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SHEAR STRENGTHENING OF STEEL PLATES USING SMALL-DIAMETER CFRP
STRANDS
Hamid Kazem1*, Sami Rizkalla1, Akira Kobayashi2
1Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC, USA
2Nippon Steel & Sumikin Material Co., Ltd, Composites Company, Japan
*Corresponding author. E-mail addresses: [email protected], Phone: 919.741.7562
ABSTRACT:
This paper presents the results of a comprehensive research program, including experimental and
analytical studies, to examine the use of small-diameter CFRP strands for shear strengthening of steel
structures and bridges. The experimental program examined the effectiveness of the proposed
strengthening system to increase the shear capacity of steel plates subjected to pure shear stresses
using a unique test set up. A nonlinear finite element analysis (FEA), calibrated the experimental results,
was used to study parameters which were not included in the experiments. Research findings indicated
that the proposed system is effective for shear strengthening of steel structures and eliminated the typical
debonding failure commonly observed by CFRP laminates.
Keywords: A. Carbon fiber, B. de-bonding, C. Finite Element Analysis (FEA), Steel
1. Introduction
Due to the known benefits of Fiber Reinforced Polymer (FRP) materials, their use for retrofitting
(strengthening and repair) of concrete structures became a common practice. The use of FRP material for
steel structures is also required due to the increasing demand for traffic loads, problems due corrosion
and deterioration due to fatigue loadings. The new bridge design codes require designing for higher
vehicular loads in comparison to that used in the initial design of the bridges. The production of high
modulus Carbon FRP (CFRP) with elastic modulus higher than that of steel, offers a promising alternative
for flexural and shear strengthening of steel structures and bridges [1].
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Due to the uncertainties and the reported debonding failure experienced by using FRP sheets/plates for
strengthening steel members, numerous studies were conducted experimentally and analytically to
investigate the bond behavior [2-4]. Understanding the bond mechanism of the CFRP to steel initiated by
testing of flexural steel members strengthened with CFRP. Based on understanding of the bond behavior,
researches introduce several schemes for the use of externally bonded, high-modulus CFRP materials for
flexural strengthening of steel members which have shown significant increase in flexural capacity and
stiffness [5-11]. However, to increase the total load-carrying capacity of the strengthened member, the
shear capacity should also be increased along with its increase of the flexural capacity.
Shear capacity of the web plate of steel girder is typically controlled by the compressive component of the
applied shear. Therefore, the ultimate shear strength of the steel web plate is typically controlled by
elastic buckling of slender webs or yielding of the steel material of compact or non-compact webs.
Therefore shear capacity of the web plate can be increased by reducing the state of stress in the web
plate. Strengthening of web plates by using Carbon Fiber-Reinforced Polymer (CFRP) materials could
help reducing the stress level and consequently increase the shear capacity.
Very limited numbers of research have been reported on the use of FRP for shear strengthening of
existing steel girders. Patnaik et al. (2008) [12] published results of experimental and analytical program
focused on shear strengthening of steel built-up I-beams. Test results confirmed the effectiveness of the
proposed CFRP shear strengthening to increase the shear capacity of steel beams up to 26%. The
reported failure mode of the strengthened specimen was due to debonding of CFRP sheet from the steel
substrate. Okeil et al. [13-15] increased the lateral stiffness of steel plate by bonding pultruded GFRP
sections to the surface. The strengthened system increased the shear strength by 56 percent. The
reported failure mode of the strengthened specimens was debonding of the GFRP stiffener followed by
immediate web buckling. The study on using T-shaped GFRP stiffeners as shear strengthening was
investigated analytically by Babaizadeh (2012) [16]. Results of FE analysis showed that strengthening
steel beams with different flange width can result in increase of shear capacity up to 66% for square
shear zones and up to 36% for rectangular shear zone. An application of CFRP strips as shear
reinforcement was also investigated by Narmashiri et al. (2010) [17]. Strengthening system consist of
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applying CFRP on one or both faces of the steel web, and the research included also different
reinforcement CFRP ratio. Results of the experimental research showed clearly that externally bonded
CFRP could increase the shear capacity of steel I-beam up to 51 percent. The reported failure modes
were longitudinal delamination and debonding of the CFRP strips.
