Evaluation of Crack Propagation and Post-cracking Hinge-type Behavior in the Flexural Response of Steel Fiber Reinforced Concrete

An experimental evaluation of crack propagation and post-cracking behavior in steel fiber reinforced concrete (SFRC) beams, using full-field displacements obtained from the digital image correlation technique is presented. Surface displacements and strains during the fracture test of notched SFRC beams with volume fractions (Vf) of steel fibers equal to 0.5 and 0.75% are analyzed. An analysis procedure for determining the crack opening width over the depth of the beam during crack propagation in the flexure test is presented. The crack opening width is established as a function of the crack tip opening displacement and the residual flexural strength of SFRC beams. The softening in the post-peak load response is associated with the rapid surface crack propagation for small increases in crack tip opening displacement. The load recovery in the flexural response of SFRC is associated with a hinge-type behavior in the beam. For the stress gradient produced by flexure, the hinge is established before load recovery is initiated. The resistance provided by the fibers to the opening of the hinge produces the load recovery in the flexural response

Role of Steel Fibers in Shear Resistance of Beams in Arch Action

Reinforced concrete beams with discrete hooked-end steel fibe rs were tested with a shear span to depth ratio equal to 1.8. Digital im age correlation (DIC) technique was used to obtain the full-field displacements from the beam during the load response. The formation and propagation of a shear crack which directly influences the load response and peak load in the load response of the beam is moni tored using the displacement fr om the DIC measurements. There is a continuous slip across the crack face s of the shear crack with increasing load carrying capacity up to the peak load. The shear crack exhibits a dilatant behavior with increasing slip. Failure in control beams is brittle which was by the opening of dominant shear crack in shear span at a small value of crack opening. At the peak load, the shear crack pattern in fiber reinforced conc rete was identical to the crack pattern in the control beam. The dilatant behavior from the measured crack opening a nd crack slip displacements obtained from the control and the SFRC beams is identical. The fiber reinforced concrete beams exhibit a ductile response with a post peak load car rying capacity even after the continued opening of the dominant shear crack

Shear behavior of steel fiber reinforced concrete using full-field displacements from digital image correlation

Reinforced concrete beams with discrete hooked-end steel fibers at 0.5% volume fraction are tested with a shear span to depth (a/d) ratio equal to 1.8. Digital image correlation (DIC) technique was used to obtain the full-filed displacements from the beam. The formation and propagation of a shear crack which directly influences the load response and the peak load in the load response of the beam is monitored using the displacement information available from DIC. There is a continuous increase in slip across the crack faces with increasing load, which produces an increase in the crack opening. The dilatant behavior indicated by the proportion of crack opening to slip displacement obtained from the control and the SFRC beams is identical. Failure in control beams is brittle and was produced by the opening of dominant shear crack within the shear span. At the peak load, the shear crack pattern in fiber reinforced concrete is identical to the crack pattern in the control beam. The fiber reinforced concrete beams exhibit post peak load carrying capacity with continued slip of the dominant shear crack. The crack bridging stress provided by the fibers results in a significant increase shear transfer across the crack which provides significant post-peak load carrying capacity with increasing slip of the shear crack

Shear behavior of steel fiber reinforced concrete using full-field displacements from digital image correlation

Reinforced concrete beams with discrete hooked-end steel fibers at 0.5% volume fraction are tested with a shear span to depth (a/d) ratio equal to 1.8. Digital image correlation (DIC) technique was used to obtain the full-filed displacements from the beam. The formation and propagation of a shear crack which directly influences the load response and the peak load in the load response of the beam is monitored using the displacement information available from DIC. There is a continuous increase in slip across the crack faces with increasing load, which produces an increase in the crack opening. The dilatant behavior indicated by the proportion of crack opening to slip displacement obtained from the control and the SFRC beams is identical. Failure in control beams is brittle and was produced by the opening of dominant shear crack within the shear span. At the peak load, the shear crack pattern in fiber reinforced concrete is identical to the crack pattern in the control beam. The fiber reinforced concrete beams exhibit post peak load carrying capacity with continued slip of the dominant shear crack. The crack bridging stress provided by the fibers results in a significant increase shear transfer across the crack which provides significant post-peak load carrying capacity with increasing slip of the shear crack

Shear behavior of steel fiber reinforced concrete using full-field displacements from digital image correlation

