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Transcript of Ductal Paper_v6_Reduced
Use of UHPC in Critical Shear Span of CFRP Prestressed Bridge Girders 1
Nabil F. Grace1, Ranjit K. Sharma2, Soubhagya K. Rout3, Kenichi Ushijima4, Mena Bebawy5 2
Abstract 3
An experimental program was conducted to access the shear performance of innovative carbon 4
fiber composite cable (CFCC) prestressed beams. Two beams were built using an innovative 5
hybrid technique; wherein the span of the beam subjected to higher shear stresses (near the 6
support regions) was built using ultra high performance concrete (UHPC) without any transverse 7
reinforcement. The remaining span (mid region) was constructed using normal high strength 8
concrete (HSC) and reinforced transversely with steel stirrups. The beam-ends of each beam 9
were tested under shear loading mechanism to failure at different shear-span-to-depth (a/d) ratios 10
of 3, 4, 5 and 6. The outcomes of the tested beam-ends were used to estimate the performance of 11
UHPC in distributing the shear stresses and also the behavior of the joint region consisting of 12
HSC and UHPC. Further, the results were compared with other beams provided with CFCC and 13
steel stirrups to get a conclusion on the shear behavior of these hybrid beams. It was observed 14
that hybrid beam at a/d ratios of 3 and 4, the beam-ends failed in shear due to diagonal tension 15
while at higher a/d ratios of 5 and 6, the beam failed in flexure due to crushing of top flange 16
concrete. In addition, the observed ultimate shear resistances of the beam-ends were significantly 17
higher when compared to the beams provided with transverse reinforcement (steel and CFCC) 18
and also exhibited higher energy absorption at failure. Finite Element (FE) models were 19
developed for the tested beam-ends to validate the experimental findings and provide a better 20
conclusion about the overall shear performance of the tested beams. The results of this 21
investigation suggests that the hybrid beams constructed with UHPC without any stirrups near 22
the support region and conventional concrete near the mid span are able to provide higher shear 23
resistance compared to transversely reinforced beams at both service limit state (SLS) and 24
ultimate limit state (ULS) with an appreciable level of warning at failure. 25
26
CE Database subject headings 27 Ultra High Performance Concrete (UHPC), Carbon Fiber Composite Cable (CFCC), Prestressed, 28
Shear. 29
1 Dean and University Distinguished Professor, College of Engineering, Lawrence Technological University, Southfield, MI,
48075, U.S.A., [email protected] 2 Graduate Research Scholar, Center of Innovative Materials Research (CIMR), Lawrence Technological University, Southfield,
MI, 48075, U.S.A., [email protected] 3 Former Graduate Research Scholar, Center of Innovative Materials Research (CIMR), Lawrence Technological University,
Southfield, MI, 48075, U.S.A., [email protected] 4 Senior Engineer, Cable Technologies North America, Inc., Novi, MI, U.S.A. [email protected] 5 Research Scientist, Center of Innovative Materials Research (CIMR), Lawrence Technological University, Southfield, MI,
48075, U.S.A., [email protected]
2
INTRODUCTION 30
Due to the involvement of large number of variables and complex shear transfer mechanisms, 31
shear behavior of concrete members is not perfectly understood even after decades of 32
experimental research and latest use of highly sophisticated computational tools. Usually, a 33
sudden collapse of concrete structure without any appreciable level of warning occurs if the 34
structure lacks proper and adequate shear reinforcement (Mitchell et al. 2011). The key to avoid 35
such catastrophic brittle shear failure of concrete structures is to overdesign against anticipated 36
shear with a high factor of safety. The traditional practice is to provide transverse reinforcement 37
in the form of stirrups at closer spacing. This overly reinforced section for shear stresses possibly 38
changes the catastrophic shear failure of a member into a more favorable flexural failure 39
characterized with sufficient warning in terms of large noticeable deflection and cracking prior to 40
collapse. However, there are several issues associated with the use of stirrups; a) shear capacity 41
of section increases directly with the decrease in the stirrup spacing, but various standards & 42
codes has limitation on the minimum spacing of stirrups to avoid congestion of reinforcement 43
cage leading to improper concrete placement and consolidation; b) limitation on the maximum 44
spacing of stirrups to avoid wider shear cracks especially in prestressed concrete sections; c) 45
susceptibility of steel stirrups towards corrosion d) CFCC stirrups experience significant 46
reduction in tensile strength due to bend effect (ACI 440 1R-06). 47
The use of steel fibers in the concrete mix design has emerged as an alternative against 48
the use of stirrups in the concrete members. Ultra High Performance Concrete (UHPC) has 49
emerged as a latest fiber reinforced concrete commercially manufactured by Lafarge North 50
America under the name Ductal® and provides innovative solutions to several challenges 51
currently faced by the US highway infrastructure. AFGC-SETRA (2002) defines UHPC as 52
concrete matrix having compressive strength above 21.7 ksi (150MPa) and internally reinforced 53
with fiber to ensure non-brittle behavior, with very low water to cementitious material ratio and 54
with minimal or no coarse aggregates. 55
Taylor et al. (2011) conducted a life cycle cost analysis for bridge girders and 56
recommended that UHPC are expected to provide at least twice the service life and low cost 57
maintenance as expected from the conventional strength concrete, thus compensating the high 58
initial investment on construction. Further, a significant improvement in mechanical properties 59
of UHPC over HSC is mainly due to the presence of steel fibers and their orientation with 60
3
respect to the direction of stress. Kim et al. (2008) conducted several studies using photographic 61
technique and four point bending test to evaluate the effect of placing and flow direction on fiber 62
orientation, dispersion and tensile behavior of UHPC. Their studies showed that placing and 63
direction of flow results in a significant difference of about 50% in the UHPC maximum tensile 64
strength. Favorable properties are generally obtained when the flow of UHPC is oriented parallel 65
to the direction of the principal tensile stresses. 66
Steel fibers are capable of increasing the shear capacity and most often up-to the nominal 67
flexural capacity (Russo et al. 1991) which ultimately leads to more of a ductile shear-flexural 68
failure. The ultimate shear resistance and failure mode depends upon the percentage of steel 69
fibers. According to Imam et al. (1997) there is a major increase in the shear capacity with the 70
increase in the fiber content compared to the increase in its nominal flexural capacity (Mn). 71
Padmarajaiah and Ramaswamy (2001) conducted a rigorous experimental and analytical work 72
