paper_design of pile caps

Design of Pilecaps

Naveed Anwar

ACECOMS, AIT

Y

X

Plan

Ø600

M

N

V

Section

2000 4000

3600

600

1200

2000 800

1500

Design of Pilecaps ACECOMS, AIT

Introduction

• Pile foundations are extensively used to support the

substructures of bridges, buildings and other structures

• Foundation cost represents a major portion

• Limited design procedure of Pile cap Design

• Need for a more realistic methods where

– Pile cap size comparable with Columns size

– Length of pile cap is much longer than its width

– Pile cap is subjected to Torsion and biaxial Bending

– Pile cap width, thickness and length are nearly the same


Beams, Footings and Pilecaps

Beam

Footing

Pile-cap

h

b

L

h

b

L

L >> (b, h)Use “Beam Flexural and

Shear-Torsion Theory”

(b, L) >> h

b <=> h <=> L

Use “Beam/Slab Flexural and

Shear Theory”

Use Which Theory ??

h

L


Current Design Procedures

• Pile cap as a Simple Flexural Member

– standard specifications (AASHTO, ACI codes) are used.

– Beam/Slab theories or truss analogies are used, and torsion is not

covered for special cases

• The Tie and Strut Model

– More realistic, post cracking model

– No explicit way to incorporate column moments and torsion

– No consideration for high compressive stress at the point where all the

compression struts are assumed to meet.

– Assumption of struts to originate at the center line is questionable

• The Deep Beam, Deep Bracket Design Approach

– Mostly favored by CRSI, takes into account Torsion, Shear

enhancement

– Complex, insufficient information on its applicability.


Conventional Design Procedure

The pile cap design load consists of column loads, weight of pile

cap, back-fill and surcharge. All horizontal loads are transferred

to the center of pile cap.

The sectional model is utilized for pile cap design and the design

of deep flexural member is considered.

For design by sectional model, Pile reactions are determined by

the combined stress equation.

The critical section for computing moment is located at the

column face in each directions.

Minimum reinforcement for flexural member to be provided is

adequate to develop a factored resistance of 1.2 x Mcr which is

equal to 0.90/fy for concrete C25.

Minimum steel ratio for bottom reinforcement is 0.0020 x b x t in

each direction


Shear Considerations

Beam shear with critical section at d from face of column

Punching shear with critical section at d/2 from face of column

Deep beam shear using CRSI recommendation with critical

section at face of column

Two-way deep corbel shear using CRSI recommendation with

critical section at perimeter of column

Punching shear of individual pile at corners

Combined shear and torsion with critical section at d from

face column

Combined shear and torsion with critical section at face

column

.

Conventional Design Procedure


Pile Reactions: Rigid Cap Method

• Each pile carries an equal amount of the load for`

concentric axial load on the cap or for n piles carrying a

total load Q , the load per pile is

The combined stress equation ( assuming a planar stress

distribution ) is valid for a pile cap non centrally loaded or

loaded with a load Q and a moment, as

• Where = moments about x and y axes, respectively

• x ,y = distances from y and x axes to any pile

• = moment of inertia of the group, computed as

22 y

yM

x

xM

n

QP xy

p

2AdII o 22 , yx

yx MM ,


• The assumption that each pile in a group carries equal

load may be nearly Correct when the following criteria

are all met:

• .The pile cap is in contact with the ground

• .The piles are all vertical.

• .Load is applied at the centre of the pile group

• .The pile group is symmetrical and cap is very thick

Pile Reactions: Rigid Cap Method


2

2

1

1

c

uv

c

uv

o

uu

J

cM

J

cM

db

Vv

Punching Shear: ACI Equations

• Concrete Capacity, Vc

• Direct Shear

• Shear with Moment Transferdb

Vv

o

uu

dbfV

dbfb

dV

dbfV

occ

oc

o

sc

oc

c

c

'

'

'