The proposed small-diameter CFRP strands shown in Figure 1, is a promising alternative strengthening
system for steel structures. The CFRP strands are provided in sheets and the strands are stitched
together leaving a gap between the strands to allow the adhesives to penetrate and totally cover the
strands.
Figure 1: Small-diameter CFRP strand sheet
Performance of small-diameter CFRP strand sheets subjected to flexure and axial compression are
documented in previous publications [8, 18]. This paper evaluates the efficiency of the proposed small-
diameter CFRP as shear strengthening system for steel girders subjected to direct shear loading.
2. Experimental Program
2.1 Test Setup
To simulate an applied pure shear stresses acting on a steel plate of typical web of steel plate girder, a
square plate specimen is used. The plate is clamped to a heavy steel frame, rotated 45 degrees and
subjected to tensile load on diagonally opposite corners as schematically shown in Figure 2(a). The
applied tensile load to the rigid steel frame induces equivalent shear forces along the edges of the steel
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test plate through uniformly distributed pre-stressed bolts as shown in Figure 2(b). The shear forces along
the edges of the specimen induced compressive stresses perpendicular to the direction of the applied
tensile load and tensile stresses parallel to direction of the applied tensile load.
Figure 2: State of forces acting on the test plate subjected to the applied tensile load
The steel plate specimen was pre-stressed to the articulated built-up steel frames through series of 40
mm (1-1/2 in.) diameter high-strength (HS) bolts. Twenty four HS bolts were torqued using 1500 kN.mm
(1100 lb.ft) impact wrench. Induced stresses were transferred to the test plate through the friction of the
connection induced by the bolts. The exposed area of test plate had a dimensions of 910x910x5 mm
(36x36x3/16 in.) resulting in slenderness ratio (h/t) of 192. The frame was made up by four very stiff steel
plate legs, each consist of stiff short and long plates having dimensions of 760x200x25 mm (30x8x1 in.)
and 1320x200x25 mm (52x8x1 in.), respectively. Each two legs were connected at the corners using
high-strength steel pins with a diameter of 100 mm (4 in.) to allow rotation. To avoid bearing of the test
plate on the pins at the corners, holes of the steel plate were machined with diameter of 127 mm (5 in.)
which are slightly larger than the pin diameter. Two 2000 kN (440 kip) capacity hydraulic actuators were
used to apply the tensile load to the steel frame. The two hydraulic actuators were connected to the same
controller to ensure that the loads are equal from each actuator. Two highly stiffened spreader beams
were especially designed to transfer the tensile load to the shear frame. The bottom spreader beam was
pre-stressed to the strong floor using high strength bars. Schematic sketch and view of the test setup are
shown in Figure 3.
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Figure 3: Pure shear test setup
2.2 Instrumentation
Vertical and horizontal strains of the plate at mid-point were measured using electrical resistance strain
gages with a gage length of 5 mm (3/16 in.). Four Strain gages were attached to both faces of the control
plate, with two strain gauges on each face. Two vertical strain gauges were attached in the direction of
the applied tensile load and two horizontal strain gauges were attached in direction of the compressive
component. Total of eight strain gauges were attached to the strengthened specimens at mid-point. Four
strain gauges were attached to the base steel and the remaining four strain gauges were attached on the
outer surface of the CFRP strand sheets. The overall out-of-plane lateral deformation of the steel plates
was measured using five linear string potentiometers. OptotrakCertus® motion capturing system was also
used. The motion capturing system measures a three-dimensional (3-D) coordinate system using Infrared
Emitting Diodes (IRED) attached to the specimen at points of interest. The IREDs were attached to the
front face of the test specimens along with the vertical and horizontal centerlines and were spaced at 75
mm (3 in.). All instrumentations were connected to an electronic data acquisition system. The
instrumentations used to measure behavior of the specimens are shown in Figure 4.