on 13 fully/partially steel prestressed high-strength concrete beams to study the influence of fiber 73
content, location of fiber, and the presence/absence of stirrups within the shear span on the shear 74
behavior of the beam. It was reported that beams having fibers located only within the shear span 75
and over the entire cross-section, showed similar load-deformation and ultimate load response to 76
that of beams, which had fibers over the entire span length. The presence of fibers within the 77
shear span altered the brittle shear failure to more of a ductile flexure failure. Thus, it was 78
recommended that the stirrups can be replaced with an equivalent amount of fibers without 79
compromising the overall structural performance of the member. 80
US bridges is presently facing the biggest challenge of its faster rate of deterioration and 81
spalling of concrete, which are primarily caused due to the corrosion of steel reinforcement as 82
the consequence of the cracks which are formed in bridge decks or girders due to increase in 83
traffic load. Thus, FRP prestressed bridges have come up as one of the feasible solution. 84
However, according to Park and Naaman (1997), reported that fiber reinforced polymer (FRP) 85
prestressed beams are susceptible to shear-tendon rupture failure which is a unique mode of 86
failure due to rupture of FRP tendon caused by dowel shear acting on the shear-cracking plane. 87
This was due to the FRPs brittle behavior and low transverse shear resistance. They 88
recommended that addition of steel fibers in the concrete section could possibly depress this 89
unique shear-tendon rupture failure of FRP prestressed beams by improving the shear capacity of 90
the section. 91
4
Further unlike steel, FRP possess a linear stress-strain behavior and do not show any 92
yielding behavior prior to failure. Irrespective of reinforcement ratio and irrespective of location 93
of load/mode of test, FRP reinforced/prestressed beams show a catastrophic brittle failure with 94
low ductility. Grace et al. (2012) conducted a flexural test on both under-reinforced and over-95
reinforced FRP prestressed decked bulb-T HSC beam. In both of these kinds of beams, a 96
catastrophic flexural failure was obtained with ductility ratio below the limit of 75% for ductile 97
flexural failure. Similarly, Grace et al. (2014) carried out extensive study on the modes of shear 98
failure on over-reinforced FRP prestressed decked bulb-T HSC beams transversely reinforced 99
with either steel/CFCC stirrups at 6 in. (152.4 mm) of spacing at varying shear span to depth 100
(a/d) ratio of 3, 4, 5 & 6 and found catastrophic shear failure mode in all beams, irrespective of 101
location of the load. 102
This paper explains an innovative approach for the optimum use UHPC through a 103
concept of hybrid formulation. The critical shear spans where the shear stresses are dominant 104
(near the support regions) are built with UHPC without stirrups, while the remaining middle span 105
of the beam where flexural stresses are dominant are built with HSC with steel stirrups at 4 in. 106
(102 mm) spacing. The main purpose of using UHPC in the critical shear span of beams were: a) 107
to eliminate the use of steel or CFCC stirrups in the critical shear span causing congestion in 108
reinforcement cage; b) to optimize the economy of beam by optimal usage of expensive UHPC 109
in high shear stress regions; c) to enhance the energy dissipation of CFCC prestressed decked 110
bulb T beams. To provide a better comparative assessment on the shear performance of hybrid 111
beams, its results were compared to that of beams reinforced with steel/CFCC stirrups. 112
RESEARCH SIGNIFICANCE 113
This paper aims to contribute a novel cognition to the engineering and design community 114
in understanding the newly developed material UHPC and its optimal usage in precast 115
prestressed beams for Accelerated Bridge Construction (ABC) by reducing on-site construction 116
time due to its novel design and construction concept. Present investigation describes the 117
ingenious techniques employed for the construction of innovative hybrid decked bulb T beam 118
models reinforced and prestressed with CFCC strands and compares its shear performance with 119
that of a traditional CFCC prestressed beams reinforced with either steel/CFCC stirrups. In 120
addition, finite element (FE) models developed for experimental beams will help the engineers to 121
consider a wide range of configurations for prestressed hybrid decked bulb T beams. 122
5
CONSTRUCTION DETAILS 123
Two one-half scale hybrid beams with an effective span length of 41 ft. (12.5 m) were built, 124
instrumented and tested at the Center for Innovative Material Research (CIMR), Lawrence 125
Technological University (LTU). The variable considered in this investigation includes; shear 126
span-to-depth ratio (a/d) ratios of 3, 4, 5 & 6. Table 1 outlines the test variables considered for 127
hybrid beam and the HSC beams tested by Grace et al. (2014). The typical cross-section of 128
hybrid beams at both critical and non-critical shear span is shown in the Figure 1, having a top 129
flange width of 18 in. (457 mm), an overall depth of 16 in. (406 mm), a web thickness of 3 in. 130
(76 mm) and bottom flange width of 12 in. (305 mm). Both of the beams were pre-tensioned 131
with an effective prestressing force of 100 kip (444.822 kN), using four CFCC (Tokyo Rope 132
2013), 1x7 strands having an effective diameter of 0.6 in. (15.2 mm) and cross sectional area of 133
0.18 in.2 (116 mm2). Figure 2 shows the longitudinal view of both hybrid beam and HSC beam 134
tested by Grace et al. (2014) with dimensions along their reinforcement cages. The material 135
properties for the reinforcements used in both of the above beams are summarized in Table 2, 136
while Table 3 outlines the mix design followed for HSC & UHPC per cubic yard of concrete 137
volume. The anchorage system used to prestress the CFCC strands employed an innovative 138
technique and discussed elsewhere (Grace et al. 2012). The new system significantly reduces 139
seating losses and avoids damage to the strands. The concrete mix was designed to achieve an 140
average 28-day compressive strength of 8,000 psi (55 MPa) and 24,000 psi (165 MPa) for HSC 141
and UHPC respectively. Such a superior strength of UHPC is mainly achieved through its finely 142
graded, homogenous granular material composition and inclusion of silica fume & super-143
plasticizer. Dimensionally largest granular material in the composition of UHPC is fine sand 144
ranging between 150 to 600 µm. 145
Based on the research finding on the modes of shear failure on CFCC prestressed decked 146
bulb-T HSC beams conducted by Grace et al (2013) as discussed earlier, length of the critical 147
shear span was decided with some factor safety to be 8 times the effective depth of the beam. 148
The critical shear span of hybrid beam experiencing higher shear stresses were constructed with 149
UHPC without shear stirrups, while the middle flexural span was constructed with HSC with 150
