Conc g
Designing structures with structural concrete P
Load F
zp
zp Concrete Concrete stresses stresses resulting resulting solelysolely from prestressing from prestressing
a
+
Tension Tension P
P
P
P
P
El
+
Fcr
Compression Compression Prestressing Prestressing
Prestressed concrete Yield
Reinforced concrete Fracture
First crack Decompression
b Concrete Concrete stresses stresses resulting resulting from load from and loadprestressing and prestressing g
+
P
P
P
+
-
- -
-
+
P
+ - +
=
F w
-
=
+
σ = 0σα = 0 Load Load α Prestressing Prestressing
c
B 4.21
Load F
Load F
F
g
Deflection w at mid-span due to F B 4.22
Epmo
Epmo
Epmo
under quasi-permanent Prestressed loads. Less cracking Pre-tensioning PrestressedReinforced Reinforced means more durable structures. Another concrete concrete concrete concreteFor pre-tensioning, profiled prestressing tenadvantage of prestressed structural compodons are tensioned in a prestressing bed Yield Yield Aρ, Ερ (0) nents isElthatElthere is less fluctuation Fracture in the between two anchor blocks and concrete is Fracture tension caused by loads on the reinforcement. poured in over them. After the concrete hardPrestressed concreteFirst construction ens, the anchoring of the strands is released crack First crack is a very Fcr Fcr appropriate method of building with concrete and the prestressing force is transferred to the Decompression Decompression and has many advantages. structural component through the composite While the aim is to have as few cracks as posaction. Prestressing components in a preSchwerlinie Schwerlinie sible in ordinary conditions of use, imminent stressing bed requires stationary production des Betondes ideellen (0) F F F F Aρ, Σρ querschnitts Querschnitts component failure in the ultimate limit state, facilities and can really only be carried out as well as in prestressed concrete elements, in a plant. Prestressed, precast concrete Aρ, Ερ (0) w w should be signalled by clearly visible cracks components are usually made using this Znp Zip and deformations. Prestressing force is usually method. Straight prestressing tendons cannot calculated in accordance with serviceability, be deflected, so prestressed, precast conDeflection wamount at mid-span Deflection wThe at mid-span due F to Fcrete components made using this technique so it should not be too high. of todue reinforcement required to ensure load-bearing are not suitable for beams, such as continuous B 4.18 Load-bearing concrete structure cast in situ, can be economically supplemented with reinbeams, whose internal moment is subject to a University library, Tokyo (J) 2007, Toyo Ito & forcing steel. change of sign. Associates Architects, Structural engineers: Sasaki Structural Consultants Prestressing have a higher strength (0)tendons Ec, p+g Eigengewicht g Aρ, Ερ Aρ, Ερ (0) B 4.19 A comparison of slab systems than ordinary reinforcing steel. Their steel can Bonded post-tensioning a Concrete slab cast in situ achieve high steel strains, and the decline Post-tensioning involves concreting sheaths b Slab made of precast elements in prestressing force caused by concrete into a structural component. If the tendons Znp made with precast B 4.20 Load-bearing structure components creep can be compensated for. They are avail- are not in sheaths during concreting, they are Pm0 Pm0 B 4.21 Principle of prestressing and stress states, able as round or oval, smooth or profiled wires threaded in or injected and tensioned against g g using the example of a single-span girder G/2 G/2 with diameters ofSchwerlinie up Schwerlinie to 10 mm, as strands of the concrete after it hardens. After post-tenSchwerlinie Schwerlinie a Self-weight not effective, no prestressing three or seven interwoven wires, and as bars sioning, the sheaths are injected with cement des Betondes Beton-des ideellen des ideellen b Self-weight not effective, prestressing (0) Ac, Ec Ac, =0Ec =0 Aρ, Σρ Aρ, Σρ (0) querschnitts querschnitts Querschnitts with thread ribs and diameters ofQuerschnitts up to 50 mm. mortar and the stressing jacks released. Injecteffective c Self-weight and prestressing effective, Prestressing(0)tendons are classified accordingEpAc, mortar creates a bond between the tendon Ac, =0 Ep =0 (0) Aρ, Ερ Aρ, Ερ decompression ing to their characteristic yield or tensile and the concrete and protects the prestressÜbertragungslänge lbp lbp Znp Znp Zip Zip B 4.22 Load-deflection diagram comparing a non- Ps=gPs=g strength, which is specified in DIN EN 10 138. ing steel tendons from corrosion. These comprestressed and a prestressed reinforced A typical specification for prestressing steel ponents are produced on site on a scaffold. concrete beam B 4.23 Prestressing a flat slab with a prestressing jack is “St 1570/1770”, for example. In contrast to prestressing in a prestressing bed, the geometry of their tendons can be g g freely chosen as long as the minimum curvaPrestressing methods and techniques SpannSpannpresse presse is taken into account, so post- ture radius Prestressing methods are systems from tensioning can be adapted to the component’s certain manufacturers thatEigengewicht includeg tendons Ec, p+g Ec, p+g Eigengewicht g P0 P0 moment. Post-tensioning of this kind internal as well as anchorage systems, couplers and creates deflection forces. The injection process sliding sheaths and are usually approved by Znp Znp authorities. In must be carried out with great care and in a national building inspection G/2 G/2 G/2 G/2 controlled manner to avoid damage. planning prePm0 Pm0the geometric dimensions of Pm0 Pm0 stressed structural components, the space G/2 G/2 G/2 G/2 Unbonded post-tensioning required for anchorage systems must be taken Unbonded post-tensioning uses strands g g into account because they can be crucial, especially in slender components. Prestressing coated with grease by the manufacturer to Up Up protect them from corrosion and a plastic techniques differ from each other in terms of Pm0 Pm0 Übertragungslänge lbp lbp lbp casing – usually a PE casing – which are Pm0 Pm0 the Übertragungslänge tendons’ positioning, the typelbpof composite action, the timing and application of prestress- laid in the formwork, fixed with spacers at ing force and composite action. Some of these the desired height and concreted in. No bondG/2 G/2 G/2 G/2 ing occurs. After the concrete hardens, the distinct methods are described below.
B 4.23
81
Ac, Ec =
Ac, Ep =
Ps=
Span press P0
Up Pm