Reinforced concrete beams with discrete hooked-end steel fibers at 0.5% volume fraction are tested with a shear span to depth (a/d) ratio equal to 1.8. Digital image correlation (DIC) technique was used to obtain the full-filed displacements from the beam. The formation and propagation of a shear crack which directly influences the load response and the peak load in the load response of the beam is monitored using the displacement information available from DIC. There is a continuous increase in slip across the crack faces with increasing load, which produces an increase in the crack opening. The dilatant behavior indicated by the proportion of crack opening to slip displacement obtained from the control and the SFRC beams is identical. Failure in control beams is brittle and was produced by the opening of dominant shear crack within the shear span. At the peak load, the shear crack pattern in fiber reinforced concrete is identical to the crack pattern in the control beam. The fiber reinforced concrete beams exhibit post peak load carrying capacity with continued slip of the dominant shear crack. The crack bridging stress provided by the fibers results in a significant increase shear transfer across the crack which provides significant post-peak load carrying capacity with increasing slip of the shear crack

Efficiency of steel fibers in shear resistance of reinforced concrete beams without stirrups at different moment-to-shear ratios

An experimental program is conducted to investigate the effect of the moment-to-shear ratio on the shear capacity of reinforced concrete beams without stirrups. Shear beams made with steel fiber reinforced concrete (SFRC) are tested at shear-span-to-depth (a/d) ratios equal to 1.8, 2.25 and 3.0. Using the digital image correlation (DIC) technique, the critical shear crack is identified. The critical shear crack is formed at the location of the highest moment in the shear span. From measurements across the critical shear crack, a continuous dilatant behavior is observed. There is a continuous increase in the crack opening displacement with progressive slip across the crack faces throughout the load response. The dilatant expansion measured across the critical shear crack depends on the a/d ratio. For a given a/d ratio, the load is sustained for large crack openings in SFRC beams. At a higher a/d ratio, there is a larger applied moment at the shear crack, which produces a larger crack opening with increasing slip displacement across the shear crack. At the peak load, the applied moment (M) to shear (V) ratio given by M/(Vd) at critical shear crack increases with increasing a/d ratio. Larger crack opening with increasing M/(Vd) decreases the efficiency of fibers in providing shear resistance for continued deformation past the peak load

Improvements in fracture behavior and shear capacity of fiber reinforced normal and self consolidating concrete: A comparative study

Flexural fracture and shear behaviors of self-consolidating concrete (SCC) and normal concrete (NC) with 0.75% volume fraction of hooked-end steel fibers are evaluated and compared. The cohesive stress-crack separation behavior obtained from the fracture test indicates that the steel fibers are significantly more effective in providing crack control in SCC than in NC. A significantly larger crack closing stress is generated in steel fiber reinforced SCC (SFSCC) even at small crack opening when compared with steel fiber reinforced normal concrete (SFNC). The fracture energy of SFSCC obtained from flexure tests is higher than the fracture energy of SFNC. In the shear response of reinforced concrete, there is a significantly larger increase in the shear capacity of SCC with the addition of fibers when compared with relative increase in NC with the addition of fibers. Full-field displacements obtained from Digital Image Correlation (DIC) is used to establish the in-situ dilatant behavior of the shear crack. The displacements measured across the primary shear crack indicates a continuous increase in the relative slip accompanied by an increase in the crack opening. The dilatant response measured in SCC indicates a smaller crack opening displacement resulting from slip across the primary shear crack when compared with normal concrete. In both NC and SCC, the shear capacity is determined by the failure of stress transfer across the shear crack. Shear failure in SCC occurs at a small crack opening, less than 0.1 mm whereas in NC it occurs at an opening of around 1.0 mm. With the addition of fibers, there is an increase in the load carrying capacity and the load transfer across the primary shear crack is sustained for a larger crack opening in both NC and SCC. The shear stress transfer across the primary shear crack in SFSCC is sustained for a crack opening up to 1 mm. The increase in the crack closing stress provided by steel fibers in SCC matrix contributes to an increase in the shear capacity through better crack control, which results in better shear stress transfer characteristics. The relative increases in the shear capacity of NC and SCC with the addition of steel fibers are consistent with the relative increases in the fracture energies

Study on Fracture Behavior and Shear Capacity of Steel Fiber Reinforced Concrete Beams