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Figure 4: Specimen instrumentations, a) IREDs and strain gauges attached on the front face of test plate, b) string potentiometers and strain gauges attached to the back face of test plate
2.3 Test Matrix
A total of nine square steel plates were included in this research as given in Table 1. The CFRP strands
were externally bonded at an angle of 45ο, 90ο, and ±45ο relative to the applied tensile load using one and
two layers of the High-Modulus (HM) CFRP strands on each side of the plate. The HM small-diameter
CFRP strands was selected as the result of the research undertaken for plates subjected to compression
proven to be the best effective strengthening system in comparison to Intermediate-Modulus (IM) and
Low-Modulus (LM) small-diameter CFRP strands [18]. The following nomenclature was adopted to
distinguish the various cases. All specimens were 915x915 mm (36x36 in.) and 5 mm (3/16 in.) thick,
consequently the slenderness ratio was 192. The first number is the set number. The second number
represents angle of the orientation relative to the applied tensile load. Last letters show the number of
layers and the elastic modulus of the CFRP material used. Figure 5 shows configuration of each
specimen including orientation of HM CFRP strands. A layer of the low-modulus polyurea putty was used
between the steel plate and the CFRP strands for all strengthened specimens. The control specimen in
each set was used for the strengthened specimen with one layer and subsequently two layers of HM
CFRP strands to eliminate the effect of plate initial imperfections.
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Table 1: Shear strengthening test matrix
Plate Designation Set # FiberOrientation
No. ofLayers
1-45-C1
NO NO1-45-1HM 45ο 11-45-2HM 45ο 2
2-90-C2
NO NO2-90-1HM 90ο 12-90-2HM 90ο 23-45W-C
3NO NO
3-45W-1HM 45ο 13-45W-2HM ±45ο 2
Figure 5: Schematic sketch of shear strengthening test matrix
2.4 Material Properties
2.4.1 Steel
All test plates were high-strength, low-alloy, ASTM A572 Grade 50 steel. Tensile coupons were prepared
and tested according to ASTM A370 [19] in order to determine the mechanical properties. Three coupons
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were tested from each set of the test specimens. The average measured tensile properties of the steel
coupons for each set of specimens are given in Table 2.
Table 2: Summary of average measured tensile characteristics of steel
Nominal ThicknessSet #
Yield Strength Modulus of Elasticity Yield Strainmm (in.) MPa (ksi) MPa (ksi) mm/mm (in./in.)
5 (3/16)1 397 (58) 195,662 (28,378) 0.002022 469 (69) 203,299 (29,486) 0.002273 410 (59) 191,068 (27,712) 0.00214
2.4.2 CFRP
Tension specimens were prepared using an individual strand in accordance with ASTM D3039 [20] and
Test Method L2 of ACI 440.3R-04 [21]. The average cross-sectional areas of the individual CFRP strands
are given in Table 3. The cross-sectional area was determined by water volume displacement of 15
randomly extracted individual strands. Due to the difficulty of attaching the extensometer to an individual
strand, the elongations of the strands were measured by using OptotrakCertus® motion capturing system.
Each coupon had two InfraRed Emitting Diodes (IREDs) attached to the individual strand to measure the
elongation. The average measured tensile stress and strain of the various CFRP strands are summarized
in Table 3 and the stress-strain relationship is shown in Figure 6. Three coupons were tested from each of
the three types of CFRP strands. It is worth noting that the rupture strain of the HM strands was larger
than the measured yield strain of the steel.
The compressive characteristics of the three types of CFRP strands were also determined. Coupons cut
from the CFRP witness panels were tested to define the properties of the composite materials. Witness
panels were fabricated under the same environmental conditions used for the strengthening of the test
plates. Compressive specimens were prepared in accordance with ASTM D6641 [22] and tested in
compression. Shortening of the witness panels coupons were measured using tee rosette strain gauges.
The CFRP strands were positioned in the longitudinal direction parallel to the compressive applied load.
Three coupons were tested from each of the three types of CFRP strands. The average measured
compressive properties of the various CFRP witness panels are summarized in Table 4 and shown in
Figure 7. Material properties of the putty and epoxy adhesive are reported by Okuyama et al. (2012) [23].
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The chemical properties and mechanical compatibility between putty, epoxy adhesive and CFRP strands
are addressed in detail by Komori et al. (2013) [24].