steel stirrups at 4 in. (102 mm) of spacing. The purpose of providing stirrups in middle flexural 151
span was to restrain extensive propagation of cracks. Due to absence of stirrups within critical 152
6
shear span, end and middle diaphragm reinforcement served the purpose for holding the 153
longitudinal reinforcement in position across the depth. 154
A very simple and innovative technique was developed for the formation of a monolithic 155
joint between UHPC and HSC. Figure 3 shows the various stages of constructions for the hybrid 156
beams. A trap door was built underneath the deck at the location of joint. HSC was placed first in 157
the middle flexural span, while the open trap doors restricted overflow of HSC into the critical 158
shear span by removing the excessive concrete. Once the HSC was placed, trap doors were 159
closed and UHPC was placed in the critical shear span region forming the monolithic joint to a 160
distance of 8·d from the beam-ends. As reviewed in the previous section, favorable mechanical 161
properties of UHPC are obtained when the fibers are oriented parallel to the direction of 162
principal tensile stress. Hence, the placement of UHPC in the critical shear span was performed 163
starting from the end of the beam moving inwards towards the joint. Owing to self-consolidating 164
property of UHPC, use of vibrators was restricted, which helped the fibers to align normal to the 165
direction of flow. 166
The curing of constructed beams were performed by covering the middle HSC with wet 167
burlap and ends UHPC with plastic sheets to prevent any loss of moisture which causes cracks 168
due to shrinkage of concrete. The calibrated load cells were used to evaluate prestress loss 169
continuously for seven days from the day of concrete placement. At the end of seven days as 170
concrete attained it’s enough designed compressive strength, prestressing force was released to 171
the beam by gradual warming of steel prestressed strands attached to CFCC prestressed strands 172
through coupler with an acetylene torch. The concrete compressive strength for all beams was 173
averaged around 5,800 psi (40 MPa) and 17,700 psi (122 MPa) for HSC and UHPC respectively 174
at the time of prestress release. Figure 4 shows the average compressive strength of HSC and 175
UHPC with curing age. 176
INSTRUMENTATION AND TEST SETUP 177
The beams were simply supported over a set of elastomeric neoprene bearing pads as 178
shown in Figure 5 and were subjected to a concentrated vertical shear load, applied by a MTS 179
hydraulic actuator having 220 kip (1,000 kN) capacity. Shear span considered for the beams was 180
45, 60, 75 and 91 in. (1.1, 1.5, 1.9 and 2.3 m) from the center of support equivalent to a/d ratios 181
of 3, 4, 5 and 6 respectively. Linear strain gauges were installed on the surfaces of the top and 182
bottom flanges of the beams near the loading point to measure the compressive and tensile strain 183
7
of the concrete respectively. However, due to the differences in material properties between 184
UHPC and HSC, strain gauges were also installed on the concrete surfaces on either side of the 185
joint, to measure any difference in the concrete strain development. Linear motion transducers 186
(LMT) were installed on the beams under the load to measure the vertical deformation due to 187
shear loading. Linear Variable Displacement Transducer (LVDT’s) were installed on the web 188
within the shear span in sets of three and arranged in a rectangular rosette fashion at 00, 450, and 189
900 directions to monitor and record the progress of cracks and crack width. All various sensors 190
were calibrated and connected to a fine-tuned digital data acquisition system using Mars Lab 191
computer interface. The beams were subject to several loading and unloading cycles prior to 192
ultimate failure to separate the elastic and inelastic energies required to determine the shear 193
ductility indices. 194
RESULTS AND DISCUSSION 195
The experimental investigation evaluated the effect of variation of shear span-to-depth 196
(a/d) ratio on cracking and ultimate shear resistance, crack width and the pattern of crack 197
development, maximum concrete compressive and tensile strains development, ductility indices 198
and modes of shear failure. Following section consists of four parts. First part compares the 199
experimental result of all hybrid beam, second part compares the experimental results of hybrid 200
beam with HSC beam conducted by Grace et al (2014) under similar load scenario, while the 201
third and fourth part compares the experimental results of hybrid beams with numerical and 202
analytical results respectively. 203
1. Hybrid Beam Results 204
Effect on deflection 205
Figure 6 shows the shear force versus deflection response of hybrid beams at various a/d ratios. 206
It was observed that the deflection of the hybrid beam under different loading point increases 207
with increase in shear span-to-depth (a/d) ratio. The maximum deflection observed for hybrid 208
beams at varying a/d ratios of 3, 4, 5 and 6 was 3.4 (86.4), 8.3 (210.8), 9.9 (251.5) and 7.7 209
(195.6) in (mm) respectively. However, the maximum deflection observed for hybrid beam at a/d 210
of 6 was lower than that of a/d of 4 and 5. Since, at a/d of 6, the point of loading was fairly close 211
to the concrete joint which eventually increased the rate of development of compressive strain on 212
HSC side and attained failure strain quickly without showing appreciable deflection 213
8
Effect on concrete cracking and ultimate shear resistance 214
Concrete cracking force and ultimate shear resistance for hybrid beam was found to 215
decrease with increase in a/d ratios as observed in Figure 14 Thus, it shows that the shear-216
moment interaction (M/Vd = a/d) plays a very vital role in determining the concrete cracking and 217
ultimate shear resistance of prestressed UHPC beam. The concrete cracking force observed for 218
the hybrid beams at a/d of 3, 4 5 and 6 was 34.2 (152.1), 21.9 (97.4), 16.1 (71.6) and 12.2 (54.3) 219
kip (kN) respectively, whereas the observed ultimate shear capacity for the hybrid beams at a/d 220
of 3, 4, 5 and 6 was 118.8 (528.5), 100.6 (447.5), 80.9 (359.9), 62.3 (277.1) kip (kN) 221
respectively. 222
Effect on concrete strains 223
Figure 13 shows the response of concrete compressive strain developed at various 224
location along the span in hybrid beams when loaded at varying a/d ratios. The above figure 225
shows that when the position of load moves away from the support i.e. with increase in a/d ratio, 226
the location of development of maximum compressive strain at top flange moves from the UHPC 227
near load to HSC near the concrete joint. The maximum concrete compressive strain experienced 228
at the top flange of hybrid beams was 2206 µε near the loading point at a/d of 3, while 3053, 229
3519 and 3224 µε was observed near the joint on HSC side at a/d of 4, 5 and 6 respectively. 230
Similarly, the maximum tensile strain of concrete experienced in the bottom flange of the hybrid 231
beam carries an inverse relationship with increase in a/d ratio. Maximum tensile experienced by 232