In the design of reinforced concrete structures, strength-based procedures are conventionally adopted, which ignore the contribution of tensile stress carried by concrete after cracking. Any delay in the onset of cracking produced by improvement in the material performance is considered through an increase in the tensile strength of the material. To assess the true potential of discrete fiber reinforcement the delay in the onset of cracking due to suppression of microcracking, and the post-cracking stress transfer across the crack have to be accounted for. The post-cracking stress transfer is particularly important in shear where the shear transfer by aggregate interlock contributes significantly to the shear capacity of reinforced concrete elements. Shear displacements along rough cracks also produce dilatancy across the shear crack. The crack bridging provided by fibers can potentially provide for increased mobilization of aggregate interlock, thereby increasing the shear capacity. An understanding of the influence of fibers on the post-cracking shear stress transfer across rough cracks surface and its influence on the shear capacity of reinforced concrete beams needs to be understood to develop design provisions which consider the influence of fibers on shear capacity. This study aims to investigate the shear behavior of reinforced concrete with discrete hooked end steel fibers. The influence of hooked-end steel fibers on the shear transfer across rough cracks in concrete and its influence on the shear behavior of reinforced concrete are investigated. A two stage investigation which involves obtaining information of the material behavior and relating it to the structural response is developed. In the first stage of evaluation, the fracture behavior of steel fiber reinforced concrete (SFRC) is investigated using flexure tests on notched specimens. Crack propagation and post-cracking behavior in the flexural load response of SFRC is evaluated using full-field displacements obtained from digital image correlation technique. Surface displacements and strains during crack propagation from a notch are presented at volume fractions of steel fibers (Vf) equal to 0.5% and 0.75%. An analysis procedure for determining the crack opening width over the depth of the vii fiber-reinforced beam in a flexural test is presented. From the analysis of displacements and strain, the crack opening width is established as a function of crack tip opening displacement and the residual flexural strength for the SFRC. Analysis of displacements shows that crack propagation in the cementitious matrix produces softening in the load response. At the volume fractions of fibers considered in this study, the softening in the post-peak load response is shown to be associated with the rapid propagation of crack in the material. Fibers control the rate of load decrease produced by crack propagation in the matrix with increasing crack opening in the softening response. The load recovery in the SFRC is associated with a hinge-type behavior in the beam. Fibers provide resistance to opening of the hinge, which results in a load recovery. For the stress gradient produced by flexure, the hinge is established at a crack tip opening displacement before load recovery is initiated. At 0.75% fiber volume fraction, there is a significant decrease in the crack advance for a given crack opening. An analytical framework for implementing a multi-linear stress-crack separation (σ-w) relationship within the cracked hinge model is presented. Multilinear σ-w relations are obtained for SFRC with different Vf using an inversion procedure. The σ-w relationship for SFRC exhibits an initial softening to values lower than the tensile strength, which is followed by a stress recovery with increasing crack separation. In SFRC, the stress attains a constant value with increasing crack separation, larger than 1 mm. For Vf equal to 0.75%, application of cracked hinge model predicts a constant stress of magnitude less than the tensile strength with increasing crack separation in the part of the load response associated with multiple cracking. In the second stage of evaluation, the shear behavior of reinforced concrete beams with and without steel fibers is investigated. Reinforced concrete beams with discrete hooked-end steel fibers at 0.5% and 0.75% volume fractions were tested with a shear span-to-depth ratio equal to 2.25. Full-field surface displacements from the beam during the load response were obtained using digital image correlation (DIC). The formation and propagation of a shear crack which directly influences the load response and peak load, is monitored. The displacement measurements from across viii the shear crack indicate a continuous increase in crack opening associated with increasing slip between the two crack faces. The relation between slip and crack opening suggests that the dilatant behavior measured within the shear region is identical in control and SFRC beams. At a given load, the crack opening in SFRC specimens is smaller than the value obtained from the control beams. Failure in control beams is brittle and is produced by the opening of the dominant shear crack in the shear span. Analysis of shear response of reinforced concrete beam shows that control specimens failed when compression generated by rebar is insufficient to sustain aggregate interlock. In SFRC beams, the crack closing stresses provided by the steel fibers allow shear stress transfer across the shear crack, which contributes to increased ductility and to residual load carrying capacity after the peak load. In SFRC beams with 0.5% volume fraction there is a continuous opening of the shear crack even after the peak load which leads to a post-peak response with decreasing residual load carrying capacity. In SFRC beams with 0.75% fiber volume fraction, the increased resistance to crack opening provided by the fibers results in further increase in the peak load. Experimental tests are conducted to study the effect of shear slenderness on the shear behavior of steel fiber reinforced concrete (SFRC) beams. Shear beams ranging from non-slender to slender were tested at shear-span-to-depth (a/d) ratios equal to 1.8 and 3.0 in addition to 2.25. At an a/d of 1.8, shear failure is very sensitive to the loading and support conditions. For the intermediate and the slender beams, flexure-shear failure is produced. Shear capacity decreases with an increase in the slenderness of the beams. DIC is used to study the propagation of cracks leading to the formation of the critical shear crack. Critical shear crack is formed at the location of the highest applied moment in the shear span. The horizontal projection of the critical shear crack is equal to the effective depth of the beam (d). At the peak load, the moment (Mu) to shear (Vu) ratio given by Mu/(Vud) at critical shear crack increases with increasing slenderness. A continuous dilatant behavior identified with a continuous increase in the crack opening displacement with progressive slip across the crack faces of the critical shear crack is observed throughout the load response. The dilatancy measured across the critical shear crack depends on the slenderness of the beam and is not altered with the addition of fibers. The applied moment contributes ix to the measured dilatancy across the critical shear crack. There is a larger crack opening with increasing slip displacement across the shear crack with an increase in the applied moment at the location of the shear crack. There is an increase in the shear capacity and the energy absorption in SFRC beams, and the load is sustained for large crack openings. The efficiency of fibers on increasing the shear capacity decreases with an increase in the Mu/(Vud) ratio at the shear crack. Based on the two stage investigation of fracture and shear behavior of fiber reinforced concrete a discrete crack model is developed for predicting shear capacity of reinforced beams without stirrups. The experimental observations of cracking and mechanism of the pivoting action of the critical shear crack are included in the formulation of the discrete crack model. The internal contact forces on the crack faces and the cohesive stress from fibers, are considered in deriving the equilibrium. The fiber contribution in providing shear resistance is quantified in terms of a cohesive stress-crack separation relationship. The prediction of the model includes an increase in the contact forces with an increase in the fiber force at peak shear resistance with an increasing volume fraction of fibers. In SFRC beams, the additional contact force mobilized across the crack by the fibers maintains the shear transfer across the crack and hence the load carrying capacity is sustained for a larger crack opening. The model derived from laboratory-sized specimens accurately predicts the scaling the shear capacity with size of the beam. The main findings of this study are as follows: (a) Improvement in the tensile fracture response of concrete results in an improvement in the shear capacity of reinforced concrete; (b) The resistance to crack opening directly contributes to the contact stresses across the shear crack; (c) Increase in shear capacity of reinforced concrete is derived from an increase in the shear transfer ability of the frictional interface. This study establishes the potential for using discrete steel fibers as structural shear reinforcement

