@article{8e5cffc3e02f4965b3a956091018dfab,
title = "Analytical approach for the design of flexural elements made of reinforced ultra-high performance concrete",
abstract = "The increasing demands of sustainable design and construction with economical sections, reduced cover, and more efficient time schedule require more flexibility in the design methodologies. The development of ultra-high performance concrete (UHPC) have gained increasing interests as an attractive option for structural members with lightweight and superior performances. Concrete members reinforced with steel bars and fibers, generally known as hybrid reinforced concrete (HRC), offer a feasible solution in terms of reducing reinforcing materials and achieving desired structural performance. This paper proposes an analytical model to predict the flexural behavior of hybrid reinforced UHPC with steel reinforcements. Moment–curvature solutions are derived for reinforced sections based on parameterized tension-compression constitutive models. The approach is applicable to customized cross section and derivation of T-section is demonstrated. The moment–curvature response is further simplified as a tri-linear model, which is used for the development of full-range displacement solutions in analytical form. The proposed model is validated with the experimental data from literature covering a range of materials and member sizes. The full-range solutions may provide insights into the serviceability design approach based on the criterion of maximum crack width or allowable deflection.",
keywords = "UHPC, analytical model, full-range solutions, hybrid reinforced concrete, moment–curvature, serviceability-based design",
author = "Yiming Yao and Barzin Mobasher and Jingquan Wang and Qizhi Xu",
note = "Funding Information: National Natural Science Foundation of China, Grant/Award Number: 51908120; Natural Science Foundation of Jiangsu Province, Grant/Award Number: BK20180383; Fundamental Research Funds for the Central Universities, Grant/Award Numbers: 2242019K40079, 2242020K40099 Funding information Funding Information: This study was supported by the Natural Science Foundation of China (51908120), the Natural Science Foundation of Jiangsu Province (BK20180383) and the Fundamental Research Funds for the Central Universities (2242019K40079, 2242020K40099). The financial supports are gratefully appreciated. Notation area of tension steel area of compression steel beam width , coefficients in Table 1 , , , coefficients in Table 2 effective depth at location of steel bar elastic tensile modulus of concrete elastic compressive modulus of concrete elastic modulus of steel ′ compressive strength of concrete stress steel stress steel yield stress force components in stress diagram , coefficients for minimum flexural reinforcement in Equation (10 ) full height of a beam section or height of each compression and tension zone in stress diagram moment of inertia moment of inertia of cracked section secant flexural stiffness of a beam section neutral axis depth ratio beam span length of uncracked region in a beam characteristic length crack spacing moment moment at first cracking moment at beginning of plastic stage normalized moment ( / ) normalized moment at beginning of plastic stage modulus ratio ( / ) ratio of compression steel to tension steel ( ′/ ) flange height of T‐section web width of T‐section moment arm from force component to neutral axis normalized depth of steel reinforcement ( / ) normalized tensile strain ( / ) normalized ultimate tensile strain ( / ) strain concrete compressive strain concrete cracking strain ultimate concrete compressive strain concrete compressive strain at top fiber steel strain steel yield strain concrete tensile strain concrete tensile strain at bottom fiber ultimate concrete tensile strain curvature curvature at first cracking maximum curvature angle of rotation normalized concrete compressive modulus ( / ) normalized postcracked flexural stiffness ( / ) normalized curvature ( / ) normalized curvature at beginning of plastic stage normalized maximum curvature ( / ) normalized compressive strain ( / ) normalized compressive strain corresponding to first cracking ultimate concrete compressive strain ( / ) normalized residual tensile strength ( / ) steel reinforcement ratio per effective area steel reinforcement ratio per gross area steel reinforcement ratio per gross area at balanced failure concrete stress concrete compressive stress concrete cracking stress concrete compressive strength residual tensile strength concrete tensile stress Poisson's ratio normalized concrete compressive yield strain ( / ) normalized steel strain ( / ) normalized flange height ( / ) normalized web thickness ( / ) normalized steel yield strain ( / ) Subscripts 1, 2, 3 tension zone 1, 2, 3 1, 2 compression zone 1, 2 1, 21, 22, 31, 32 Stage 1, 2.1, 2.2, 3.1, 3.2 according to the value of Superscripts' normalized parameters if not specified A s A s ′ b A 1‐7 B 1‐11 C 1‐8 D 1‐9 E 1‐8 F 1‐9 d E E c E s f c f f s f sy F G 1 G 2 h I I cr K k L L e L p l cs M M cr M p m M M cr m p n E s E r A s A s t f t w y α d h β ε t ε cr β tu ε tu ε cr ε ε c ε cr ε cu ε ctop ε s ε sy ε t ε tbot ε tu φ φ cr φ max θ γ E c E η EI cr EI g κ φ φ cr κ p κ max φ max φ cr λ ε c ε cr λ 1 R λ cu ε cu ε cr μ σ p σ cr ρ ρ g ρ , g bal σ σ c σ cr σ cy σ p σ t ν ω ε cy ε cr χ ε s ε cr ζ t f h ο b w b ψ ε sy ε cr t t t c c λ Publisher Copyright: {\textcopyright} 2020 fib. International Federation for Structural Concrete",
year = "2021",
month = feb,
doi = "10.1002/suco.201900404",
language = "English (US)",
volume = "22",
pages = "298--317",
journal = "Structural Concrete",
issn = "1464-4177",
publisher = "Wiley-Blackwell",
number = "1",
}