UHPC under load was 5980, 6280, 4781 and 3024 µε at a/d ratio of 3, 4 5 and 6 were 233
respectively as shown in the Figure 8. 234
Effect on crack width and crack pattern 235
The presence of UHPC in the critical shear span of hybrid beam greatly influenced the 236
patterns of shear cracks at various shear span-to-depth (a/d) ratio (loading point) as illustrated in 237
Figure 9. Flexural cracks were first seen at the bottom flange of the hybrid beam underneath the 238
loading point. Gradually, several distributed micro-cracks starts to initiate diagonally near the 239
web regions within critical shear span. The shear cracks in the web propagated diagonally 240
outwards towards the top and bottom flange with an increase in the shear force. The hybrid 241
beams were characterized by tightly spaced cracks normal to principal tensile stress direction. 242
This showed the ability of UHPC in redistributing the stresses through three dimensional (3D) 243
9
steel fiber reinforcements over multiple cracking before the fibers pullout. With further 244
increment in shear force, the steel fiber starts to pullout as the load carried by individual steel 245
fiber exceeds the ability of the UHPC matrix to grip the fiber and it eventually leads to diagonal-246
tensile failure of the beam. The displacements measured by LVDT’s were used to determine the 247
crack width by using the equation given by Shehata et al. (1999). Figure 10 shows the shear 248
force versus crack width response for hybrid beam. It was observed that crack width increases 249
with the increase in the a/d ratio. 250
Shear and flexural cracks in hybrid beam were observed to cross the diagonal monolithic 251
UHPC-HSC joint from one to adjacent concrete, confirming the satisfactory behavior of 252
monolithic concrete joint in distributing stresses. No parallel cracks or premature failure were 253
noticed along the diagonal seam of concrete joint. This shows that concrete joint in hybrid beam 254
had sufficient bond in binding together both types of concretes till the ultimate failure of the 255
beam as observed in the investigation. Further as illustrated by Figure 11, initiation of diagonal 256
cracks within shear span of hybrid beams was much delayed due to the presence of UHPC in the 257
critical shear span as compared to non-critical shear span (HSC section) in hybrid beams. UHPC 258
has higher tensile capacity and greater ability to bridge across micro-cracks through 3D steel 259
fibers. Thus, presence of UHPC within the critical shear span of hybrid beam greatly influences 260
the initiation and pattern of cracks under shear loading and eventually enhances the concrete 261
cracking under service limit state (SLS) and ultimate capacity under the ultimate limit state 262
(ULS). 263
Effect on ductility indices 264
The traditional way of calculating the ductility indices of concrete beams prestressed with 265
steel strands is not suitable for concrete beams prestressed with FRP tendons because unlike 266
steel, FRP does not have any yield plateau. Naaman and Jeong (1995) proposed the energy-267
based method to evaluate the ductility indices for the FRP prestressed beams. Due to the 268
presence of steel fibers, hybrid beams showed more efficiency in dissipating the shear forces 269
through elastic & inelastic energy across the shear crack. The ductility indices for hybrid beam 270
were within the range of 37-29%. Prior to ultimate failure, hybrid beams showed extensive 271
cracks and loud fiber pull-out signals. 272
10
Shear Mode of Failure 273
At a/d of 3 and 4, hybrid beam failed in diagonal shear while at a/d of 5 and 6, hybrid 274
beam exhibited extensive flexural cracks on HSC side (non-shear span) near the joint region 275
leading to compression flexural failure characterized by crushing of top flange. Figure 12 276
illustrates various modes of failure observed in hybrid beams at various a/d ratio. It was noticed 277
that as the load moved away from the support (higher a/d ratio), the hybrid beam experienced 278
increase in the concentration of flexural cracks on the flexural span (HSC) and decrease in the 279
concentration of diagonal shear cracks within the shear span (UHPC). Thus, hybrid beams 280
showed more of ductile flexural-shear failure. 281
2. Comparison with Grace et al. (2014) results 282
As discussed earlier, to provide a better assessment on the performance of hybrid beam, 283
the results of a hybrid beam were compared with the results obtained by Grace et al. (2014) on 284
HSC beams transversely reinforced with steel/CFCC stirrups and tested under similar load 285
scenarios. Table 4 summarizes the comparison of experimental results between hybrid beams 286
and HSC beam. 287
Effect on deflection 288
The maximum deflection observed for HSC beam at a/d of 3, 4, 5, and 6 was 1.4 (35.6), 289
2.6 (66.0), 3.5 (88.9), 4.8 (121.9) in (mm) and 1.6 (40.6), 3.0 (76.2), 4.1 (104.1), 5.5 (139.7) in. 290
(mm) for HSC beam-end with steel and CFCC stirrup respectively. However, on comparison, it 291
was observed that hybrid beams on average deflected 2.3 times the maximum deflection of HSC 292
beams with stirrups under similar a/d ratios. 293
Effect of varying a/d ratios 294
The influence of varying a/d ratio on relative flexural capacity (Mu/Mfl) of the same 295
section with different type of shear reinforcement can be understood from Figure 13, which 296
eventually determines the mode of beam failure. It was observed that the relative flexural 297
capacities (Mu/Mn) and its rate of growth with an increase in a/d ratio for hybrid beam were 298
higher than as compared from HSC beams. Or in other words, it can be explained as when the 299
position of load moves away from the support (increase in a/d ratio), ultimate moment (Mu) is 300
close or higher to nominal flexural capacity (Mn) of HSC section in hybrid beam (or Mu/Mn ≈ 1 301
or > 1), and the beam eventually fails in flexure without exceeding the shear capacity of UHPC 302
11
in the critical shear span as observed in the experimental program. Thus, presence of UHPC in 303
the critical shear span of hybrid beams helps in increasing the relative flexural capacity (Mu/Mn) 304
of HSC section in flexural span and changes the catastrophic shear failures as observed in all 305
HSC beams under similar loading scenarios into more ductile shear-flexural failure. 306
Effect on concrete cracking and ultimate shear resistance 307
After comparison of hybrid beams with HSC beam, it was observed that the cracking and 308
ultimate shear force followed the inverse relationship with a/d ratio as shown in the Figure 6 309
irrespective of type of shear reinforcement within the critical shear span i.e. either steel fibers in 310
UHPC without stirrups or steel/CFCC stirrups. The concrete cracking force for HSC beams at 311
a/d ratio of 3, 4, 5 and 6 was 27.3 (121.4), 20.1 (89.4), 15.8 (70.3), 12.4 (55.2) kip (kN) and 26.8 312
(119.2), 19.2 (85.4), 15.6 (69.4), 14.2 (63.2) kip (kN) for steel and CFCC stirrups beam-ends 313
respectively. However, it was observed that concrete cracking force for hybrid beams was on 314