Table 3: Measured tensile properties of small-diameter CFRP strands
CFRP Strand Strand Area Rupture Strain Rupture Stress Elastic Modulusmm2 (in2) mm/mm (in./in.) MPa (ksi) MPa (ksi)
Low-Modulus (LM)
1.03226 (0.00156) 0.0168 2,353 (341) 140,253
(20,342) Intermediate-Modulus
(IM)1.23871
(0.00192) 0.0104 2,220 (322) 212,752 (30,857)
High-Modulus (HM)
1.14193 (0.00177) 0.0032 806 (117) 255,430
(37,047)
Table 4: Measured compressive properties of CFRP witness panels
CFRP Witness Panel Area Compressive Strength Elastic Modulusmm2 (in2) MPa (ksi) MPa (ksi)
Low-Modulus (LM)
56.765(0.0880) 95.29 (13.82) 24,766 (3,592)
Intermediate-Modulus (IM)
60.855(0.0943) 121.44 (17.61) 40,987 (5,945)
High-Modulus (HM)
70.518(0.1093) 69.89 (10.14) 47,358 (6,869)
Figure 6: Typical tensile stress-strain behavior of the three types of CFRP strands
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Figure 7: Typical compressive stress-strain behavior of the three types of CFRP witness panels
3. Application of the Strengthening System
Initially, the steel plates were sandblasted prior to the commencement of the application process. The
strain gages were attached to the steel plate after the plates were cleaned using pressurized air. The
primer resin was applied to the steel plates after sandblasting and cleaning. The polyurea putty layer was
applied after at least two hours from the application of the primer resin. The epoxy was applied after at
least six hours from the application of the polyurea putty layer. Application of epoxy was performed while
the steel plate was laid horizontally. After applying the epoxy layer, the cut CFRP sheets were attached
the steel plate matching the proper orientation in each case. The strain gauge leading wires were passed
through the gap between the strands. The applied CFRP sheet was firmly pressed using hand rollers until
the excessive epoxy was squeezed out to ensure the elimination of any air pocket. A second layer of
epoxy was applied on the top of the CFRP sheets. Finally, the strengthened plate remained in control
environment for at least seven days to cure before it was tested. The application process is illustrated in
Figure 8 (a), (b), and (c), respectively.
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Figure 8: Application of strengthening system, a) Application of primer resin on sandblasted steel plate, b) Application of polyurea putty, c) Application of epoxy and attaching the CFRP sheet
4. Test Results
Due to the initial imperfection of the steel plates, the web buckles before reaching the theoretical buckling
load (Pb) and the behavior shows a gradual increase of load with increasing in-plane or lateral deflections.
The transition point between pre-buckling and post-buckling behavior vanishes at large deformation [25].
At loads far beyond buckling load (Pb) the curve may approach the curve for flat plate [25]. Using the
recorded data from the Optotrak system, the imperfections were measured and the deformed shape was
curved with a maximum deformation nearby mid-point and flat tangents at the edges.
4.1 Measured Principle Strain
The total applied load versus measured horizontal strain at mid-point of the specimens are shown in
Figure 9 (a), (b), and (c) for the plates strengthened with CFRP strands with an angle of 45ο, 90ο and
±45ο, respectively. Each figure contains the results of the control plate, plate strengthened with one layer
and plate strengthened with two layers of HM CFRP strands.
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Results confirm the effectiveness of the proposed externally bonded CFRP small-diameter strands in
increasing the shear capacity of the steel plate. Since buckling was not observed, the shear capacity of
the strengthened plates is compared to the control plates prior to the steel yielding. The strengthening
system contributed to the load carrying capacity by significantly reducing the horizontal strains due to the
applied load therefore resulted in an increase in shear capacity. Test results indicated clearly that
increasing the number of layers of CFRP strands increases the shear capacity.
(a) (b)
(c)
Figure 9: Applied load vs. horizontal steel strain for plates under pure shear strengthened with HM CFRP at an angle of a) 45ο, b) 90ο, and c) ±45ο
The percentage increase in the shear capacity for different CFRP strands orientations is shown in Figure
10. Results show that two layers of externally bonded HM CFRP strands can increase shear capacity of
the strengthened plates up to 79 percent. The differences in the percentage increase of the shear
capacities may be attributed to the different imperfections for the tested plates.
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Figure 10: Shear capacity percentage increase of plates strengthened with one and two layers of HM CFRP strands
4.2 Load - Lateral Deformation
The net lateral deformation at mid-point with respect to its edges versus the applied tensile load are
shown in Figure 11 (a), (b), and (c) for the test plates strengthened with CFRP strands with an angle of
45ο, 90ο and ±45ο, respectively.