Investigation of the dilatant behavior of cracks in the shear response of steel fiber reinforced concrete beams

Steel fiber reinforced concrete beams with fiber volume fractions equal to 0.5% and 0.75% are tested with a shear span to depth ratio equal to 1.8. The cracking in the beams is evaluated using the full-field surface displacements obtained from the digital image correlation (DIC) technique. Analysis of images shows that a full depth shear crack is established before the peak load. The displacements measured from across the shear crack indicate a continuous increase in the crack opening displacement associated with increasing slip between the two crack faces. From crack opening and sliding measurements across the shear crack, the dilatant behavior is identical in beams with and without steel fiber reinforcement. Failure in control beams is brittle and results in a large opening of the shear crack. In the SFRC beams with 0.5% volume fraction, there is a continuous decrease in the residual load carrying capacity after the peak load which is associated with an increase in the crack opening displacement. In SFRC beams with 0.75% fiber volume fraction, the increased resistance to crack opening provided by the fibers results in a significantly smaller crack opening and a large increase in the peak load. The crack opening due to dilatancy is arrested, resulting in shear failure by the formation of a secondary shear crack or by flexural failure. The crack opening displacement across the shear crack at the peak load in the load response of the control and the SFRC beams are nominally identical. Failure in shear occurs when the crack opening control provided by the flexural reinforcement and steel fibers is inadequate to sustain the aggregate interlock

Shear Behavior of Slender and Non-Slender Steel Fiber- Reinforced Concrete Beams.

Steel fiber-reinforced concrete (SFRC) beams without shear reinforcement are tested at shear span-depth ratios (a/d) equal to 1.80, 2.25, and 3.0. Cracking behavior up to the peak load is evaluated and the critical shear crack is identified from the full-field measurements on the surface of the beam obtained using digital image correlation (DIC). The in-place movements across the shear crack show a dilatant behavior with a continuous increase in the crack opening and slip across the crack faces. The critical shear crack is formed at the location of the highest applied moment-to-shear ratio in the shear span. At the peak load, there is an increase in the moment to shear ratio (Mu/(Vud)) at the critical shear crack with an increase in shear slenderness. Dilatancy across the shear crack increases with an increase in the slenderness due to the increased contribution of flexure to crack opening. While there is an increase in shear capacity with the addition of fibers, the efficiency of the fibers in increasing shear capacity decreases with an increase in the Mu/(Vud) at the critical shear crack