Gali, Sahith and K V L, Subramaniam
(2019)
Study on Fracture Behavior and Shear Capacity of Steel
Fiber Reinforced Concrete Beams.
PhD thesis, Indian institute of technology Hyderabad.
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Abstract
In the design of reinforced concrete structures, strengthbased 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 postcracking
stress transfer across the crack have to be accounted for. The postcracking 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 postcracking 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 hookedend 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 postcracking behavior in the flexural load response of SFRC is
evaluated using fullfield 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
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fiberreinforced 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 postpeak 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 hingetype
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 multilinear stresscrack
separation (σw) relationship within the cracked hinge model is presented. Multilinear σw relations are obtained for SFRC with different Vf using an inversion
procedure. The σw 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 hookedend steel fibers at 0.5% and 0.75% volume fractions were tested with
a shear spantodepth ratio equal to 2.25. Fullfield 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
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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 postpeak 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 nonslender to slender were tested at shearspantodepth (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,
flexureshear 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
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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
stresscrack 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 laboratorysized 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.
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