Pile Caps

Design of Pilecaps 3600 600

Y

2000

4000

1200

2000

X

800

Ø600

N

Plan M

V 1500

Naveed Anwar Section

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

Design of Pilecaps

ACECOMS, AIT

Beams, Footings and Pilecaps Beam

L

L >> (b, h) Use “Beam Flexural and Shear-Torsion Theory”

h

Footing L

(b, L) >> h Use “Beam/Slab Flexural and Shear Theory”

h b

Pile-cap b h L L

Use Which Theory ?? h

b Design of Pilecaps

ACECOMS, AIT

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. Design of Pilecaps

ACECOMS, AIT

Major Areas of Concern • Consideration for the relative stiffness of the piles and the pile cap. • Consideration for the relative location and size of column with respect to piles and pile cap center.

• Considerations of more than one column on the pile cap. • Considerations of the relative dimensions and proportions of the pile cap (length, width, depth ratios). • Considerations of the column load and biaxial moments, with associated eccentric shear and torsion.

• A consistent model and approach for flexure, shear and torsion design.

Design of Pilecaps

ACECOMS, AIT

Important Observations • Pile cap acts as a 3D elastic solid. • Beam/slab theory can not be used for all cases

• Relative size of the column plays a very significant role in the stress profiles of smaller pile caps. • Pile reactions do not strictly follow Combined stress equation. • For long pile caps, – distribution of longitudinal flexural stresses is more or less linear and closely responds to the simple beam theory – Deep Beam behavior is not significant for flexural computations in the longitudinal direction

Design of Pilecaps

ACECOMS, AIT

… Important

Observations

• Flexural stress and strain distribution is highly non linear for – long pile caps in the transverse direction – small pile caps in both directions • Torsion is not applied at the center and is not uniform over the length. • For small pile caps the column moments are transferred to the pile cap by the formation of inclined compression and tension stress zones. • Ordinary beam or slab design methods do not appear to be applicable to piles of the same size and propositions. • Elastic FEM analyze not useful for Reinforcement Design

Design of Pilecaps

ACECOMS, AIT

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 Design of Pilecaps

ACECOMS, AIT

Conventional Design Procedure  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 . Design of Pilecaps

ACECOMS, AIT

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 Q M yx Mx y Pp    n  x2  y2

• Where

Mx,M y

= moments about x and y axes, respectively • x ,y = distances from y and x axes to any pile •  x , y = moment of inertia of the group, computed as I  I o 2

2

Design of Pilecaps

 Ad 2

ACECOMS, AIT

Pile Reactions: Rigid Cap Method • 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

Design of Pilecaps

ACECOMS, AIT

Practical Considerations • In a practical case of a four- pile symmetrical group centrally loaded, each pile. Will carry one-fourth of the vertical load regardless of cap rigidity (or thickness). With a fifth pile directly under the load, cap rigidity will be a significant factor. The structural design of pile caps is only minimally addressed in the literature. But the following may be used as a guide: • Bending moments are taken at the same sections as for reinforced-concrete footings and defined in Art. 15-4 of the ACI Code – Pile caps must be reinforced for both positive and negative bending moments. Reinforcement should be placed so there is a minimum cover of 75 mm for concrete adjacent to the soil. Where piles extend into the cap only about 75 mm the bottom reinforcement should be 75 mm above the pile top in case of concrete cracking around the pile head. Design of Pilecaps

ACECOMS, AIT

Practical Considerations – .Pile caps should extend at least 150mm beyond the outside face of exterior piles and preferably 250mm. When piles extend into the cap more than 75 mm the bottom rebars should loop around the pile to avoid splitting a part of the cap from pile head moments and shears. – .When pile heads are assumed fixed they should extend into the pile cap at least 300 mm. The minimum thickness of pile cap above pile heads is 300 mm ( required by ACI 318 Art15-7 ) – .Some kind of tension connectors should be used on the pile heads if the piles are subjected to tension forces.

• Pile cap shear is computed at critical sections same as spread footings

Design of Pilecaps

ACECOMS, AIT

Punching Shear: ACI Equations • Concrete Capacity, Vc

 4 ' Vc  2   f c bo d c    sd  ' Vc  2   f c bo d bo  

• Direct Shear

• Shear with Moment Transfer

Vc  4 f c' bo d

Vu vu  bo d

vu 

Design of Pilecaps

Vu  v M u1c  v M u 2c   bo d J c1 J c2 ACECOMS, AIT

Punching Shear: BS Equations • Concrete Capacity

vmax 

0.8 f cu 5 N / mm2 min

• Effective Direct Shear – General Equation – Corner/ Edge column with bending perpendicular to edge

 1.5M t  Vt 1  Vt x 

  

 1.5M t Veff  Vt 1.25  Vt x 

  

Veff

• Actual Shear stress – Max at face of column/ load

vmax 

– At any other section

v

Design of Pilecaps

V uo d

V ud ACECOMS, AIT

Footing - Column Connection - ACI • Transfer of Moment – Partially by flexure: Top or Bottom Bars near the column  f  1.0 on edge / outer sup port

1 M f  M f   f  2 b 1   1  3  b2

when Vu  0.75VC Vu  0.5VC

edge column corner column

 f  1.25 f on inerior sup ports when Vu  0.4VC

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

M v  M v   v  (1   f )

Design of Pilecaps

ACECOMS, AIT

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

Design of Pilecaps

ACECOMS, AIT

Simple Vs Modified Truss Model a=1.6

a=1.6 P=10,000 kN

d=1.4

d=1.4 

T

h=1.6

d=1.4

h=1.6

 

L=2.5

T

L=2.5 1

a) Simple "Strut & Tie" Model

  T T

= tan-1 d/0.5L = 48 deg = 0.5P/tan = 4502 kN

Design of Pilecaps

c) Modified Truss Model B   T T

= tan-1 d/0.5(L-d1) = 68.5 deg = 0.5P/tan = 1970 kN

ACECOMS, AIT

A Space Truss Model for Pilecap P1

a2

a2

P4

P2

P3 d

L2 L1 Main members Secondary members

Design of Pilecaps

ACECOMS, AIT

a

a

d

Tie-Strut Model

d L/d =1 L/a =0.5 L

L/d =2 L/a =1

Effect of Span:Depth Ratio

L

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

Design of Pilecaps

ACECOMS, AIT

Not OK: Too Shallow

Tie-Strut Model Tension in Bottom Chord

Effect of Strut Angle

Angle = 18 De g

OK: Most Ecconomical

Angle = 34 De g

OK: USed by ACI Code

Angle = 45 De g

NOT OK: Too Steep and Expensive

Angle = 64 De g

Design of Pilecaps

ACECOMS, AIT

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

Design of Pilecaps

ACECOMS, AIT

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.

Design of Pilecaps

ACECOMS, AIT

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

Design of Pilecaps

ACECOMS, AIT

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

Design of Pilecaps

ACECOMS, AIT

Application of MSTM P D

D

P P P

L

L1

a) Two Pile Case

d) Six Pile Case L1 < (3D + b)

P 1

L2 < (3D + b)

a2

a2

P

P 4

2

P d

3

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

L1

L2 Main members Secondary members

c) Four Pile Case

Design of Pilecaps

d) Three Pile Case

ACECOMS, AIT

Application of MSTM

L1

b

b

a L2

a

D

D

L

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

L1

4- Pile

Design of Pilecaps

ACECOMS, AIT

Application of MSTM L1 b

b a L2

a

5- Pile

D D

L1

L

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

Design of Pilecaps

ACECOMS, AIT