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Twelve tests were conducted on reinforced concrete beams with
three steel fiber-volume fractions (0, 0.5, and 0.75%), three shear
span-depth ratios (2, 3, and 4), and two concrete compressive
strengths (31 and 65 MPa). The results demonstrated that the nom-
inal stress at shear cracking and the ultimate shear strength
increased with increasing fiber volume, decreasing shear span-
depth ratio, and increasing concrete compressive strength. As the fiber
content increased, the failure mode changed from shear to flexure.
The results of 139 tests of fiber-reinforced concrete beams with-
out stirrups were used to evaluate existing and proposed empirical
equations for estimating shear strength. The test population
included beams with a wide range of beam properties, but most of
the beams were small. The evaluation indicated that the equations
developed by Narayanan and Darwish and the equations proposed
herein provided the most accurate estimates of shear strength and
the onset of shear cracking. For the proposed procedure, the ratio
of the measured strength to the calculated strength had a mean of
1.00 and a coefficient of variation of 15%.
Keywords: beam; cracking; shear strength.
INTRODUCTION
The addition of steel fibers to a reinforced concrete beam
is known to increase its shear strength and, if sufficient fibers
are added, a brittle shear failure can be suppressed in favor
of more ductile behavior.1,2 The increased shear strength and
ductility of fiber-reinforced beams stems from the post-
cracking tensile strength of fiber-reinforced concrete. This
residual strength also tends to reduce crack sizes and
spacings. The use of steel fibers is particularly attractive for
high-strength concrete, which can be relatively brittle without
fibers, or if conventional stirrups can be eliminated, which
reduces reinforcement congestion.
The literature describes numerous studies of rectangular,
fiber-reinforced beams without stirrups,2-21 of which 163-18
were reviewed by Adebar et al.2 Batson, Jenkins, and Spat-
ney performed the first large experimental study of such
beams,4 which included 42 tests of fiber-reinforced beams with-
out stirrups that failed in shear. Subsequent investigations of
normal-strength concrete6,7,9-17 (primarily in the 1980s) and
high-strength concrete3,5,19,21 (primarily in the 1990s) con-
firmed the effectiveness of adding steel fibers and identified
key parameters that affect shear strength. The increase in
shear strength can vary drastically depending on the beam
geometry and material properties. For example, in tests reported
by Narayanan and Darwish,13 the increase in shear strength
attributable to steel fibers varied from 13 to 170%.
As with conventional reinforced concrete beams,22-24 the
ultimate shear strength decreases with increasing shear span-
depth ratio a/d;3,4,5,9-13,21 increases with increasing flexur-
al reinforcement ratio;3,5,13 and increases with increasing
concrete compressive strength fc′ .13,21 These effects are
attributable to the development of arch and dowel action in beams with low values of a/d, and to the diagonal-tension
failure mode (beam action) in beams with higher values of
a/d. Li, Ward, and Hamza9 also report that, as has been ob-
served in conventional beams, the average shear stress at
failure decreases with increasing beam depth.
The increase in shear strength attributable to the fibers
depends not only on the amount of fibers, usually expressed as
the fiber volume fraction Vf , but also on the aspect ratio6,7,9,12,13
and anchorage conditions for the steel fibers.9,13,21 For example,
from the point of view of workability, it may be convenient to
use stocky and smooth fibers, but after the concrete cracks, such
fibers will resist tension less well than elongated fibers with end
deformations (hooked or crimped).
Investigators have also developed empirical expressions
for calculating shear strength. For example, Sharma;16
Narayanan and Darwish;13 Ashour, Hasanain, and Wafa;3
and Imam et al.25 have proposed equations for predicting the
ultimate average shear stressu. Although the onset of shear
cracking is difficult to establish reliably, Narayanan and
Darwish13 also proposed a procedure for estimating the
average shear stress at the onset of shear crackingcr .
Despite this research activity, the existing design expres-
sions have not been evaluated with a large amount of test
results and, in some cases, the data used to calibrate models of
shear strength included tests of beams that failed in flexure
rather than in shear. Proposed and existing design procedures
for estimating shear strength need to be evaluated using a large
collection of test results for beams that failed in shear.
RESEARCH SIGNIFICANCE
Previous studies have documented many tests of fiber-
reinforced concrete beams without stirrups that failed in
shear. The results of new tests, combined with the results
of previous tests, provide the opportunity to evaluate the
accuracy of existing and proposed design procedures. Such an
evaluation is needed before building codes22 will recognize
the contribution of steel fibers to the shear strength of reinforced
concrete beams.
TEST PROGRAM
Twelve reinforced concrete beams were tested to failure to
evaluate the influence of fiber-volume fraction a/d and
concrete compressive strength on beam strength and ductility
(Table 1). The first 9 beams, denoted by the letters FHB (fiber-
reinforced, higher-strength concrete beams) were constructed