ANALYSIS & DESIGN OF MULTI STOREYED BUILDINGS
V.M.RAJAN,M.E.(Struct),FIE,
Former CE/Civil/TANGEDCO
Pile cap design –Two pile group
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Design of Two pile group (By bending theory) :
Two pile group will incapable of taking moment about X-X axis. The cap for Two pile
group must be connected for twin piles by grade beams in a line transverse to the
common axis of the piles.
Spacing of piles:
(i) Piles founded on hard stratum minimum spacing is 2,5 times pile dia.
(ii) Piles resting on rock is 2.0 times pile dia.
(iii) Friction piles (Piles founded in clay or sandy soil) is not less than 3.0 times pile
dia.
Check for Truss action:
Find the shear span av.
av =S/2- horizontal width of column /2- pile dia/2+ pile dia (hp)/5 where S is pile
spacing. If d/av > 2, truss action exist. Then pile cap has to be designed using truss
theory. Truss theory can be used for design up to five piles only. If d/av < 2,
bending theory may be applied.
Overloading: when a pile in a group , designed for a certain safe load is found,
during or after execution, to fall just short of the load required to be carried by it, an
overload up to 10% of the pile capacity may be allowed on each pile. The total
overloading on the group shall not ,however be more than 10% of the capacity of
the group subject to the increase of the load on any pile being not more than 25%
of the allowable.
Transient loading :
The maximum permissible increase over the safe load of a single pile in wind load
case is 25%.
In case of seismic loads the increase of safe load on a single pile may be limited to
the provisions contained in IS1893 part1-2016
(i) friction piles in clay or sand 25%
(ii) Hard clay or rock 50%
Data:-
Pile Diameter hp : 500 mm
Spacing of piles 3 hp = 3 x 500 : 1500 mm (Friction pile)
Column Dimension a x b : 300 x 500 mm
Fx=50 KN ; Fy=700 KN; Fz=0; Mx=0; My =0; Mz=75 KNm
(From Staad reactions).
Bottom of pile cap is 1500mm from ground level.
Load from column : 700 KN
Concrete Mix : M25
Steel Grade : Fe 500
Soil Density (ℽs) : 20 KN/m3
DESIGN : -
1.Pile Cap Dimension :
Length of Pile Cap = C/c of Pile + hp /2+ 150 + hp /2 + 150
= 1500 + 500/2+ 150 +500/2+ 150 =2300 mm
Width of pile cap = hp + 150 + 150 = 800 mm
Consider depth of Pile cap = 1.5 hp = 1.5 x 500 = 750 mm.
2.Calculation of pile reactions :-
Total factored axial compressive load
= P +/- M
N L
P=Total load =Fy + cap weight +Soil weight above cap.
N= Number of piles.
M=Total BM=Mz +Moment due to Horizontal force+ Eccentric BM
In our case Eccentric BM=0
L=distance between piles/ lever arm distance.
Load from column= Fy=700 KN
Cap weight =2.30 x0.80x 0.75 x 25= 34.5 KN
Soil weight above pile cap }
2.3 x0.80 x (1.50-0.75) x 20 } = 27.6 KN
Total P =700+34.5+27.6 =762.1 KN
Bending moment due to horizontal force=Fx x depth of pile cap=50 x 0.75=37.5
KNm
Note: In analysis the column is considered to be fixed at the top of the pile cap or
footing. Therefore, the horizontal force obtained from staad analysis will act at the
top of the pile cap, footing or pedestal.
Moment at ground level in Z direction =Mz =75 KNm
Total BM M= Mz + Moment due to horizontal force
= 75 +37.5 =112.5 KNm
Since BM is clockwise Pile no. 1 will get uplifted (-) and Pile no. 2 will be
compressed (+).
Reaction in pile no.1 = P - Mz =762.1 - 112.5
N L 2 1.5
= 381 -75 =306 KN (C) Safe.
Reaction in pile no.2 = P + M =762.1 + 112.5
N L 2 1.5
= 381 +75 =456 KN (C) <700 KN. Safe.
Pile reaction PR 1= 306 KN
Pile reaction PR2 = 456 KN
3.Design :
Calculation of Bending moment:
Bending moment will be calculated from face of column or pedestal.
Muz =1.5 x Force x distance
Force= Maximum load occur of two piles=456 KN
Distance= Distance from centre of pile to face of column =0.50m
Theoretically speaking we consider 0.5 times pile spacing =0.5 x1.50=0.75m
However from Practical consideration, we take the distance from face of column or
pedestal instead centre line of column=0.75-0.50/2=0.50m
Muz =1.5 x 456 x 0.50 =342 KNm
Check for effective depth of pile cap :
Depth of pile cap D=750mm
Assuming clear cover as 60 mm and dia of bar=20mm
d= effective depth of pile cap provided =750-60-20-20/2 =660 mm
For M25 concrete and Fe 500 steel MR= 0.133 fck b d2 = Mu=342 x 106 Nmm
Here B= 800 mm fck =25
d= √342 x 106/ 0.133 x 25 x 800 =358.57 mm < 660mm
Reinforcement :-
Area of steel required
Ast= 0.5 x fck [1-√1-4.6 x Muz /(fck xBx d2) ] xB xd
fy
Ast= 0.5 x 25 [1-√1-4.6 x342 x106/(25x800x6602) ]x800 x660
500
Ast =1251.1 mm2
Mini Ast=(0.12/100) x 800 x750=720 mm-2
Using 20mm dia bars for 800 mm width spacing =800 x 314/1251.1 =201 mm
Provide 20mm dia bars at 150 mm C/c along X-X axis along length of pile cap.
4.Check for one way shear :-
One way shear will be critical for a distance ‘d’ from face of column. Critical section
of ‘d’ falls act at centre line of pile so one way shear check is not mandatory.
However, lets check here for conservatively considering shear force proportionately.
Vu=1.5 x [(456/0.50) x0.09] =123.12 KN
Nominal shear stress ↊v = Vu /b x d =123.12 x 103 /(1000 x 660) =0.187 N/mm2
<0.36 N/mm2 for M25 and % of steel of 0.25%
↊v < ↊c i.e 0.187 N/mm2 < 0.36 n/mm2 Hence safe.
5. Check for punching Shear :-
Two way or punching shear is critical at a distance d/2=660/2=330 mm from face of
column. Critical section d/2 is falling before pile centre along the length of pile cap
and falling outside the pile cap in width directions.
Hence consider only the sections along the length of pile cap.
Nominal shear stress ↊v’ = Vu’ /(perimeter x d)
Vu’ = column load i.e.=700 KN
Vu’=1.5 x 700 =1050 KN
Periphery length = 2 x 800 =1600 mm
↊v’= Vu’/ (b0 xd) =1050 x 103 /(1600 x 660) =0.99 N/mm2
↊c’ =ks x ↊c= (0.5+βc) x(0.25 x √fck ) Here ks should not greater than 1.0
↊c’ =1 x 0.25 x √25 ) =1.25 MPa
↊v’ ≤ ↊c’ i.e 0.99 MPa ≤ 1.25 MPa .Hence Safe.
6. Sketch :
