2. Review of Design and Construction of FRP reinforced concrete design
2.7. Design Philosophy of FRP Reinforced Concrete
The available and updated codes being used today are the American Concrete Institute 440.1R-06 (ACI), fib and the Canadian Standards Association S806-029 (CSA). The design philosophies are based on the standpoint of the Ultimate Limit State (ULS) and Serviceability Limit States (SLS).
2.7.1. Ultimate Limit State
During the design phase of structural elements, the modes of flexural failure in concrete reinforcement with Fiber Reinforced Polymers (FRP) or Steel are.
• Under-reinforced – At failure, FRP bars rupture initially and is followed by the crushing of the concrete.
• Balanced Section – At failure, the simultaneous crushing of concrete and rupture of FRP bars.
• Over-reinforced – At failure, concrete crushes initially and is followed by the rupture of FRP bars.
Conventional sections in design are usually balanced sections but once safety factors are implemented they are considered to be under-reinforced. It is said the strength to stiffness ratio of steel is similar to that of concrete. These are observed in the strain distribution of a balanced section with steel in comparison to a balanced with FRP.
Figure 19 Strain Distribution of GFRP and Steel sections
It shows that in order for the FRP strength to be most effective, a large portion of the section will undergo high tensile strains. Utilizing prestressing or post-tensioning would negate many issues such as larger flexural deflections and cracks in the tension zone of the section. The stress that has developed in the FRP bars in the compression zone and the tension zone will vary significantly (Stuart and Cunningham, 2017).
The failure modes can be deduced once the FRP reinforcement ratio is compared to the balanced reinforcement ratio, which in turn describes if the section is over-reinforced, under- reinforced, or is balanced. The equation used to calculate the FRP reinforcement ratio is:
𝜌𝑓= 𝐴𝑓
𝑏𝑑 (1)
The balanced reinforcement ratio uses the tensile strength of the FRP due to lack of distinct yield strength. The equation varies between the available standards.
𝜌𝑓𝑏= 0.85𝛽1𝑓′𝑐 𝑓𝑓𝑢
𝐸𝑓𝜀𝑐𝑢
𝐸𝑓𝜀𝑐𝑢+𝑓𝑓𝑢 (2)
𝜌𝑓𝑏= 𝛼1𝛽1∅𝐶
∅𝐹 𝐹′𝐶
𝐹𝐹𝑅𝑃
(
𝜀𝐶𝑈𝜀+𝐶𝑈𝜀𝐶𝑈)
(3)𝜌𝑓𝑏= 0.81(𝑓𝑐𝑘+ 8)𝜀𝑐𝑢
𝑓𝑓𝑘
(
𝐹𝑓𝐹𝐾𝐹𝐾𝜀𝑐𝑢)
(4)Equation (2) and (3) from ACI and CSA use similar equations. The non-linear stress distribution is replaced with a corresponding stress block, Eurocode 2 approach is used to produce Equation (3) which takes into consideration the material variability of the concrete and premature failure. These precautions result in higher balanced reinforcement ratio than Equation (2) and Equation (3). The balanced reinforcement ratio ρfb can be compared with the FRP reinforcement ratio ρf which will indicate the failure mechanism that will be followed. Then the moment capacity can be determined.
Moment Capacity
In the design procedure of concrete flexural members, it states that the flexural design strength multiplied by a strength reduction factor ϕMn must surpass the factored moments that resulted from the factored load Mu (ACI et al., 2002).
The moment resistance equations used depends on if the section being designed is over or under-reinforced. These are the equation used if the section is over-reinforced, ρf > ρfb, which indicates that crushing of the concrete will take place first.
𝑀𝑛=𝜌𝑓𝑓𝑓
(
1―0.59𝜌𝑓𝑓′𝑓𝑐𝑓)
𝑏𝑑2 (5)(6)
Strength reduction factors for flexure ϕ have to be used in order to address the lack of
The reduction factors are meant to take into account the lack of ductility in the FRP. A conservative strength reduced is adopted in order to maintain a higher strength reserve in the concrete member. Environmental factors also influence the reduction factors such as the presence of alkali, temperature, time and moisture.
Figure 20 Strength Reduction Factor as function of reinforcement ratio (ACI Committee 440, 2003)
As shown in table above, the reduction factor depends on the reinforcement ratio. The strength reduction factor is 0.65 once the ρf > ρfb, which indicates that the concrete member will fail through crushing of concrete. The strength reduction factor is 0.55 once ρf <ρfb, which indicates that the concrete member will failure due to rupture of the FRP. The formula used for the strength reduction factor is ρfb < ρf < 1.4ρfb is given:
The strength factor is then implemented in the the flexural capacity of the concrete member.