(a) (b)
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(c)Figure 11: Applied load vs. net lateral deformation of the plates under pure shear with CFRP strands angled
at, a) 45ο, b) 90ο, c) ±45ο
The behavior clearly indicates that increasing the reinforcement ratio for all CFRP strand orientations
increase the lateral stiffness as shown in Figure 12. For the plates strengthened with one layer, increase
in the lateral stiffness remain within the similar range. However, the increase of the lateral stiffness using
two layers is highly dependent on the fiber orientation of the second layer. The lateral stiffness was
increased up to 350 percent for plate strengthened with two layers with an angle of ±45ο relative to the
applied load. The behavior suggests that the ±45ο orientation is the most efficient orientation due to
reduction of the buckling length of the strands supported by the orthogonal layers, hence increase of the
lateral stiffness of the strengthened plate.
Figure 12: Increase of the lateral stiffness for the plates strengthened with one and two layers of HM CFRP strands
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4.3 Deformed Shape
The typical measured lateral net deformed shape versus the applied load in both horizontal and vertical
directions of the test plates for the ±45ο orientation of the strands are shown in (a)
(b). The lateral deformed shapes are shown for the control, one layer and
two layers of HM CFRP using the Optotrak system.
The behavior indicates that the maximum deformation occurred at the mid-point of the steel plate.
Deformed shapes indicate that the lateral deformation decreased by increasing the reinforcement ratio of
the CFRP strengthening system at the same load level. Furthermore, adding more layers of the CFRP
strands induces less distortion of deformed shape. It should be noted that in spite of the experienced
large deformation, there was no sign of CFRP de-bonding or rupture up to the yielding of the steel plate.
(a) (b)Figure 13: Lateral deformed shape of plates strengthened with HM CFRP at an angle of ±45ο (3-45W) at, a)
horizontal direction, b) vertical direction
5. Model Analysis
To consider additional parameters that were not considered in the experimental program, an analytical
study was performed using 3-D nonlinear finite element (FE) analysis using 20-node solid element to
model the behavior of the steel plates strengthened with CFRP strands subjected to shear forces. The FE
model was calibrated by the experimental results and the model was used to develop design guidelines.
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The nonlinear finite element analysis was based on ANSYS® Workbench (v16.1) [26] using the same
geometry and dimensions of the test specimens and material constitutive relationship. The steel material
constitutive relationship was simulated by bilinear isotropic hardening material with strain hardening
values given in Table 5. Due to use of high strength bolts, isotropic-elastic steel material with Young’s
modulus of 200 GPa (29000 ksi) was used. The specified Poisson’s ratio of the steel was 0.3. Mechanical
properties of CFRP composite and polyurea putty are given in Table 6. Compressive properties of CFRP
composite material, measured from witness panels were used. The CFRP composites were defined as
orthotropic elasticity material using similar properties in transverse direction. Pulyurea putty was also
defined as isotropic elastic material based on the measured results reported by Okuyama et al. (2012)
[23].
Table 5: Mechanical properties of steel considered in FE model
Set#Yield Strength Modulus of Elasticity Strain Hardening
MPa ksi MPa ksi MPa ksi
1 396.6 57.519 195,662 28,378 400 57.522 468.7 67.972 203,299 29,486 470 67.973 410.1 59.485 191,068 27,712 410 59.49
Table 6: Mechanical properties of CFRP composite and putty considered in FE model
Property Component HM CFRP IM CFRP LM CFRP PuttyYoung’s Modulus
Ex MPa(ksi)
47,400 (6,869) 41,000 (5945) 24,800 (3,592) 76 (11)Ey, Ez 33,000 (4,784) 33,000 (4,784) 33,000 (4,784)
Shear Modulus
Gxy 18,600 (2,696) 15,600 (2,264) 9,300 (1,345) 24,900 (3,612)Gyz, Gxy 15,700 (2,278) 15,700 (2,278) 15,700 (2,278)
Poisson’s Ratio
υxy 0.274 0.313 0.3350.05
υyz, υxy 0.05 0.05 0.05
3-D 20-node second order structural solid element (SOLID186) was used to model all steel plate, steel
frame, and bolts. SOLID186 is a higher order element that exhibit quadratic displacement behavior. The
element can be used to orient the material properties and stress/strain output [27]. SOLID elements were
used for modeling the bolts and the nuts which simplifies defining the surfaces of the contacts elements.
