2. Review of Design and Construction of FRP reinforced concrete design
2.8. Design Philosophy of Pre-Stressed FRP concrete elements
Figure 27 Shinmiya Bridge
ππ=πππ’β πππβ ππβ πππ (19)
Figure 28 shows that this is for a single layer of prestressed reinforcement used. The total strain capacity of the tendon can be computed using (19).
This equation gives us a relationship between the available strains and c / d ratio.
π
π = πππ’
πππ’β πππ’β πππβ ππβ πππ (20)
Equilibrium shows that the tension within the tendon is equal to the compression on the concrete.
0.85πβ²ππ½1ππ=ππππππ’ (21)
(21) can be solved for Ο = Οb, where Ο = Ap/bd is the prestressed reinforcement ratio gives.
ππ= 0.85π½1 πβ²ππ
πππ’π (22)
The balanced ration can be expressed in materials properties as shown in (23) by substituting (19) and (20).
ππ= 0.85π½1 πβ²π
πππ’
πππ’
πππ’+πππ’β πππβ ππβ πππ (23)
(23) can be further simplified into (24) because certain variables can be negligible which then can be considered as zero.
ππ= 0.85π½1 πβ²π πππ’
πππ’
πππ’+πππ’β πππ (24)
Where the available strain that is present in the tendon for flexure is represented by (Ξ΅pu β Ξ΅pe).
This material property ranges from 1.3% to 3.8% for Aramid and Carbon fibre tendons.
During the design of a flexural prestressed FRP concrete member, it is certain that the modes of failure govern the initial design process. The two modes of failure are presented below
ο· Tension-controlled section
ο· Compression- controlled section.
Tensioned-controlled section is when the prestressed reinforcement ratio (Ο) is less than the balanced reinforcement ratio (Οb). The strength of the prestressed member will rely on the tensile strength of the tendon used. Failure takes places once the FRP tendon ruptures which suggests that the concrete does not reach its ultimate strain of 0.003 during failure. The moment capacity can be calculated using a rectangular stress block which would accurately represent the stress distribution in the concrete (reference).
ππ=ππππππ’
(
π βπ2)
(25)a can be deduced by the equilibrium of forces in the concrete section.
π= ππππππ’
0.85πβ²π (26)
Compression-controlled section is when the prestressed reinforcement ratio (Ο) is more than the balanced reinforcement ratio (Οb). The strength of the prestressed member is governed by the concrete compressive strength, this means that its ultimate strain will be achieved but the strain value in the tendon is unknown at this point in time. The neutral access is found and the tendon is assumed to be linear elastic. The concrete member behaves in a nonlinear stress- strain manner which lets us make the appropriate consideration of using a rectangular stress block. The neutral axis can be found by the using the force equilibrium of the section.
π=ππ’π (27)
ππ’= ππ+
[
ππ2(
1βππππ’ππ) ]
2βππ2(
1βππππ’ππ)
(28)Since FRP are perfect linear elastic up until failure, the stress in the tendon is governed by the modulus of elasticity in the tendon and its strain. This is incorporated into the material constant Ξ».
π= πΈππππ’
0.85πβ²ππ½1 (29)
The moment of forces can be summed about the prestressed tendons, which will give us the nominal moment capacity of the compression β controlled element.
ππ= 0.85πβ²πππ½1ππ’π2
(
1βπ½12ππ’)
(30)2.8.2. Strength Reduction Factors
The strength reduction factors presented are extracted from Dolan and Burke (1992) who have done an extensive research paper on the prestressed FRP concrete beams who conclude that the strength reduction factors correlate mainly to the type of tendon used (ACI Committee 440, 2004) These factors have been adopted by ACI 440.4R-04 which show the net tensile strain vs. strength reduction factor for carbon and aramid tendons.
Figure 29 Net tensile strain vs. Strength reduction factor
The Net tensile strain achievable is less than or equal to 0.002 because the concrete section will not reach its ultimate strain capacity of 0.003 if the section is considered to be a Tension- controlled section. Furthermore, if the section is Compression-controlled section the maximum net tensile strain that can be reached is greater than or equal to 0.005.
2.8.3. Prestressing Anchorage
Prestressing FRP tendons in concrete has its limitations since it is an anisotropic material,
gripping force in order to reduce the a slippage failure is key to the prestressing mechanism.
There are several different anchorage systems that have been used before which have resulted to the desired failure mechanism , rupture of FRP tendons.
These are the different types of anchorage systems according to ACI 440.4R-04:
ο· Clamping anchorage
ο· barrel and spike anchorage
ο· Straight sleeve anchorage
ο· Contoured sleeve anchorage
ο· Metal overlaying
ο· Split-wedge anchorage
The clamping system consists of the FRP tendon compressed between two grooved steel plates that are bolted together as shown in Figure 30. The compressive force from the bolts and shear-friction mechanism between the grooved inner surface of the plates and FRP tendon provide substantial gripping force. This system can be further improved by using a sheath around the FRP tendon. The sheath will uniformly distribute the forces evenly on to the surface of the FRP without providing high amount of shear force.
Figure 30 Clamped System
The barrel and spike system is made of a tube where the conical spike can fit in as shown in Figure 31. This system is used for the FRP fibres that are not encapsulated in resin. In this manner the fibres can be evenly distributed around the spike in order to create the anchorage.
The compressive force from the spike once it is forced into place together with the friction between the fibres and the barrel produce the gripping mechanism, similar to the split-wedge system.
Figure 31 Barrel and Spike
Straight sleeve system contains a straight tube that is filled with different mediums such as epoxy based materials, non-shrink and expansive cement as shown in . The bonding between the sleeve-medium- FRP tendon produce the anchorage needed for prestressing. The load transfer can be improved by adding a threaded sleeve within the initial sleeve to increase friction to the interface between the medium and sleeve. Also, manufacturing the FRP tendons to be braided, ribbed or twisted would increase the surface bond between the rod and the medium. Expansive cementitious material has been used as the medium between the FRP rod and the sleeve before. Once it has cured, it provides sufficient lateral force in order to stabilize and grip the FRP within the metallic sleeve.
Figure 32 Straight Sleeve
Contoured sleeve is very similar to the straight sleeve but the metallic sleeve has a linear or parabolic tapered inner surface which is where the name βcontouredβ sleeve came from as shown in Figure 33.
Metal overlaying is a die-cast wedge system. The FRP tendon length has to be predefined because a metal tube will be fabricated into specific locations, usually at the ends of the
through de-moulding which is put in place during the manufacturing process. The anchorage works by shear stress.
Figure 33 Contoured Sleeve
Split-wedge anchorage is the most widely used anchorage system mentioned. It is the most functional anchorage because of its reliability, reusability and can be easily set up whether it is on site or in controlled environment. It consists of a metallic barrel that has a conical shaped inside and the wedges used are usually made out of steel but the number of wedges can vary from two to six segments as shown in Figure34. Often, the interface between the wedge and the tendon is further cushioned by adding a sheath around the tendon. Such a system is used to anchorage steel tendons but has to be adapted towards the properties of FRP tendons. The length of the wedges are increased which aids in regulating the roughness of the inner surface and reduces the transverse stress. The gripping force is through the friction generated between the barrel-wedges-tendons.
Figure 34 Split Wedge System