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]
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