Boundary conditions used were compatible to the actual boundaries used in the experiments as shown in
Figure 14 (a). Bolts and nuts were modeled. Very large number of contact elements was used in the
model. A frictional contact element with friction coefficient of 0.15 was used between all steel pieces that
were in touch. The two faces of the frictional contact elements are free to separate; however, when they
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are in contact, they will slide when the shear stress between them exceeds a critical shear stress. Using
frictional contact elements between bolts and test plate was used to simulate the edge bearing observed
from the tests. Nuts were bonded to the bolts using bonded contact elements. Bonded contacts coupled
faces together in their tangential direction and normal direction. Since no sign of CFRP de-bonding was
observed in the tests, layers of CFRP material and test plate were coupled using bonded contact
elements. The top pin was given displacement upward. Bottom pin was treated as a fixed support. Left
and right pins could have in-plane translations. All the elements except the test plate and CFRP layers
were restrained from any out-of-plane translations. To count on the geometrical nonlinearities, large
deflection analyses were considered. The effect of bolts pre-tensioning was neglected due to observed
bearing effects on the holes. The edge bearing showed that the shear stress between the frame legs and
the test plates exceeded the critical value and sliding occurred at a certain load level.
The mesh configuration used for the FE analysis is shown in Figure 14 (b). Thickness of the test plate
was modeled by two elements through the thickness. Mesh sensitivity analysis was performed using two
different mesh sizes. The effect of mesh size on mid-point horizontal steel strain and net lateral
deformation of plate strengthened with one layer of HM CFRP from FE analysis are shown in Figure 15
(a) and (b), respectively. Two different mesh sizes investigated were 25x25 mm (1x1 in.) and 13x13 mm
(0.5x0.5 in.). The total number of elements varied from 139,006 elements to 702,297 elements. The
figures show almost identical results, where no change in the behavior is occurred by refining the mesh
size. However, using small number of elements reduced dramatically the computation time for the
analysis. Therefore, mesh size of 25x25 mm (1x1 in.) was used in the remaining analyses.
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Figure 14: a) Finite element model and the boundary conditions for the test, b) Mesh configuration used for specimen strengthened with one layer of HM CFRP (25x25 mm (1x1 in.))
(a) (b)
Figure 15: Applied load vs. a) horizontal steel strain, b) net lateral deformation, at mid-point of a specimen strengthened with one layer of HM CFRP at an angle of 45ο
Based on the measured initial imperfections, a simplified shape was assumed by applying small
horizontal pressure on the surface of the test plate. The imperfection configuration was two-way parabolic
shape with an apex at mid-point and zero tangent near the edges of the frame as shown in Figure 16. The
applied pressure induces a residual stress/strain to be considered in the analysis.
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Figure 16: Assumed initial imperfection as a two-way parabolic curve, control specimen
5.1 Calibration of the FE Model
The equivalent elastic strain contours are plotted in Figure 17. FE shows deformed shape in the form of
full wavelength cosine and half wavelength sine across the horizontal and vertical diagonal of the
specimen, respectively, as observed from the test specimens shown in (a)
(b).
Figure 17:a) Equivalent elastic steel strain for control specimen (1-45-C), b) Equivalent elastic CFRP strain for specimen strengthened with one layer of HM CFRP at an angle of 45ο (1-45-1HM) (Scale Factor: 20)
All tested specimens were modeled and the imperfection values were calibrated by comparing the overall
behavior to the measured net lateral deformation and the steel strain at mid-point. The average calibrated
imperfection value used in the analysis was 0.13 in. (3.4 mm) [28].
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Predictions of the behavior for all tested specimens are compared by measured data in Figure 18 with
CFRP strands with an angle of 45ο. The general trends of the curves are captured and were in good
agreement with the measured values. Like experimental tests, results of FE confirm the effectiveness of
the externally bonded CFRP strands in increasing the shear capacity of the steel plate. Also,
strengthening system increased lateral and axial stiffness for each additional layer of CFRP
strengthening. Discrepancy between the predictions and measurements can be attributed to
imperfections of the tested plates which is different from the assumption used and inadequate bearing of
the bolts to the holes. Consequently, FE model could build enough confidence to be used as a tool in the
parametric studies with the assumed boundary conditions.