𝜙𝑀𝑛 >𝑀𝑢 2.7.2. Serviceability Limit State
Serviceability can be described as adequate performance under service load conditions. FRPs have a higher tensile strength than steel does but its Young’s Modulus is lower which restricts the use of the full strength once it is embedded within the concrete. Once cracks are observed in the concrete member, the stiffness drastically decreases due to the reliance on the stiffness of the FRP. Hence, the design of the FRP concrete section is governed by service loads that produce significant deflections and crack widths (ACI et al., 2002).
Deflection
Deflections are controlled in the ACI by limiting the thickness of the concrete member depending on it full length. These limits can be seen Table 3.
Table 3 Recommended minimum thickness as per ACI 440-1R-06
Minimum thickness h
Simply Supported
One end continuous
Both ends continuous
Cantilever
Solid one way slabs
L/13 L/17 L/22 L/5.5
Beams L/10 L/12 L/16 L/4
The limits are based on three aspects. The lower elastic modulus in comparison to steel and the variability in bond strength to the surrounding concrete. The brittle failure of the concrete element is also taken into consideration. Whereas as the maximum long term deflection under total service load is 1/240.
The procedure to calculate deflection using the ACI guidelines is done by calculating the cracked properties and cracking moment of the FRP reinforced concrete member. When the applied moment from the live load surpasses the cracking moment Mcr occurs. The equations below are used to calculate the cracking moment.
𝑓𝑟= 0.62 𝑓′𝑐 (7)
𝑀𝑐𝑟= 2𝑓𝑓𝐼𝑔
ℎ (8)
Once the cracks occur, there is a decline in gross moment of Inertia Ig and gross moment of inertia is based on the cracked section Icr.
𝐼𝑐𝑟= 𝑏𝑑3
3 𝑘3+𝑛𝑓𝐴𝑓𝑑2(1― 𝑘)2 (9) 𝑘= 2𝜌𝑓𝑛𝑓+(𝜌𝑓𝑛𝑓)2― 𝜌𝑓𝑛𝑓 (10)
K is the ratio between the neutral axis and depth of main reinforcement. nf is the modular ratio of FRP bars to concrete. Since the concrete has experienced cracking at service loading, the stiffness of the member will vary between EcIg and EcIcr depending on the moment applied. Branson (1977) did research on this aspect and developed an equation which was adjusted by a reduction coefficient produced from research done by Toutanji. H, Saafi. M, and Yosh. The reduction coefficient was able to take into consideration the reduction in tension stiffness from the usage of FRP reinforcement (Toutanji and Saafi 2000; Yost et al.
2003).
𝛽𝑑= 0.2 ×
(
𝜌𝜌𝑓𝑏𝑓)
(11)𝐼𝑒(𝐷𝐿+𝑙𝑙)=
(
𝑀𝑀𝑐𝑟𝑎)
3𝛽𝑑𝐼𝑔+⌈
1―(
𝑀𝑀𝑐𝑟𝑎)
3⌉
𝐼𝑐𝑟 (12)∆𝐷𝐿+𝐿𝐿= 5𝑀𝐷𝐿+𝐿𝐿𝐿2
48𝐸𝑐𝐼𝑒(𝐷𝐿+𝐿𝐿) (13)
This procedure can be mimicked to find the deflection that is directly produced by the dead load and live load if necessary.
Load deflection tests were carried out on FRP reinforced beams that used CFRP and GFRP as the main reinforcement by Dr. Jinping Ou and his colleagues at the Harbin Institute of Technology in China (Ou et al., 2004). The experiments conducted consisted of 28 concrete beams that were reinforced with CFRP, GFRP and HFRP (a hybrid of carbon fibre and E- glass fibre) where each type of FRP was either helically wound glass fibre strands or sand- coated during the manufacturing process to improve bonding to the concrete. It was found that all FRP reinforced beams displayed a linear response to continuous loading before the initiation of cracking, this is due to the linear elastic behaviour of the FRP material. During the analysis of the Load- deflection curves, there was a sudden drop in the curve shown below.
Figure 21 GFRP beams with helically wound glass fibre strandson surface (Ou et al., 2004)
Figure 22 GFRP beams with helically wound glass firer strands on surface (Ou et al., 2004)
Figure 23 CFRP beams with helically wound glass fibre strands on surface (Ou et al., 2004)
Figures 10-12 show the sudden drop in bars FB09, FB13, and FB19. The drop was directly related to the difference surface indentation since this drop was not present in the load- deflection curves that used the sand-coated bars. This concluded that sand-coated bars had a better bond strength to concrete than helically wound bars.