average 8% higher than HSC beams. The increase in the shear cracking force for hybrid beams 315
can be related to UHPC higher tensile cracking strength as compared to the low tensile strength 316
of conventional concrete. The ultimate shear capacity for the HSC beams at a/d of 3, 4, 5 and 6 317
was 61.2 (272.2), 53.6 (238.4), 49.7 (221.1), 44.2 (196.6) kip (kN) and 58.6 (260.7), 52.2 318
(232.2), 49.1 (218.4), 46.3 (205.9) kip (kN) for steel and CFCC stirrups beam-end respectively. 319
Thus it can be noticed that the ultimate shear capacity of hybrid beams was 94, 88, 63 and 41 % 320
higher than HSC beam-end with steel stirrup and 103, 93, 65, and 34 % higher than the HSC 321
beam-end with CFCC stirrups under similar load configuration. Figure 14 illustrated the cracking 322
and ultimate shear capacity of hybrid beam in comparison with HSC beams. Due to the presence 323
of steel fibers, UHPC served as a three dimensional (3D) reinforcement and increases capability 324
of UHPC in dissipating shear stresses across cracks. This phenomenon significantly increases the 325
post-cracking tensile strength of UHPC through superior bonding between the concrete matrix 326
and distorted fibers even after the initial cracking, which eventually leads to increased shear 327
capacity for hybrid beam in comparison with HSC beam reinforced with stirrup. 328
Effect on concrete strains 329
The maximum concrete compressive strain observed at top flange near loading point for 330
HSC beam-ends with steel stirrups at a/d ratios of 3, 4 5 and 6 was 1642, 2038, 2639 and 2649 331
µε respectively, while it was 1282, 1767, 2624 and 2732 µε respectively for HSC beam-end with 332
12
CFCC stirrups. However, it was observed that the maximum compressive strain experienced by 333
the hybrid beam was on average 1.42 times than that of HSC beams. It was be due to higher 334
compressive strength properties of UHPC over HSC. Again, the maximum tensile strain 335
observed by hybrid beam was on average 13.75 times the typical average tensile strain of 350 µε 336
in HSC beams irrespective of a/d ratio. Apart from superior material characteristics of UHPC in 337
terms of compressive strength, the above experimental results also prove the effectiveness of 338
steel fibers in increasing the tensile strength of UHPC. 339
Effect on crack width and crack pattern 340
The presence of UHPC in the critical shear span of hybrid beam greatly influenced the 341
patterns of shear cracks as compared to HSC beams. Analogous to hybrid beam, HSC beam was 342
also initially marked by flexural cracks in the bottom flange underneath the loading point. But 343
unlike hybrid beam, HSC beam was characterized by an irregular diagonal cracks in the shear 344
span with sparsely spaced wider cracks. Having the same Shehata equation, the crack width 345
observed for hybrid beams was on an average of 40-50% less than those of HSC beam with 346
stirrups. However, irrespective of types of shear reinforcement type i.e. either steel fibers in 347
hybrid beams or steel/CFCC stirrups in HSC beams, crack width increases with the increase in 348
the a/d ratio. 349
Effect on ductility indices 350
Due to the presence of steel fibers, hybrid beams showed more efficiency in dissipating 351
the shear forces through elastic & inelastic energy across the shear crack as compared with HSC 352
beams. Hybrid beams on average showed 4 to 5 times more efficient in absorbing the elastic and 353
inelastic energies than that of HSC beams under similar a/d ratios as outlined by Table 5 and 354
illustrated by Figure 15. However, there was not much significant difference in the calculated 355
ductility indices of hybrid beams based on the energy method in comparison with HSC beams. 356
As discussed earlier, hybrid beam showed higher ultimate deflection than HSC beam. Thus, 357
hybrid beams showed sufficient warning prior to failure in terms of higher deflection, extensive 358
cracks and loud fiber pull-out signals prior to ultimate failure unlike HSC beam with either 359
steel/CFCC stirrups which failed with little or no warning. 360
361
13
Shear Mode of Failure 362
All HSC beam-end reinforced with steel stirrups failed in shear tension with yielding of 363
steel stirrups while all HSC beam-end reinforced with CFCC stirrups failed in shear compression 364
followed by crushing of either web or top flange concretes. The linear stress-strain relationship 365
of CFCC stirrups causes a linear increase in the strain of stirrups until the concrete begins to 366
crush. Thus, all HSC beams failed in shear irrespective of a/d ratio, however hybrid beam 367
changes its modes of failure from diagonal shear to compression flexure with increase in a/d 368
ratio. Thus, hybrid beams showed more of ductile flexural-shear failure rather than a typical 369
catastrophic shear failure as observed in all HSC beams. 370
3. Comparison with Finite Element Analysis Results 371
The finite element models were generated in an attempt to reproduce the structural 372
response of hybrid beams and to validate the observed experimental results. The Concrete 373
Damage Plasticity (CDP) model was tailored to simulate hybrid beams within a commercially 374
available Finite Element Analysis (FEA) package ABAQUS. The CDP model simulates isotropic 375
damage elasticity combined with isotropic tensile and compressive plasticity to represent the 376
inelastic behaviors of concrete materials. Table 6 shows the detailed information on material 377
properties and meshed finite elements used separately for reinforcement, HSC and UHPC in the 378
hybrid beams. Table 7 presents the comparison between the results obtained from the numerical 379
models and the experimental investigation. 380
Diagonal shear failure predicted by numerical model matches with the observed experimental 381
failure as observed in Figure 16. It was noticed that the behavior of the FEA model matched 382
fairly close to that of the tested beams behavior as shown by the Figure 17 with an accuracy level 383
exceeding above 90%. Therefore, these FEA models can be efficiently utilized in further 384
exploration of the wide ranges of configurations for prestressed hybrid decked bulb T beams by 385
changing parameters which influence shear capacities. 386
4. Comparison with Analytical Results 387
Apart from design guidelines provided by the Federal Highway Administration (FHWA), 388
United States has no unified and accepted design method for using Ultra High Performance 389
Concrete (UHPC). Thus, it is very essential to compare the experimental results with the 390
predicted values given by various empirical formulas available internationally for UHPC such as 391
14
JSCE (2006) from Japan and AFGC-SETRA (2000) from France. Both design guidelines 392
divides the shear resistance of UHPC section at Ultimate Limit State (ULS) into three 393
components; i) composite contribution of UHPC matrix and the fibers (Vc) and the shear 394
resistance provided by the average fiber tensile resistance before fiber pullout, acting along the 395
diagonal cracks (Vf), ii) the contribution from prestressing strands (Vp), iii) the contribution from 396
