9 dp9 anchorage zone detailing

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Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 1 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. Y. Guyon, (1974), Limit-State Design of Prestressed Concrete, Halsted Press, J. Wiley & Sons. 2. P. Collins, D Mitchell, (1991), Prestressed Concrete Structures, Prentice Hall (Englewood Cliffs).

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Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 1

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

REFERENCES: 1. Y. Guyon, (1974), Limit-State Design of Prestressed Concrete, Halsted Press, J. Wiley &

Sons. 2. P. Collins, D Mitchell, (1991), Prestressed Concrete Structures, Prentice Hall (Englewood

Cliffs).

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 2

Transversal tensile stress computation through the deep

beam analogy.

From P. Collins, D Mitchell

Prestressed Concrete Structures Prentice Hall Ed.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 3

Strut and Tie modellization

(Morsch, Leonhardt, Schlaich, Marti)

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 4

Deep Beam Analogy

(P. Collins, D Mitchell Prestressed Concrete

Structures Prentice Hall Ed.)

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 5

END BLOCK CHARACTERISTIC VALUES

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

1a 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.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 6

DIFFUSION ZONES

a) Primary distribution zone

b) Forces within the prisms

(a)

(b)

(c) Transverse pressures due to curved lines of thrust

(c)

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 7

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)

Surface forces

ST and bursting forces

ET

(S=surface, E=eclatement)

3'0.04 0.20'S

a aT Pa a

13E

PT where 12

2

a

a

218

sN mm (suggested)

• Limit Stress in the concrete immediately behind the anchorage plate (§ 4.1.8.1.4.): 0.9c ck j

f

• Reinforcement to contrast the spalling (EN 1992 Appendix J): ,

1.20.03s spalling

yd

PAf

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 8

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”.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 9

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.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 10

(A) SURFACE FORCES COMPUTATION [kN]

Distance from

anchorage Distance from

anchorage Prestressing

Force Surface Force

Surface Force

Total 1/3

Prism a a' P [kN] (a) (b) (a+b)   [m]  [m]  [kN] [kN] [kN] [kN] [kN]

1-2-3 0,15 0,40 1200 48 22,5 70,54 23,51 4 0,40 0,075 400 16 25,6 41,62 / 5 0,075 0,075 400 16 0,0 16 / 6 0,075 0,075 400 16 0,0 16 / 7 0,075 0,075 400 16 0,0 16 / 8 0,075 0,075 400 16 0,0 16 / 9 0,075 0,075 400 16 0,0 16 /

10-11-12 0,075 0,15 1200 48 8,9 56,89 18,96

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

24 8 201

sA legs mm mm

For the others anchors in the same vertical line, a single mesh is used, consisting of 4 8

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.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 11

(B) BURSTING FORCES

13E

PT where 12

2

a

a

220s

N mm (suggested)

Vert. Dist. from anchorage Vert. Dist. from anchorage Ratio Prestress Force Bursting Force

a1 a P TE [m] [m] [kN] [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 (by assuming a tensile contribution from the concrete): 1 group of 2 bars 12 mm at 0,08m from the end face. 1 group of 4 bars 12 mm at 0,16m from the end face. 1 group of 2 bars 12 mm at 0,24m from the end face. Reinforcement (by ignoring the contribution of the concrete in tension): 1 group of 2 bars 16 mm at 0,08m from the end face. 1 group of 4 bars 16 mm at 0,16m from the end face. 1 group of 2 bars 16 mm at 0,24m from the end face. Or a spiral with 5 turns of bars 10 for each anchorage.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 12

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

Details and Dimensions

Forces per unit of depth

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 13

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 2 1D h m .

Forces per unit of depth. Profiles of lines of force.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 14

The radial pressure 0

Q computation is given in the following Table.

Distance from top face at support

Distance of line of thrust from upper face at the inner section Q0 from

top surface

y0 yu y0-yu (y0-yu)/D P Q0 Q0 Anchors [m] [m] [m] [kN] [kN] [kN]

1-2-3 0,15 0,17 -0,02 -0,02 1200 -24 -24 4 0,95 0,57 0,38 0,38 400 152 128 5 1,1 0,98 0,12 0,12 400 48 176 6 1,25 1,3 -0,05 -0,05 400 -20 156 7 1,4 1,54 -0,14 -0,14 400 -56 100 8 1,55 1,66 -0,11 -0,11 400 -44 56 9 1,7 1,74 -0,04 -0,04 400 -16 40

10-11-12 1,85 1,89 -0,04 -0,04 1200 -48 -8

The last column contains, level by level, the cumulative values of 0

Q through the depth, from

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.

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 15

Results: At the left side:

Tensile forces 0,i i

Q between the lines of thrust corresponding to set of

anchors (1-2-3) and 4 (max value 24kN). Compressive below this level.

At the right side:

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

(zone 0

s ): Two bars 12 mm are placed at 0.22m from the end face, to resist the tensile force of 24kN.

At the left side (zone

us ):

Six stirrups 12 mm, with 2 legs are placed, uniformly spaced, within the zone

us , between 2 6 0,66h m and 5 6 1,66h m to resist the tensile force of

184kN.

See Figure below

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 16

End block reinforcement

(Guyon)

Prof. P. Giorgio MALERBA BRIDGE THEORY AND DESIGN SHEAR IN PRESTRESSED BEAMS 17

END