4

2

42


Footing - Column Connection

• Transfer of Moment

– Partially by flexure: Top or Bottom Bars near the column

– Partially by eccentricity of shear: Non-uniform distribution of

shear stresses

2

1

3

21

1

b

bMM fff

)1( fvvv MM

Cu

ff

Cu

Cu

f

VVwhen

portsinerioron

columncornerVV

columnedgeVVwhen

portouteredgeon

4.0

sup25.1

5.0

75.0

sup/0.1

The Space Truss Model

Naveed Anwar

ACECOMS, AIT


Truss Model for behavior of Pile caps

• Truss analogy already in use

– For shear design of “Shallow” and “Deep” beams

– For Torsion design of shallow beams

– For design of Pilecaps

– For design of joints and “D” regions

– For Brackets and corbels

• Proposed use of “Modified Space Truss Model”

– Unified and integrated design of RC Members for combined

moment, shear and torsion where significant cracking is

expected

– Does not apply to design of compression/ tension members


Simple Vs Modified Truss Model

L=2.5

a=1.6

d=1.4 h=1.6

T

P=10,000 kN

a) Simple "Strut & Tie" Model c) Modified Truss Model B

L=2.5

a=1.6

d=1.4

d=1.4 h=1.6

T

1

= tan-1 d/0.5L

= 48 deg

T = 0.5P/tan

T = 4502 kN

= tan-1 d/0.5(L-d1)

= 68.5 deg

T = 0.5P/tan

T = 1970 kN


A Space Truss Model for Pilecap

P1

P2

P4

P3

a2

a2

d

L2

L1

Main members

Secondary members


L/d =2

L/a =1

L

d

a

L/d =1

L/a =0.5

L/d = 3

L/a = 1.5

L/d = 4

L/a = 2

L/d = 5

L/a = 2.5

L/d = 6

L/a = 3

L

d

a

Tie-Strut Model

Effect of Span:Depth Ratio


Angle = 18 Deg

Angle = 34 Deg

Angle = 45 Deg

Angle = 64 Deg

Not OK: Too Shallow

NOT OK: Too Steep and Expensive

OK: USed by ACI Code

OK: Most Ecconomical

Tension in Bottom Chord

Tie-Strut Model

Effect of Strut Angle


Modified Space Truss Model

• General

– MSTM is created using the basic assumptions of the Space Truss

Theory and the Tie-Strut approach with appropriate modifications.

– MSTM gives more realistic results taking into account the

• Uses actual dimensions of the column and its location.

• The stiffness of the piles, ratios the dimensions of the pile cap.

• Assumptions

– The concrete in the pile cap is assumed to resist no direct tension.

– All tension is resisted by the reinforcement. The reinforcement in a

particular zone can be lumped together as a single Tie.

– All compression is resisted by the concrete.

– The columns axial loads and moments are assumed to be

transferred to the pile cap at the corners of the equivalent

rectangular column section


Construction of Model

• Identify the overall form and geometry of the truss.

• Connect the primary nodes with each other by primary

horizontal and diagonal members.

• Add secondary members to the basic truss to provide static

stability for anticipated load cases.

• Generally use a spring element to represent the piles, however

for determinate trusses (2, 3, 4 pile) simple support; can also be

used.

• Add lateral restraint, to the nodes at the top of the piles to

ensure the overall stability of the truss. Determine the

approximate areas of the cross-section of these truss members.

• Apply equivalent loads to the truss model at the column nodes.

• Analyze the structure using any appropriate computer program.


Interpretation of the Results

• Reinforcement should be provided along all directions where

truss members are in significant tension.

• This reinforcement should be provided along the direction of the

truss member

• The distribution of the reinforcement should be such that its

centroid is approximately in line with the assumed truss element.

• The compression forces in the struts should be checked for the

compressive stresses in the concrete, assuming the same area to

be effective, as that used in the construction of the model.

• The Bearing Stress should be checked at top of piles and at base

of columns


L

D

d) Three Pile Case

d) Six Pile Case

P

1

P

2

P

4

P

3

a2

a2

d

L2L

1

a) Two Pile Case

c) Four Pile Case

D

L1

L1 < (3D + b)

L2 < (3D + b)

Main members

Secondary members

e) Sixteen Pile Case (Also for 12 pile, 14 pile, 20 pile)

P

P

P

P

Application of MSTM


b

a

2- Pile, Small L L < (3D + b)

L

D

4- Pile

b

L1

D

L1

L2 a

Application of MSTM


5- Pile

b

L1

D

L1

aL2

a

L

D

2- Pile, Large L L > (3D + b)

b

Application of MSTM

paper_design of pile caps

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