D es e s i g n o f P il i l ec ec a p s 3600 600
Y
2 00 0
4 00 0
1200
X
2000
800
ACECOMS, AIT Ø600
N
Plan M
V 1500
Section
N ave avee ed An A n war
Introduction •
Pile foundations are extensively used to support the substructures substructur es of bridges, buildings and other o ther structures structures
•
Foundation cost represents a major portion
•
Limited design procedure 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 Torsion and biaxial Bending
–
Pile cap width, thickness and length are nearly the same
B eam s , Fo o t i n g s an d P il ec a p s Beam
L
L >> (b, h) Use “Beam Flexural and
h
Shear-Tors ion Theor y ”
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
C u r r e n t D es i g n P r o c ed u r es •
Pile cap as a Simple Flexural Member –
–
•
Beam/Slab theories or truss analogies are used, and torsion is not covered for special cases
The Tie and Strut Model –
–
–
–
•
standard specifications (AASHTO, ACI codes) are used.
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
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
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 P p M x , M y
Q n
M y x
M x y
x y 2
2
•
Where
•
x ,y = distances from y and x axes to any pile
•
x 2 ,
y2
= moments about x and y axes, respectively
= moment of inertia of the group, computed as I I o
Ad 2
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
P u n c h i n g S h ear : A C I E q u a t i o n s
•
Concrete Capacity, Vc
•
Direct Shear
4 ' V c 2 f c bo d c s d ' V c 2 f c bo d bo ' V c 4 f c bo d
vu •
Shear with Moment Transfer vu
V u bo d
V u bo d
v M u1c J c1
v M u 2c J c 2
F o o t i n g - C o lu m n C o n n ec t i o n
•
Transfer of Moment –
Partially by flexure: Top or Bottom Bars near the column f 1.0 on edge / outer sup port
M f M f f
1
2 b1 1 3 b2
when V u 0.75 V C V u 0.5 V C
edge column corner column
f 1.25 f on inerior sup ports
when V u 0.4 V C –
Partially by eccentricity of shear: Non-uniform distribution of shear stresses
M v M v v (1 f )
T he Sp a ce Tr u s s M o d el
Naveed Anwar ACECOMS, AIT
Tr u s s M o d e l f o r b eh a v i o r o f P i le c a p s
•
•
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
S im p l e Vs M o d i f i ed T r u s s M o d el a=1.6
a=1.6 P=10,000 kN
d=1.4
d=1.4
d= 1. 4
h=1.6
T
L=2.5
T
L=2.5 1
a) Simple "Strut & Tie" Model
= tan-1 d/0.5L = 48 deg T = 0.5P/tan
T = 4502 kN
c) Modified Truss Model B = tan-1 d/0.5(L-d1) = 68.5 deg T = 0.5P/tan
T = 1 970 kN
h= 1. 6
A S p ac e Tr u s s M od el f o r P il ec ap P1
a2
a2
P4
P2
P3 d
L2 L1 Main members Secondary members
a
a
d
Tie-Strut Model
d L/d =1 L/a =0.5 L
L/d =2 L/a =1
Eff ect 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
Not OK : Too Shallow
Tie-Strut Model Tension in Bottom Chord
Ef f ect of Strut Angle
Angle = 18 Deg
OK: Most Ecconomical
Angle = 34 Deg
OK: USed by AC I Code
Angle = 45 Deg
NOT OK: Too Steep and Expensive
Angle = 64 Deg
M o d i f i ed S p ac e Tr u s s M o d e l •
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
C o n s t r u c t i o n o f M o d el •
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
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
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
d) Three Pile Case
Application of MSTM
L1
b
b
a L2
a
D
D
L
2- Pile, S mall L L < (3D + b)
L1
4- Pile
Application of MSTM L1 b
b a L2
a
5- Pile
D D
L1
L
2- Pile, Large L L > (3D + b)
