New Model for Evaluation of FRP Debonding Strain for Russian Design Code

Table 1

Existing theoretical models and guidelines.

No.	Formula		Reference
	Characteristic value of FRP debonding strain	Design value of FRP debonding strain
1	𝜀^char.𝑓𝑑=0,41𝑓^′𝑐𝑛𝐸𝑓𝑡𝑓≤0,9𝜀^∗𝑓𝑢	𝜀^design𝑓𝑑=𝜓𝑓0.41𝑓^′𝑐𝑛𝐸𝑓𝑡𝑓≤0.9𝜓𝑓𝜀𝑓𝑢,; 𝜀𝑓𝑢=𝐶𝐸𝜀^∗𝑓𝑢, 𝜓𝑓=0.85	[7]
2	𝜀^char.𝑓𝑑=0.544𝑘𝑏𝑓^′𝑐−1.6^5/6𝑛𝑡𝑓𝐸𝑓,; 𝑘𝑏=2−𝑏𝑓/𝑏1+𝑏𝑓/400≥1	𝜀^design𝑓𝑑=0.544𝛾𝑓,𝑑√𝛾𝑐𝑘𝑏𝑓^′𝑐−1.6^5/6𝑛𝑡𝑓𝐸𝑓,; 𝑘𝑏=2−𝑏𝑓/𝑏1+𝑏𝑓/400≥1, 𝛾𝑓,𝑑=1.2, 𝛾𝑐=1.5	[8]
3	—	𝜀^design𝑓𝑑=2Γ𝐹𝑘𝑛𝐸𝑓𝑡𝑓, Γ𝐹𝑘=0.5	[11]
4	𝜀^char.𝑓𝑑=0.48𝑘𝑏𝑓^′𝑐𝐸𝑓𝑡𝑓, 𝑘𝑏=2−𝑏𝑓/𝑏1+𝑏𝑓/𝑏	—	[12]
5	—	𝜀^design𝑓𝑑=0.114(4.41−𝛼) 𝜏max/𝐸𝑓𝑡𝑓,; 𝛼=0.777𝐸𝑓𝑡𝑓/𝐿𝑑, 𝜏max=1.5𝑘𝑏𝑓𝑡,; 𝑘𝑏=2.25−𝑏𝑓/𝑏1.25+𝑏𝑓/𝑏	[13]
6	—	𝜀^design𝑓𝑑=0.1725𝑓^′𝑐^0.2/𝐸𝑓𝑡𝑓^0.35	[14]
7	𝜀^char.𝑓𝑑=𝑘𝑚𝜀^∗𝑓𝑢,	𝜀^design𝑓𝑑=𝑘𝑚𝜀𝑓𝑢,
	𝑘𝑚=160𝜀^∗𝑓𝑢1−𝑛𝐸𝑓𝑡𝑓360000≤0.9for𝑛𝐸𝑓𝑡𝑓1≤18000060𝜀^∗𝑓𝑢90000𝑛𝐸𝑓𝑡𝑓≤0.9for𝑛𝐸𝑓𝑡𝑓>180000	𝑘𝑚=160𝜀𝑓𝑢1−𝑛𝐸𝑓𝑡𝑓360000≤0.9for𝑛𝐸𝑓𝑡𝑓1≤18000060𝜀𝑓𝑢90000𝑛𝐸𝑓𝑡𝑓≤0.9for𝑛𝐸𝑓𝑡𝑓>180000,	[16–19]
		𝜀𝑓𝑢=𝐶𝐸𝜀^∗𝑓𝑢𝛾𝑓, 𝛾𝑓=1.1
8	𝜀^char.𝑓𝑑=0.45𝐵𝑛𝐸𝑓𝑡𝑓≤0.9𝜀^∗𝑓𝑢	𝜀^design𝑓𝑑=0.45𝐵𝑛𝐸𝑓𝑡𝑓≤0.9𝜀𝑓𝑢, 𝜀𝑓𝑢=𝛾𝑓1𝐶𝐸𝜀^∗𝑓𝑢𝛾𝑓2,; 𝛾𝑓1=0.9, 𝛾𝑓2=1.1forstrip1.2forsheet	[20]
9	𝜀^char.𝑓𝑑 =0.41𝑅𝑏,𝑛𝑛𝐸^𝑛𝑓𝑡𝑓≤𝜀^∗𝑓𝑢	𝜀^design𝑓𝑑=0.41𝑅𝑏,𝑛𝑛𝐸𝑓𝑡𝑓≤𝜀𝑓𝑢, 𝐸𝑓=𝐸^𝑛𝑓𝛾𝐸,𝑓𝛾𝑚, 𝜀𝑓𝑢=𝜀^∗𝑓𝑢𝛾𝜀,𝑓𝛾𝑚, 𝛾𝑚=1.1forstrip1.25forsheet	[21]
10	𝜀^char.𝑓𝑑=𝑘𝑚𝜀^∗𝑓𝑢,	𝜀^design𝑓𝑑=𝑘𝑚𝜀𝑓𝑢,
	𝑘𝑚=160𝜀^∗𝑓𝑢1−𝑛𝐸𝑓𝑡𝑓360000≤0.9for𝑛𝐸𝑓𝑡𝑓1≤18000060𝜀^∗𝑓𝑢90000𝑛𝐸𝑓𝑡𝑓≤0.9for𝑛𝐸𝑓𝑡𝑓>180000	𝑘𝑚=160𝜀𝑓𝑢1−𝑛𝐸𝑓𝑡𝑓360000≤0.9for𝑛𝐸𝑓𝑡𝑓1≤18000060𝜀𝑓𝑢90000𝑛𝐸𝑓𝑡𝑓≤0.9for𝑛𝐸𝑓𝑡𝑓>180000	[15]
		𝜀𝑓𝑢=𝐶𝐸𝜀^∗𝑓𝑢𝛾𝑓, 𝛾𝑓=1.1forstrip1.2forCFRPsheet1.4forAFRPsheet1.8forGFRPsheet

𝑓^′_𝑐 is the specified compressive strength of concrete; 𝑛 is the number of plies of FRP reinforcement; 𝐸_𝑓 is the tensile modulus of elasticity of FRP; 𝑡_𝑓 is the nominal thickness of one ply of FRP reinforcement; 𝜀^∗_𝑓𝑢 is the ultimate rupture strain of FRP reinforcement; 𝜀_𝑓𝑢 is the design rupture strain of FRP reinforcement; 𝜓_𝑓 is the FRP strength reduction factor; 𝐶_𝐸 is the environmental reduction factor; 𝛾_𝑓,𝑑, 𝛾_𝑓, 𝛾_𝑓1, 𝛾_𝑓2, 𝛾_𝐸,𝑓, 𝛾_𝑚, 𝛾_𝜀,𝑓 are the partial factors; 𝛾_𝑐 is the partial factor for concrete; Γ_𝐹𝑘 is the characteristic value of specific fracture energy; 𝜏_max is the maximum shear bond stress; 𝐿_𝑑 is the distance from the loaded section to the end of the FRP plate; 𝑓_𝑡 is the tensile strength of concrete; 𝑘_𝑚 is the bond-dependent coefficient; 𝑅_𝑏,𝑛, characteristic value of compressive strength of concrete in compliance with Russian codes; 𝐵 strength classes for concrete in compliance with Russian codes.