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pile cap design

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Pile cap design
fc’=40MPA
fy=420 MPA
reduction factor Ï•=1.0
ultimate load transferred to column=3000 kn
Concrete cover=50mm
dimension as shown in the figure below.

Design the pile cap. Assuming the shear will be resisted by concrete. 


since the shear will be resisted by concrete. then the ultimate shear will determine pile cap depth. Pile cap shall be designed for one-way and two-way shear from column and piles. the critical section of shear will be checked to verify pile cap capacity. also, it will be designed for flexural.

 1.the shear capacity of pile cap will be provided by concrete so Vc≥Vu. The critical section for two-way shear located at d/2 around column edge.
Ultimate load for each pile =3000/6=500kn.
In this example all piles are outside the perimeter of two-shear. So all pile will cooperate fully in ultimate shear so
Vu=3000 kn
Vc=(0.33λ√(fc'))b*d
Vc=0.33*1*√40.(350+d+600+d)*d=2.087*(950+d)*d=1982.75*d+2.087*d2
B is the perimeter of two-way critical section
Ï•Vc=Vu
1982.75*d+2.087*d2=3000,000
2.087*d2+1982.75*d-3000,000=0
d=777.48mm
assume 800 mm
so the depth of pile cap is 800 mm.
now we will check one-way shear for column. Also don’t forget to check one-way and two-way shear for piles.



One-way shear for column.
The critical section for one-way shear located at a distance d from column edge as show in figure below. We can notice that three piles contributing in shear. So Vu-500*3=1500 kn
Ï•Vc=0.166 λ√(fc' ) bwd
bw is the length of critical section.
Ï•Vc=0.166*1*√40*6000*800=503940.57N
∴Ï•Vc>Vu then safe.

Two-way shear for piles
The critical section for piles shall be similar to column. The critical section will be located around the pile at d/2=400 mm. the shear capacity for the section shall be verified using same equations. Only the shape around pile will be adjusted as shown in figure below. In this section one pile only contribute to ultimate shear=500kn.
Ï•Vc=(0.33λ√(fc'))b*d
=0.33*1*√40*((2*3.14*650)/4+500+500)*800=4216.99kn>Vu so section is safe.
One-way shear for piles
The critical section for corner pile shall be at 45 angle with pile cap edge as shown in figure below. The ultimate shear is Vu=500kn.
Ï•Vc=0.166 λ√(fc' ) bwd
Ï•Vc=0.166*1*√40*1353*800=1136385.98≥Vu
Similarly, you can check for other piles.
Flexural design for pile cap

The critical section is at the edge of the column. Pile cap will be designed for long and short direction

The moment for short direction

The moment for short direction will be produced from three pile 
Mu=500*3*1.825=2737.5kn.m
Mn=As.fy*(d-a/2)
a=As.fy/0.85bfc.=β1.c
β1={   (0.85      for 17≤ fc'≤28MPA 
                                   0.85-0.05((fc'-28)/7)≥0.65   for fc'≥28MPA

Ï•Mn=Mu assuming  Ï•=0.9 (tension control)
.0.9As.fy*(d-a/2)=2737500000
0.9*As.420*(700)=2737500000 assuming d-a/2=700mm

As=10345.8mm2
Using 21 of T25 steel
d=800-(50+25/2)=737.5mm
a=As.fy/0.85bfc.=21.3mm

β1=0.85-0.05((fc'-28)/7)≥0.65
=0.76
C=a/β1=28.02mm
εt=εc/C*(d-c)=(0.003*(737.5-28.02))/(28.02)=0.0759≥0.005 so assumption valid

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