shear reinforcement or stirrups (Vs). The composite shear resistance of UHPC matrix and the 397
fibers according to AFGC-SETRA (2000) is given below: 398
zb'f24.0
V 0cc γ= (1) 399
While according to JSCE (2006); 400
zbfV cc 0'18.0
γ= (2) 401
Where, 402
'f c = 28 days concrete compressive strength, 403
b0 = web width, 404
z = lever arm between the centroids of the compression block and the prestressing strands at 405
ultimate moment, 406
γ = factor of safety which was considered equal to 1 for the purpose of comparison with 407
experimental results. 408
The average fiber tensile resistance before fiber pullout according to both design guidelines is 409
given as: 410
βγσ
=u
0pf
tan
zbV (3) 411
Where, 412
σp = residual tensile stress carried across the shear crack from the time of cracking until a certain 413
limiting tensile strain. 414
βutan = tangent of the compression strut angle in the shear span measured from the horizontal 415
and it has the lower bound value of 30°. 416
However, according to Graybeal (2006), the residual tensile stress values are determined 417
experimentally from the tension tests. Based on the typical values found in various literature 418
(Graybeal 2006, Gowripalan and Gilbert 2000, and AFGC-SETRA 2002), a conservative 419
15
values of 1000 psi (6.9 MPa) was used for residual tensile strength in predicting the shear 420
capacity. In this experimental program, Vp and Vs were set equals to zero as the prestressing 421
strands were straight without any draping and the absence of transverse reinforcement. It was 422
observed that shear capacity predicted by both existing codes were conservative when compared 423
with experimental results as illustrated by Table 8. Further, it should be noticed that none of the 424
above design codes take into account the variation of shear capacity with respect to a/d ratio and 425
thus it was critical to compare the experimental results with analytical results. 426
SUMMARY AND CONCLUSIONS 427
This paper brings an experimental investigation addressing the use of UHPC without shear 428
stirrups in the critical shear span of CFCC prestressed decked bulb T beams. The experimental 429
program included construction, instrumentation and testing of two hybrid beams and four control 430
beams with CFCC and steel stirrups at its beam-end under shear load setup at a/d ratios of 3, 4 5 431
and 6. The experimental results were compared and several conclusions were drawn as follows: 432
1. Irrespective of type of shear reinforcement, cracking and ultimate shear resistance were 433
found to be indirectly proportional to a/d ratios. Thus it is very important for take into 434
consideration the effect of shear span-to-depth ratio or shear-moment interaction while 435
predicting the shear capacity of a UHPC section which is currently ignored in shear design 436
guidelines. 437
2. Hybrid beams with UHPC in the critical span without stirrups exhibited remarkably superior 438
shear performance with an average increase of 8% in the concrete cracking shear force and 439
an average increase of 72% in the ultimate shear resistance as compared to similarly 440
prestressed HSC beam-ends reinforced with either steel/CFCC stirrups under similar loading 441
configuration. 442
3. Hybrid beams showed 4-5 times more efficient in absorbing the elastic and the inelastic 443
energy as compared with HSC beams. Further, hybrid beams demonstrated sufficient 444
warning prior to ultimate shear failure in terms of excessive deflection, extensive multiple 445
cracks and loud fiber pull-out signals unlike HSC beams with either steel/CFCC stirrups 446
which showed catastrophic shear failure. 447
4. Monolithic concrete joint between HSC and UHPC did not acknowledge any parallel cracks 448
or premature failure along the diagonal seam of joint. Shear and flexural cracks were noted to 449
16
cross the diagonal concrete joint from one to adjacent concrete conforming the satisfactory 450
bond behavior of monolithic concrete joint between UHPC-HSC in distributing stresses. 451
5. The pattern of crack initiation and its progress observed in hybrid beams was remarkably 452
different from those of HSC beams. Hybrid beams experienced 40-50% reduction in the 453
shear crack width. 454
6. UHPC in the critical shear span of hybrid beams was effectual in changing the mode of 455
catastrophic shear failure to more ductile shear/flexural failure with the increase in a/d ratio. 456
7. Critical shear span with shear stirrups in CFCC prestressed decked bulb T beams can be 457
effectively replaced by UHPC without any requirement of stirrups with an additional 458
advantage of increased shear capacity at both SLS and ULS. 459
8. The developed FEA models of the tested beams accurately predicted the shear cracking 460
force, the ultimate shear capacity, ultimate deflection, maximum compressive and tensile 461
strains in the concrete and finally the modes of failures. The average percentage error in 462
predicting these experimental values were within 10%. 463
9. Both Japanese (JSCE) and the French Code (AFGC) predicted approximately the same shear 464
capacity, neglecting the major influential shear-span-to-depth (a/d) factor in their equation 465
and were also found to be conservative when compared with experimental ultimate shear 466
capacity. 467
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1. ACI Committee 318 (2011). “Building Code Requirements for Structural Concrete and
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2. AFGC-SETRA (2002). “Civil Interim Recommendation for Ultra High Performance Fiber-
Reinforced Concrete.” Association with Franćaise de Génie Civil (AFGC).
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characterization of new carbon FRP stirrups for concrete members.” Journal of Composites
for construction, 11(4), pp. 352–362.
4. Gowripalan, N., Gilbert, R.I. (2000). “Design guidelines for RPC prestressed concrete
beams.” School of Civil and Environmental Engineering, University of New South Wales,
Sydney, Australia, pp.XX-XX
17
5. Grace N. F., Enomoto T., Baah P., Bebawy M. (2012). “Flexural Behavior of CFRP Precast
Prestressed Decked Bulb T-Beams.” Journal of Composites for Construction, ASCE, 16 (3),
29 pp. 225-234.
6. Graybeal, B.A. (2006). “Material Property Characterization of Ultra-High Performance
Concrete.” Federal Highway Administration, U.S. Department of Transportation, FHWA-
HRT-06-103, pp.XX-XX.
7. Higgins, C., Farrow III, W.C., Potisuk, T., Miller, T.H., Yim, S.C., Holcomb, G.R., Cramer,
S.D., Covino, B. S., Bullard, S.J., Ziomek-Moroz, M., and Matthes, S.A. (2003). “Shear
Capacity Assessment of Corrosion damaged Reinforced Concrete Beams.” Department of
Civil Engineering, Oregon State University, U. S. Department of Energy, Albany Research
Center, pp.XX-XX.
8. Homeland Security of Science and Technology. (2010). “Ultra High Performance Concrete
(UHPC) Pathway to Commercialization.” pp. XX-XX
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Fiber-Reinforced High-Strength Concrete Beams.” Engineering Structures, 19(9), pp. 738-
747.
