Abstract
A numerical approach is proposed to predict the flexural stress–crack mouth opening displacement (CMOD) relationship of fiber-reinforced concrete (FRC) beams. The compressive strength and density of concrete as well as various fiber parameters are considered in the compressive and tensile stress–strain relationships of concrete employed in the analysis. The nonlinear hinge model for fictitious crack propagation generalized by Olesen is also utilized to calculate the CMOD from the curvature determined from critical beam sections. The theoretical flexural stress–CMOD curves corresponded well with the measured curves. They indicated that the mean and standard deviation of normalized root mean square error values determined from 136 FRC beams were 0.237 and 0.118, respectively. A comprehensive parametric study is then conducted by numerically analyzing the primary variables influencing the CMOD response of FRC beams at extensive ranges. This enables the formulation of simple closed-form equations to determine the residual flexural strengths straightforwardly. The residual flexural strengths yielded by the derived equations agree better with the test results than with those given by previous empirical equations, yielding fewer scatters in the ratios between the experimental results and predictions is observed. Consequently, the present equations have potential in reliably assessing the residual flexural strengths of FRC with a wide range of variables, such as compressive strength, density, aggregate size, and fiber parameters.
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Abbreviations
- b w :
-
Section width of the beam
- d 0 :
-
Reference value (= 25 mm) of da
- d a :
-
Maximum aggregate size
- E cf :
-
Elastic modulus of FRC
- F :
-
Applied load
- f 0 :
-
Reference value (= 10 MPa) of f′c
- f′ c :
-
Compressive strength
- f r,j :
-
Residual flexural tensile strength
- f t :
-
Tensile strength of FRC
- g :
-
Snubbing factor of discontinuous fiber
- h :
-
Overall depth of the beam section
- h sp :
-
Distance between the tip of the notch and top surface of the beam
- i :
-
Type of fiber used in each concrete specimen
- j :
-
1, 2, 3, and 4 to identify the specified CMOD
- L :
-
Span of the beam
- l p :
-
Hinge length
- M(i):
-
Moment in the critical section at loading step i
- S f :
-
Aspect ratio of fiber
- V f :
-
Volumetric ratio of fiber
- w cmod :
-
Crack mouth opening displacement (CMOD)
- x 0(i):
-
Neutral axis depth on the extreme layer at loading step i
- α :
-
Normalized depth of the fictitious crack
- β f :
-
Fiber reinforcement index
- γ em :
-
Mean of NRMSE
- γ es :
-
Standard deviation of NRMSE
- γ s :
-
Ratio between the experimental residual flexural strength and prediction
- γ s,m :
-
Mean of γs
- γ s,s :
-
Standard deviation of γs
- ε ct(i):
-
Compressive strain on the extreme layer at loading step i
- ϕ(i):
-
Curvature in the midspan at loading step i
- η j :
-
Coefficient in the bilinear stress–CMOD relationship
- ρ 0 :
-
Reference value (= 2,300 kg/m3) of ρc
- ρ c :
-
Concrete density
- τ :
-
Interfacial bond strength of the fiber versus cement matrix
- ξ :
-
Common coefficient in each expression of residual flexural strength
- ψ j :
-
Normalized fracture parameter
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Acknowledgments
This work was supported by a grant from the Korea Agency for Infrastructure Technology Advancement (KAIA) funded by the Ministry of Land, Infrastructure and Transport (Grant RS-2020-KAC156177).
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Kim, HY., Lee, HJ., Yang, KH. et al. Numerical Approach for Residual Strengths of Fiber-Reinforced Concrete Beams with Different Densities. KSCE J Civ Eng 28, 220–230 (2024). https://doi.org/10.1007/s12205-023-1819-9
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DOI: https://doi.org/10.1007/s12205-023-1819-9