Crack widths and patterns
During the design phase of steel reinforced concrete, the serviceability limit state usually doesn’t govern the design but the crack width is checked because as the concrete cover has been compromised it creates an environment that is vulnerable to deterioration mechanisms,
however, FRPs are inert materials which means the maximum crack width would not be determined by reinforcement deterioration. Aesthetic and shear reactions would be catered towards.
The Japan Society of Civil Engineers (JSCE) use aesthetics as the main factor, in which the maximum allowable crack width is taken as 0.5 mm. However, the CSA S806-02 maximum allowable crack widths of 0.5 mm for exterior exposure and 0.7 mm for interior exposure when FRP reinforcement is used. Furthermore, the ACI does not provide a maximum allowable crack width but does recommend to follow the provisions given by CSA S806 – 02 for guidance.
The procedure to estimate the crack widths in the ACI is as follows:
The stress in the FRP reinforcement ff is determined 𝑓𝑓= 𝑀𝐷𝐿+𝐿𝐿
𝐴𝑓𝑑(1 ―𝑘
3) (14)
The strain gradient is determined and used to transform reinforcement level strains to the near surface of the beam where cracking is expected.
𝛽= ℎ ― 𝑘𝑑
𝑑(1 ― 𝑘) (15)
The distance from the maximum tension fibre of the concrete to the centre of the flexural reinforcement is calculated.
𝑑𝑐=ℎ ― 𝑑 (16)
The spacing between the flexural bars.
𝑠=𝑏 ―2𝑑𝑐 (17)
Then the crack width formula is used as presented. The kb variable is a bond- dependent coefficient that represent the bond strength to the surrounding concrete.
The ACI recommends using 1.4 if there is no experimental data on the commercial FRP bonding capability available.
𝑤= 2𝑓𝑓
𝐸𝑓𝛽𝑘𝑏 𝑑2𝑐+
(
2𝑠)
2 (18)An experimental study was done (Adam et al., 2015) to understand the flexural behaviour of beams reinforced with GFRP bars that were made of locally produced glass fibres. 10 beams were cast with dimensions of 2800mm×120mm×300mm and were tested under four-point bending. A control beam was cast using steel reinforcement that was similar to one of the GFRP beams in order to do a comparison between FRP and steel reinforcement. The crack pattern observed initiated from the tension zone where the moment is constant. The crack progressed towards the compression zone while new ones were forming, this was at around 60% of the maximum load. When the loading stages increases, there was a significant decrease in crack initiation however, the present cracks increased in width. Small short cracks were observed located adjacent to the tension GFRP bars. These adjacent cracks are due to the bond between the GFRP and the surrounding concrete, due to the inadequate bond, there is usually a slippage between the GFRP and concrete which produces the adjacent cracks.
Figure 24 Crack Width Patterns of FRP RC beams (Adam et al., 2015)
There were three sets of beams. A25,A45, and A70. Each series has a beam with reinforcement equal to the reinforcement ratio μb (-1), 1.7μb (-2), and 2.7μb (-3). The crack width at a load of 40kN was 4.4mm, 2.7mm, and 1.2mm for beams A25-1, A25-2, and A25- 3. While, the crack width is 2.1 mm, 1.15 mm, and 0.70 mm for beam A45-1, A45-2, and A45-3 respectively. Also, for series A70 the crack width recorded values of 0.90 mm, 0.50 mm, and 0.25 mm for beam A70-1, A70-2, and A70-3 respectively. This indicated that crack widths have a tendency to decrease from 25MPa to 45 MPa and 25MPa to 45 MPa by 52%
and 80% respectively. Majority of the specimens would not pass the crack width requirements adopted by fib, CSA, and the ACI. This is due to the standards limiting the amount of strain FRPs should undergo. The fib shows that the strain limit for FRPs is between 0.2%-0.45%, while the Intelligent Sensing for Innovative Structures (ISIS) is strict with using 0.002 as the limiting strain. Once these strains are used in measuring the crack widths, majority of the specimens pass the crack width requirements.
2.7.3. Bonding Issues Reinforcement Anchorage
Once the amount of reinforcement for the reinforced concrete member is calculated. The exact lengths of the reinforcement is needed for procurement. This is when a bar bending schedule is produced which shows details of the shapes and lengths of bars needed for a concrete member. During this phase, the requirements for reinforcement curtailment and anchorage is extracted from the standards that is being used. The requirements vary depending on the end conditions and the standards. For research purposes the focus will be on simply supported concrete members and the SANS 10100-1 standard.