10. Japan Society of Civil Engineers. (2006). “Recommendation for Design and Construction of
Ultra High Strength Fiber Reinforced Concrete Structures (Draft).” JSCE Guidelines for
Concrete, No. 9. September, pp.XX-XX.
11. Kim, S., S. Kang, J. Park, and G. Ryu. (2008). “Effect of Filling Method on Fiber Orientation
& Dispersion and Mechanical Properties of UHPC.” Proceedings, Second International
Symposium on Ultra High Performance Concrete, Kassel, Germany, pp. 185-192.
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Structural Aspects.” Journal of Performance of Constructed Facilities., 25(6), pp. 545–553.
13. Naaman, A. E., and Jeong, S. M. (1995). ‘‘Structural ductility of concrete beams prestressed
with FRP tendons.” Non-metallic (FRP) Reinforcement for concretes structures, Taerwe, L.
ed., E. & FN Spoon, London, pp. 379–401.
14. Nabipay, P., and Svecova, D. (2012). “Shear Resistance of Concrete T-Beams Prestressed
With CFRP Cables.” CICE 2012 proceeding, International Institute for FRP Construction.
18
15. Padmarajaiah, S.K., and Ramaswamy, A. (2001). “Behavior of Fiber-Reinforced Prestressed
and Reinforced High-Strength Concrete Beams Subjected to Shear.” ACI Structural Journal,
98(5), pp. 752-761.
16. Park, S.Y., and Naaman, A.E. (1999). “Shear Behavior of Concrete Beams Prestressed With
FRP Tendons.” Precast/Prestressed Concrete Institute (PCI), Jan-Feb (7), pp. 74-85.
17. Rout, S.K. (2013). “Shear Performance of Prestressed Concrete Decked Bulb T Beams
Reinforced with CFCC Stirrups.” MS thesis, Lawrence Technological University, MI, USA.
18. Russo, G., Zingone, G., and Puleri, G. (1991). “Flexure-Shear Interaction Model for
Longitudinally Reinforced Beams.” ACI Structural Journal, 88(1), pp. 60-68.
19. Shehata, E. F. G. (1999). “Fibre Reinforced Polymer (FRP) for Shear Reinforcement in
Concrete Structures.” Ph.D. Dissertation, Department of Civil and Geological Engineering,
University of Manitoba, March, pp. 316.
20. Shehata, E., Morphy, R., and Rizkalla, S. (2000). “Fiber reinforced polymer shear
reinforcement for concrete members: Behavior and design guidelines.” Can. J. Civ. Eng., pp.
859–872.
21. Tadepalli, P., Dhonde, H., Laskar, A., Mo, Y., and Hsu, T. (2010). “Effect of Steel Fibers on
Shear Behavior of Prestressed Concrete Beams.” Earth and Space, pp. 2755-2764.
22. Taylor, C., Montoya, K., Jáuregui, D., Newtson, C., and Weldon, B. (2011). “Feasibility
Analysis of Using UHPC in Prestressed Bridge Girders.” Structures Congress, pp. 203-214.
19
Table 1. Experimental Variables for Tested Beams 468
Beam
Designation
a/d
ratio
Concrete type, 28th day Compressive
Strength, ksi (MPa)
Stirrups, Spacing,
in. (mm)
Prestressing
Force,
Kip
(kN)
Critical Shear Span Non-Critical Shear
Span
Critical
Shear
Span
Non-
Critical
Shear
Span
Concrete
Type,
ksi
(MPa)
Critical
Shear
Span,
in. (m)
Concrete
Type,
ksi
(MPa)
Non-
Critical
Shear
Span,
in. (m)
HB-100-3-0 3
UHPC,
24.2
(166.8)
8d,
118
(3)
HSC,
8.3
(57.2)
17.6d,
256
(6.5)
None,
0
(0)
Steel,
4
(101.6)
104
(463)
HB-100-4-0 4
HB-100-5-0 5
HB-100-6-0 6
SS-100-3-6 3
HSC,
8.3
(57.2)
Steel,
6
(152.4)
95
(422.6)
SS-100-4-6 4
SS-100-5-6 5
SS-100-6-6 6
SC-100-3-6 3
HSC,
8.3
(57.2)
CFCC,
6
(152.4)
SC-100-4-6 4
SC-100-5-6 5
SC-100-6-6 6
a/d ratio = Shear span (a) / effective depth (d), 469
HB-XXX-Y-Z = Hybrid beam-Prestressing force (kip)-a/d ratio-Stirrup spacing,
SS-XXX-Y-Z = HSC beam with steel stirrup-Prestressing force (kip)-a/d ratio-Stirrup spacing, 470
SC-XXX-Y-Z = HSC beam with CFCC stirrup-Prestressing force (kip)-a/d ratio-Stirrup spacing. 471
472
473
474
475
476
477
478
479
480
20
Table 2. Material Properties for Reinforcements 481
Material Property units CFCC Longitudinal Steel Stirrups
Designation - CFRP 1 X 7 # 3
Diameter in. (mm) 0.60 (15.2) 0.375 (9.5)
Effective Cross Sectional Area in.2 (mm2) 0.179 (115.5) 0.11 (71)
Linear Density lb/ft (g/m) 0.15 (223) 0.38 (565)
Guaranteed Breaking Load kip (kN) 60.7 (270) --------
Yield Strength ksi (MPa) --------- 60 (414)
Tensile Strength ksi (MPa) 373 (2,930) 90 (620)
Elastic Modulus ksi (MPa) 22,480 (155,000) 29,000 (200,000)
Elongation % 1.7 4.9
482
Table 3. Mix Design for Concretes per Cubic Yard 483
High Strength Concrete (HSC)
Coarse
Aggrega
te, lb
(kg)
Fine
Aggrega
te, lb
(kg)
Cement
(type 1),
lb (kg)
Slag
Cement
(Grade
100), lb
(kg)
Water
reducing
admixture,
gal, (m3)
High
Range
Water
reducer,
gal, (m3)
Water
gal,
(m3)
Water
Cement
ratio
(%)
Slump,
in.
(mm)
1,710
(775.6)
1,290
(585.1)
534
(242.2)
288
(130.6) 0.9 (2) 4.5 (10)
0.12
(31.8) 0.37
8
(203.2)
Ultra High Performance Concrete (UHPC)
Premix, lb (kg) Water, lb (kg) Premia 150,
lb (kg)
Steel fiber (2%
by Volume)
Flow table, in.