Figure 18: Comparison between experimental results and FE predictions at mid-point of specimens
strengthened with HM CFRP at an angle of 45ο (1-45); applied load vs. horizontal steel strain
5.2 Parametric Studies
The developed nonlinear FE model was used to study parameters not included in the experimental
program including, 1) behavior within a wide range of slenderness ratio ranging from 44 to 192, 2)
behavior of the three CFRP strengthening materials under the above parameters, 3) effect of stress
distribution, and 4) effect of the CFRP strand orientation.
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Effect of Slenderness ratio, Reinforcement Ratio, and CFRP Material
To examine the effects of the slenderness ratio, plate thicknesses were varied from 5 mm (3/16 in.) to 19
mm (3/4 in.) covering a wide range of plate slenderness ratio ranging from 48 to 192. The selected FE
model considered the steel plates subjected to diagonal vertical tensile load and CFRP strands with an
angle of 45ο relative to the vertical tensile loads. The percentage increase in shear capacity vs
slenderness ratio of steel plates strengthened by HM, IM, and LM CFRP strands as shown by Figure 19.
Results of two reinforcement ratio including one and two layers of the CFRP strands are compared.
Results confirm that the CFRP strengthening system is more effective for the plates with higher
slenderness ratio. Increase of the reinforcement ratio also increases the shear capacity. The relationship
indicates that doubling the reinforcement ratio almost doubles the percentage increase the shear
capacity. The indicates also that the most effective material is HM CFRP followed by IM CFRP for the
shear strengthening of steel plates regardless to any slenderness ratio and reinforcement ratio. This
behavior is attributed to the higher modulus of the HM CFRP in both tensile and compressive directions
compared with other two CFRP materials which results in higher shear capacity. The shown percentage
increase of the shear capacity is realistic to the typical values required in practice.
Figure 19: Percentage increase in shear capacity vs slenderness ratio of plates strengthened with one and two layers of HM, IM, and LM CFRP strands oriented 45ο relative to the vertical tensile load
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Effect of the Shear Stress Distribution
The experimental program simulated pure shear stresses by subjecting the steel plates to diagonal tensile
vertical load as shown in Figure 20 (a). However, the state of pure shear may be also obtained by
subjecting the steel plates simultaneously to diagonal vertical tensile and diagonal horizontal compressive
loads as shown in Figure 20 (b). The effectiveness of the strengthening system is examined using uniform
shear stress distributions along the edges of the steel plate. In this case the right and left pins were
subjected to horizontal compressive loads and could move in two directions. Based on the square
geometry, the applied displacements on the right and left pins were one half of the top pin displacement.
Figure 20: Loading conditions to simulate pure shear on steel plate, a) Applied vertical tension only, b) Applied vertical tension and horizontal compression
The shear force, V, versus horizontal steel strain at mid-point of the steel plate under applied uniform
shear is shown in Figure 21. The figure contains results of the control plate, plate strengthened with one
and two layers of HM CFRP strands. General behaviors confirm the effectiveness of the externally
bonded CFRP material in increasing the shear capacity of the steel plates. Predicted results of the
uniform shear capacity prior to the steel yielding obtained from the strengthened plates are also
compared to the control plates and are shown as a bar chart in Figure 22. The trend indicates that
increasing the reinforcement ratio of the CFRP strands contributes to higher shear capacity
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Figure 21: Applied load vs. horizontal steel strain at mid-point of the plates strengthened with 45ο CFRP
strands subjected to uniform shear stresses
Effect of the CFRP Orientation
The measured results of the experimental program previously showed that effect of the CFRP
strengthening system is similar for plates strengthened with different orientations and selected
reinforcement ratio as shown in Figure 10. The FE models were developed using different boundary
conditions to determine the effectiveness of the CFRP orientations on the shear capacity of the
strengthened steel summary of FE results shown in Figure 22 indicates that strengthened plates with
CFRP strands oriented with an angle of 90ο can be slightly more effective than other orientations.
However, cutting CFRP strands in the orientation of 90ο relative to the tensile stresses could produce
significant wastes of the material. Therefore, it is recommended to use CFRP strands in the orientation of
45ο relative to the tensile stresses and additional layers in an orthogonal direction creating an angle of
±45ο relative to applied tensile load. This configuration for two layers of material efficiently decreases the
effective length of the CFRP strands in compression and results in increasing the shear capacity and
lateral stiffness of the strengthened plate compared with using two layers of CFRP strands both with an
angle of 45ο.