The requirements stated in the SANS 10100-1 for tension steel in concrete beams is as stated:
The effective anchorage length of a hook or bend is measured from the start of the bend to a point four times the bar diameter beyond the end of the bend. This effective anchorage length may be taken as follows:
In the case of a 180º hook: the greater of either eight times the internal radius of the hook with a maximum of 24 times the bar diameter, or the actual length of bar in the hook including the straight portion;
in the case of a 90 º bend: the greater of either four times the internal radius of the bend with a maximum of 12 times the bar diameter, or the actual length of the bar.
Any length of bar in excess of four bar diameters beyond the end of the bend and that
lies within the concrete to which the bar is to be anchored may also be included for effective anchorage.
Extend at least 50 % of the tension reinforcement provided at mid-span to the supports and give it an effective anchorage of 12Φ past the centre of the support. Extend the remaining part of the reinforcement to within 0.08l of the centre of the support.
The statement above a specifically relates to reinforcement made out of steel. In a structure, the main bars in beams are extended as anchorage, which ends as hooks, are connected to the column in order to produce a beam-column joint which is essential for the structures stability mechanism.
There was a study done on the hysteretic behaviour of reinforced concrete joints reinforced with deformed hooked bars. Deformed hooked bars were cast in confined concrete elements and were subjected to monotonic and cyclic loadings which enabled them to understand the force- slip relationship between the concrete and the hooked bars.
Test specimens that represent an exterior beam-column joint were casted with only the hook enclosed in the concrete. The mandrel used had a diameter of 6db, the length of the bar before and after the bend was 1db and 5 db respectively. No. 8 bars of db = 25mm were used for the experimental testing. A specially designed testing frame was made and the specimens were tested to possible maximum capacity of 1350kN. The frame was able to apply direct tension ,compression forces ,or displacement , to the hook under investigation.
The threaded end of the bar was subject to a specific force in order to create a desired slip , which was measured at the beginning of the hook using LVDTs. A straight bars was used as a control with a rate of 1.7mm/min. The slip was measured by the probe which was welded to the bar but not embedded in the concrete that reached outside of the specimen. The slip was also measured at the unloaded bar as well. The differential between the loaded and unloaded bars was calculated through two X-Y recorders.
Figure 25 Concrete specimen arrangement (Bertero and Popov, 1982)
It was found that the maximum resistance of the hooked bars under monotonic loading produced 60 to 70% more than the straight bars with an equivalent anchorage length of Lb. This is due to the hooked bar contained a larger bonded length that the straight bar.
The resistance of hooks under monotonic loading was almost constant over a range of slip values whereas the straight bars dropped by 1/3 of the maximum value at large slips.
These conclusions have shown that the bond behaviour of a hook anchorage is superior to a straight bar of equivalent length and even after a large range of slip values the maximum resistance is constant nonetheless. Furthermore, the use of 90º or 180º hooks as anchorage in concrete members is very important for the stability of the structure and proper usage of material properties of steel (Bertero and Popov, 1982).
Since FRPs have different material properties, the anchorage system within concrete elements cannot be the same as steel. As shown by the research above, using hooked bars as anchorage into joints is more adequate for bonding and special requirements. This anchorage system cannot be utilized when using FRPs as reinforcement. Due to the micro structure of FRPs,
Test bar (db = 25mm)
Probe (db = 5 mm)
Vertical Bar (db = 12.7mm)
Rubber Hose
when a 90 º hook is made with FRP bars, the fibres bend as well. This produces a reduction in tensile strength. The subsequent reduction in tensile strength can reach up to 50% at the bends (ACI Committee 440, 2003).
Studies have been done on the loss of tensile strength at the bend of FRP reinforcement by (Shehata et al. 2000, Ehsani et al. 1995, El-Sayed et al. 2007, Ahmed et al. 2010). This loss of strength was mostly ascribed to the bending effect in which the curvature of the fibres situated at the bend or hooked section causes localised stress concentrations that further exasperated buckling of the fibres at the interior of the bend as shown in Figure 26, however the fibres at the exterior are not affected.
Figure 26 Localized Deformation
This develops the question, how are we able to anchorage the FRP bars adequately without deforming the microstructure? This aspect is under current research in the area of prestressing FRP bars.
Pre- tensioning or Post- tensioning of internal FRP in concrete has been used in different applications, it has mainly been used in the design of bridge decks and concrete flexural members. The tensioning of FRPs in concrete has been in use for over the last 30 years. This can be seen in Japan, where CFRP was prestressed in the construction of the Shinmiya Bridge in 1988.
Figure 27 Shinmiya Bridge