ORIGINAL ARTICLE Predicting the pullout response of inclined straight steel fibers F. Laranjeira • A. Aguado • C. Molins Received: 18 December 2008 / Accepted: 12 October 2009 / Published online: 14 November 2009 Ó RILEM 2009 Abstract Fiber pullout tests have been used for decades to characterize and optimize bond strength on fiber reinforced concretes. However most of the investigations focus on the behavior of fibers aligned with load direction whose pullout mechanisms are not representative of the ones existing in real applica- tions, where random orientation of fibers is likely to occur. In this paper a new predictive model for the pullout response of steel fibers embedded in cement matrices with any inclination respect to loading direction is provided. Comparisons with experimental results highlight the capacity of the model on describing appropriately the entire load–crack width behavior. The procedure differentiates itself from previous works by introducing clear and comprehen- sive concepts within a straightforward approach. Keywords SFRC  Pullout  Fiber  Straight geometry  Orientation  Matrix spalling List of symbols P Pullout load (orthogonal to cracked surface) (N) d Displacement along load direction (mm) w Crack width along load direction (mm) h Fiber inclination angle relatively to load direction (°) d Diameter of the fiber cross-section (mm) r y Average tensile yield strength of the steel fibers (MPa) f ctm Average tensile strength of the cement matrix (MPa) E f Elastic modulus of the steel fibers (MPa) E m Elastic modulus of the cement matrix (MPa) l Friction coefficient between steel fibers and cement matrix (–) s max Maximum interfacial shear stress (MPa) s fric Friction interfacial shear stress (MPa) s* Apparent interfacial shear stress (MPa) s(s) Distribution of interfacial shear stress (MPa) L e Shorter fiber embedded length within the cement matrix (mm) L SP1 Length of spalled matrix generated by P S01 (mm) L eff(S2) Effective fiber length factor at point S 2 (–) L d Extension of the debonded segments of the fiber (mm) L S,crit Critical fiber embedded length (mm) F. Laranjeira (&)  A. Aguado  C. Molins Department of Construction Engineering, Universitat Polite `cnica de Catalunya (UPC), Edifici C1, Campus Nord UPC, Jordi Girona 1-3, 08034 Barcelona, Spain e-mail: filipe.laranjeira@upc.edu A. Aguado e-mail: antonio.aguado@upc.edu C. Molins e-mail: climent.molins@upc.edu Materials and Structures (2010) 43:875–895 DOI 10.1617/s11527-009-9553-4