9 Dp9 Anchorage Zone Detailing

Prof. P. Giorgio MALERBA

BRIDGE THEORY AND DESIGN

SHEAR IN PRESTRESSED BEAMS

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DESIGN PRACTICE ANCHORAGE ZONE DETAILING CONTENTS 1 . SEQUENCE OF THE DIFFUSION ZONES. 2 . SURFACE FORCES 3 . BURSTING FORCES 4 . SECONDARY DIFFUSION ZONE (BALANCING ZONE)

R EFERENCES: 1. 2.

Y. Guyon, (1974), Limit-State Design of Prestressed Concrete, Halsted Press, J. Wiley & Sons. P. Collins, D Mitchell, (1991), Prestressed Concrete Structures, Prentice Pr entice Hall (Englewood Cliffs).



Transversal tensile stress computation through the deep beam analogy.

From P. Collins, D Mitchell Prestressed Concrete Structures Prentice Hall Ed.


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Strut and Tie modellization (Morsch, Leonhardt, Schlaich, Marti)


3


Deep Beam Analogy (P. Collins, D Mitchell

Prestressed Concrete Structures Prentice Hall Ed.)



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END BLOCK CHARACTERISTIC VALUES

End block subjected to a centered force. Transversal tensile stresses as a function of

 

a

1

a

   

(A) Position of the point of maximum stress. (B) Maximum stress intensity. (C) Position of the point of zero stress. (E) Magnitude of the resultant bursting force.

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DIFFUSION ZONES

a) Primary distribution zone

b) Forces within the prisms (a)

(c) Transverse pressures due to curved lines of thrust

(c)

(b)

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FIRST DIFFUSION ZONE. SURFACE AND BURSTING FORCES The high and concentrated prestressing force gives rise to an intense compression zone immediately behind the anchorage, followed by a high transversal stresses zone (bursting zone)

3   a  a'   T  0.04  0.20     P S a a '     

(S=surface, E=eclatement)

•

•

 



2  18 N mm (suggested)

Surface forces T and bursting forces T

E

1   



E

S

P

T

s

3

where

2a

2a

Limit Stress in the concrete immediately behind the anchorage plate (§ 4.1.8.1.4.):  Reinforcement to contrast the spalling (EN 1992 Appendix J):

A

s , spalling

 0.03 

1

c

 0.9 f

1.2 P

f

yd

ck j




WORKED EXAMPLE – From Yves Guyon Ref. 1. SURFACE FORCES.

Details and Dimensions

Primary distribution zone. Lines drawn at 45° from the quarters of each anchor plate. Construction of the line “ab, bc, cd, …, hi”.

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PRIMARY DIFFUSION ZONE - Hypotheses and working criteria. (From Y. Guyon Ref. 1) 

 













The force applied by each anchor is diffused within a zone bounded by two planes at 45°. These planes intersect each other at points b, c , d, …, i . The uppermost plane cuts the top face at “a” and the lower plane cuts the lower face at “i”. The stress along this line abcdefghi is irregular. It also marks the boundary of the zone of zero stress, which lies between this line and the end face. We consider the horizontals through these points of intersection. We assume that each anchor is associated with a corresponding prism bounded by the horizontal lines that enclose it. Within these prisms and the in the immediate region of the anchors the primary force redistribution takes place. This gives rise to very high local stresses which need a first group of reinforcement. This primary zone extends approximately to a line “ L” whose abscissas measured from the end face, are twice those of the line abcdefghi. As known, the webs are usually thickened near the support. It is desirable that this thickening is sufficiently extended beyond this line “L”. Within each prism, the line of force extending from the anchor have profiles such as those shown in the Figure.

In the following we shall compute: (A) The surface forces; (B) the bursting forces; (C) the tensile forces in the balancing zone.




