
4
l
. o-700 I
v I [// v v v ~ v /
./
/ /
I ,, 16 11
~-4 0 r
/. lO 1 0 8 .s:! ~ 6
-iiQ:) 4
l
1 lO 30 40 B,deg