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Figure 22: Shear capacity percentage increase of plates strengthened with one and two layers of HM CFRP strands under uniform shear stresses
6. Simple Analytical Approach
This section introduces simple approach to determine the shear strength of plates strengthened with
small-diameter CFRP strands. Use of the transferred section is due to the observed perfect bond of the
strengthening system to the steel substrate. The shear stress, τ, for the strengthened specimen with one
and two layers of CFRP strands was estimated using following equations,
τ=VQI t t t
(1)
where,
I t=I s+∑i=1
n E fiEsI fi (2)
t t= ts+∑i=1
n t fit st fi (3)
V is shear force, Q is first moment of area, Es and Efi are elastic modulus of steel and the compressive
elastic modulus of each CFRP layer, respectively. It, Is, and Ifi are moment of inertia of the transformed
cross-section, moment of inertia of steel, and moment of inertia of each CFRP layer. tt, ts, and tfi are
thickness of the transformed cross-section, moment of inertia of steel, and moment of inertia of each
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CFRP layer. Compressive elastic modulus of CFRP of the witness panels was used in calculations. The
predicted shear forces of control specimen and strengthened specimens are compared and the
percentage increases in shear strength are given in Table 7. The shear forces were predicted at shear
stress equal to 60% of yield strength over the cross-section. The average measured percentage
increases of the strengthened specimens are also provided in the table. It is worth noting that the
proposed analytical approach is not considering the effects of the CFRP strands orientation. The
comparisons shown indicate that the shear load can be conservatively estimated using transformed
section properties of the strengthened plate. For the design, the above analysis indicates that the shear
capacity can be adequately predicted by using the composite transformed section properties of the
strengthened steel plates.
Table 7: Comparison between measured and predicted Shear capacities
Plate DesignationAnalytical Approach Measured Increase (%)
Shear Yielding Increase(%)
Set#1(45ο)
Set#2(90ο)
Set#3(±45ο)kN kip
Control 781 176 - -1 Layer HM Strengthened 978 220 25 36 23 242 Layer HM Strengthened 1175 264 51 65 67 79
7. Summary & Conclusion
The study presented in this paper explores the use of small-diameter CFRP strands for strengthening of
steel plates subjected to pure shear stresses. In general, test results show that the small-diameter CFRP
strands provided an excellent strengthening system for steel structures and eliminated any possible
debonding of the strengthening material up to failure. Several conclusions were made from the measured
behavior in the specimens tested in the experimental program. The conclusions are summarized as
follows,
1. The small-diameter CFRP strands have proven to be an effective strengthening system for
increasing the shear capacity of the steel plates.
2. The proposed strengthening system exhibits excellent bond characteristics in compression and in
tension and eliminated any possible debonding at failure.
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3. The effectiveness of the small-diameter CFRP strengthening system increased by increasing the
slenderness ratio of the plates subjected to shear loads.
4. High-Modulus (HM) small-diameter CFRP strands provides a more effective strengthening
system in comparison to Intermediate-Modulus (IM) and Low-Modulus (LM) CFRP strands for
shear strengthening of steel plates.
5. Increase of CFRP reinforcement ratio increases the shear capacity of the strengthened plate.
6. It is recommended to use small-diameter CFRP strands for the shear strengthening of steel
plates in an orientation parallel to the induced shear stresses. Additional layers of CFRP
reinforcement are more effective if it is orthogonal to the bottom layer.
7. For design purposes, simple analytical approaches can be effectively used to estimate the shear
capacity of the strengthened specimens using the transformed cross-section properties.
8. Acknowledgments
The authors would like to acknowledge the contribution of the following parties for their support to this
research: Nippon Steel & Sumikin Material Co., Ltd, Composites Company, Japan for financial support,
and the National Science Foundation (NSF) Center of Integration of Composites into Infrastructure (CICI)
at North Carolina State University. Thanks are also due the staff of the Constructed Facilities Laboratory
(CFL) at North Carolina State University for their assistance throughout the experimental program, and
Mr. Wes Ballew for his supportive advice during Finite Element Modeling, without whom this research
would have ever been possible.
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