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(A) SURFACE FORCES COMPUTATION [kN]

Prism 1-2-3 4 5 6 7 8 9 10-11-12



Distance from anchorage a

Distance from anchorage a'

[m]

[m]

0,15 0,40 0,075 0,075 0,075 0,075 0,075 0,075

0,40 0,075 0,075 0,075 0,075 0,075 0,075 0,15

Surface Force (a) [kN]

1200 400 400 400 400 400 400 1200

48 16 16 16 16 16 16 48

Surface Force (b) [kN]

Total

1/3

(a+b) [kN]

[kN]

22,5 70,54 23,51 25,6 41,62 / 0,0 16 / 0,0 16 / 0,0 16 / 0,0 16 / 0,0 16 / 8,9 56,89 18,96

Maximum force behind each of the anchors 1-2-3: F = 23,51 kN s



Prestressing Force P [kN] [kN]

 4 legs  8mm  201 mm

2

For the others anchors in the same vertical line, a single mesh is used, consisting of 4 mm bars, anchored by means of 90° bends at top and bottom.



Horizontal meshes are also provided.



All these meshes are placed as closely as possible to the anchors.

 8




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(B) BURSTING FORCES

T

E



P 3

1   

where

 

2a

1



2a

Vert. Dist. from anchorage Vert. Dist. from anchorage a1 [m]

a [m]

s

 20 N mm

Ratio 

2

(suggested)

Prestress Force Bursting Force P [kN]

TE [kN]

1-2-3

0,1

0,3 0,3333

1200

266,7

4 to 9

0,1

0,15 0,6667

400

44,4

10-11-12

0,1

0,15 0,6667

1200

133,3

Reinforcement  1 group of 2  1 group of 4  1 group of 2

(by assuming a tensile contribution from the concrete): bars  12 mm at 0,08m from the end face. bars  12 mm at 0,16m from the end face. bars  12 mm at 0,24m from the end face.

Reinforcement  1 group of 2  1 group of 4  1 group of 2

(by ignoring the contribution of the concrete in tension): bars  16 mm at 0,08m from the end face. bars  16 mm at 0,16m from the end face. bars  16 mm at 0,24m from the end face.

Or a spiral with 5 turns of bars

 10

for each anchorage.



(C) SECONDARY DIFFUSION ZONE. From Yves Guyon Ref. 1

Details and Dimensions

Forces per unit of depth


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Forces per unit of depth and profiles of lines of force. 

The lines of force corresponding the forces applied at the anchors are shown in Figure.



The lever arm is D

 h 2  1m .

Forces per unit of depth.

Profiles of lines of force.

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The radial pressure Q computation is given in the following Table. 0

Anchors 1-2-3 4 5 6 7 8 9 10-11-12



Distance from top face at support

Distance of line of thrust from upper face at the inner section

y0 [m]

yu [m] 0,15 0,95 1,1 1,25 1,4 1,55 1,7 1,85

Q0 from top surface

y0-yu [m] 0,17 0,57 0,98 1,3 1,54 1,66 1,74 1,89

-0,02 0,38 0,12 -0,05 -0,14 -0,11 -0,04 -0,04

(y0-yu)/D

P [kN]

Q0 [kN]

-0,02 1200 0,38 400 0,12 400 -0,05 400 -0,14 400 -0,11 400 -0,04 400 -0,04 1200

-24 152 48 -20 -56 -44 -16 -48

Q0 [kN]

-24 128 176 156 100 56 40 -8

The last column contains, level by level, the cumulative values of Q through the depth, from 0

which the resultant of these pressures at each corresponding level may be obtained. 

The sign of these forces may be obtained by inspection of the curvatures of the lines of thrust.



The compressive force has a maximum value of 176kN, here increased to (176+8)=184kN, to take into account of the closing error of -8kN.




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Results:

At the side:

left





At the right side:





 

Tensile forces

Q i

between the lines of thrust corresponding to set of 0, i

anchors (1-2-3) and 4 (max value 24kN). Compressive below this level. At the right side, the relative position of the tensile and compressive forces is the opposite. We have a compressive force of 24kN between the lines of thrust (1-2-3) and 4. Tensile forces below this level. The compressive force has a maximum value of 176kN, here increased to (176+8)=184kN, to take into account of the closing error of -8kN

Reinforcement

At the left side Two bars 12 mm are placed at 0.22m from the end face, to resist the tensile force of 24kN. (zone s ): 0

At the left side Six stirrups 12 mm, with 2 legs are placed, uniformly spaced, within the zone (zone s ): s , between 2h 6  0, 66 m and 5h 6  1,66 m to resist the tensile force of u

u

184kN. See Figure below



End block reinforcement (Guyon)


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END


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9 Dp9 Anchorage Zone Detailing

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