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Jansze (1997Jansze, W., (1997). Strengthening of RC members in bending by externally bonded steel plates. Ph.D. Thesis. Delft University of Technology.) |
The critical shear force at the FRP plate end which causes debonding, , is given as a function of the shearing stress, , by:
, with,
where is a modified shear span, equal to:
If is greater than the actual shear span, , then the value should be used. |
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Chen and Teng (2001Teng, J.G., Cao, S.Y., Lam, L., (2001). Behaviour of GFRP-strengthened RC cantilever slabs. Constr. and Build. Mat. 2001; 15(7): 339-349.) |
The maximum tensile load, , at the end of the FRP reinforcement is given by:
where is a coefficient taken 0.427 for mean values and 0.315 for characteristic ones; is a factor related to the effect of width ratio between the EB FRP and concrete; is a factor representing the effect of the bond length of the EB FRP; is the effective bond length. The previous factors could be determined by the following equations:
, in case . |
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Smith and Teng (2002bTeng, J.G., Chen, J.F., Smith, S.T., Lam, L., (2002). FRP strengthened RC structures. England: John Wiley & Sons, Ltd.) |
The debonding shear force at the plate end, , is given by:
,
where is the shear capacity of the concrete beam alone without the contribution from the shear reinforcement; and is taken equal to 1.5. |
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Colotti et al. (2004Colotti, V., Spadea, G., Swamy, R.N., (2004). Structural model to predict the failure behavior of plated reinforced concrete beams. Journal of Composites for Construction ASCE 8(2): 104-122.) |
The ultimate shear load for the plate-end failure mode of FRP-strengthened beam is:
,
with; ;;
The limiting bond strength, , is given by:
where ; is the width of the tie element, suggested by Colotti et al. (2004Colotti, V., Spadea, G., Swamy, R.N., (2004). Structural model to predict the failure behavior of plated reinforced concrete beams. Journal of Composites for Construction ASCE 8(2): 104-122.) equal to: , in which the crack spacing, , could be calculated according to Eurocode2 by: , where and are 0.8 and 0.5, respectively; and , in which . |
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Teng and Yao (2007Yao, J., Teng, J.G., (2007). Plate end debonding in FRP-plated RC beams-I: Experiments. Engineering Structures 29: 2457-2471.) |
The flexural debonding moment of FRP plate end located in a pure bending region is:
,
where , and are parameters defined by:
, , ,
where and are the flexural rigidities of the cracked section with and without EB FRP, respectively and is the theoretical ultimate moment of the un-plated section, which is also the upper bound of the flexural debonding moment .
The debonding shear force at an FRP plate end located in a region of (nearly) zero moment is:
,
where is the shear force carried by the shear steel reinforcement per unit strain, given by:
,
The effective strain in the shear steel reinforcement, , is given by (in µε):
, with; ,
For the predictions of the shear capacity contributed by the concrete and FRP plate , The authors proposed that Oehlers et al.’s (2004Oehlers, D.J., Liu, I.S.T., Seracino, R., Mohamed Ali, M.S., (2004). Prestress model for shear deformation debonding of FRP- and steel-plated RC beams. Magazine of Concrete Research 56(8): 475-486., 2005) prestress model be adopted.
An interaction between plate-end shear and bending was proposed as follows:
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fib Bulletin 14 (International Federation for Structural Concrete, 2001) |
where the maximum anchorage length,
for beams with sufficient internal and external shear reinforcement and for slabs, otherwise ; and can be taken 0.64 and 2.0, respectively for CFRP strips; , but for concrete with low compaction, ; and is a geometry factor, given by:
, with
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| Concrete Society (2012) TR55 |
where is a geometry factor given by:
, with
The maximum anchorage length, , is given by:
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| CNR DT200 (CNR, 2013) |
where is a partial factor (1.2‒1.5); is the design value of the specific fracture energy of the FRP-concrete interface, given by:
in which is a corrective factor taken for pre-cured FRP (0.063 mm for the mean value and 0.023 mm for the 5% fractile value) and for wet lay-up FRP (0.077 mm for the mean value and 0.037 mm for the 5% fractile value); is a geometric coefficient given by:
The effective bond length, , is calculated by:
where , with , and as a corrective factor. |