(mm)
3700 (2195) 219.1 (130) 50.6 (30) 262.9 (156) 9 (228.6)
484
485
486
21
Table 4. Summary of Experimental Results for Tested Beams 487
Beam
Designation
Ultimate
Shear Force,
kip (kN)
Cracking
Shear Force,
kip (kN)
Ultimate
Deflection
Under Load, in.
(mm)
Maximum
Concrete Strain
at Top Flange,
µε
Maximum
Concrete Strain
at Bottom
Flange, µε
Modes
of
Failure
HB-100-3-0 118.8 (528.5) 34.2 (152.1) 3.4 (85.9) -2,206 5980 DS
HB-100-4-0 106.6 (447.5) 21.9 (97.4) 8.3 (210.3) -3,053 6280 DS
HB-100-5-0 80.9 (359.9) 16.1 (71.6) 9.9 (250.2) -3,519 4781 CF
HB-100-6-0 62.2 (276.7) 12.2 (54.3) 7.7 (195.58) -3,244 3024 CF
SS-100-3-6 61.2 (272.2) 27.3 (121.5) 1.4 (36.0) -1,642 416 ST
SS-100-4-6 53.6 (238.2) 20.0 (89.0) 2.6 (66.0) -2,038 280 ST
SS-100-5-6 49.7 (220.8) 15.8 (70.3) 3.5 (90.0) -2,639 416 ST
SS-100-6-6 44.2 (196.6) 12.4 (55.2) 4.8 (122.0) -2,649 312 ST
SC-100-3-6 58.6 (260.7) 26.8 (119.2) 1.6 (41.0) -1,282 412 SC-W
SC-100-4-6 52.2 (232.0) 19.2 (85.4) 3.0 (76.0) -1,767 407 SC-W
SC-100-5-6 49.1 (218.0) 15.6 (69.4) 4.1 (104.0) -2,624 334 SC-T
SC-100-6-6 46.3 (206.1) 14.2 (63.2) 5.5 (139.0) -2,732 390 SC-T
DS - Diagonal Shear Failure, CF – Compression Flexural Failure, SC-W – Shear Compression Failure due to 488
Crushing of Web, SC-T – Shear Compression Failure due to Crushing of Top Flange, ST – Shear Tension Failure 489
due to yielding of Stirrup 490
22
Table 5. Ductility Indices 491
Beam
Designation
Inelastic Energy Absorption (Ei) Elastic Energy Absorption (Ee) Ductility
Indices (%)
= ��
������100
kip-in.
(kN-m)
× Less than
Hybrid Beam
kip-in.
(kN-m)
× Less than
Hybrid Beam
HB-100-3-0 104.3 (11.8) - 180.7 (20.4) - 36.6
SS-100-3-6 21.5 (2.4) 4.85 41.7 (4.7) 4.34 34.1
SC-100-3-6 25.6 (2.9) 4.07 56.7 (6.4) 3.19 34.1
HB-100-4-0 168.7 (19.1) - 413.6 (46.7) - 29.0
SS-100-4-6 23.6 (2.7) 7.15 65.3 (7.4) 6.33 26.5
SC-100-4-6 53.5 (6.0) 3.15 49.6 (5.6) 8.34 51.9
HB-100-5-0 159.9 (18.1) - 341.8 (38.6) - 31.9
SS-100-5-6 43.9 (5.0) 3.64 79.7 (9.0) 4.29 35.5
SC-100-5-6 38.6 (4.4) 4.14 126.1 (14.3) 2.71 23.4
HB-100-6-0 90.9 (10.3) - 244.2 (27.6) - 27.2
SS-100-6-6 48.7 (5.5) 5.01 82.4 (9.3) 1.10 37.2
SC-100-6-6 65.0 (7.3) 3.76 108.1 (12.2) 0.84 37.6
23
Table 6: Material Parameters and Elements used in the FEA Model (Abaqus) 492
UHPC HSC CFCC STRANDS STEEL
STIRRUP
Density, lb/ft3 (kg/m3)
160 (2563) 150 (2397) 76.6 (1228) 497.7 (7972)
Concrete Elasticity
Young Modulus, ksi (GPa)
8000 (55.2) 4910 (33.9) 21170 (146.0 29000 (200.0)
Poisson’s Ratio
0.18 0.2 0.3 0.3
Concrete Compression hardening Plasticity
Compressive
Stress, ksi
(MPa)
Plastic
Strain (-)
Compressive
Stress, ksi
(MPa)
Plastic
Strain (-)
Yield
Stress,
ksi
(MPa)
Plastic
Strains
(+)
14.0 (96.5) 0.000000 5.0 (34.5) 0.000000 372.748
(2570) 0.00
16.0 (110.3) 0.0000284 8.3 (57.2) 0.001167 0.0 (0.0) 0.018
20.0 (137.9) 0.0000720 0.0 (0.0) 0.003100
24.0 (165.5) 0.0001410
27.5 (189.6) 0.0004140
Concrete Tension Stiffening
Compressive
Stress, ksi
(MPa)
Plastic
Strain (+)
Compressive
Stress, ksi
(MPa)
Plastic
Strain (+)
2.3 (15.9) 0.00000 0.65 (4.5) 0.0000 Expansion
2.3 (15.9) 0.00836 0.325 (2.2) 0.0015 0.000001
0.0 (0.0) 0.009 0.0 (0.0) 0.005
Parameters of CDP Models
Dilation
Angle 0° 56°
Eccentricity 0.1 0.1
fb0/fc0 1.16 1.16
k 0.67 0.67
Viscosity
Parameter 0 0
Type of Elements
Three Dimensional Eight
Node Linear Brick
Elements (C3D8R)
Three Dimensional Eight
Node Linear Brick
Elements (C3D8R)
Three Dimensional
Two Node Linear
Truss Elements
(T3D2)
Three
Dimensional
Two Node
Linear Truss
Elements
(T3D2)
493
24
Table 7. Comparison of Experimental and Numerical Results 494
Beam
Designation
Ultimate Shear
Force, kip (kN)
Cracking Shear
Force, kip (kN)
Ultimate Deflection
Under Load, in.
(mm)
Maximum Concrete
Strain at Top Flange,
µε Modes of
Failure
Exp. Num. Exp. Num. Exp. Num. Exp. Num.
HB-100-3-0 118.8
(529)
118.2
(526)
34.2
(152)
38.7
(172)
3.4
(86)
3.7
(93.9) -2,206 -2,350 DS
HB-100-4-0 106.6
(474)
99.8
(443)
21.5
(96)
22.4
(100)
8.3
(210) 7.9 (201) -3,053 -2,933 DS
HB-100-5-0 80.9
(360)
79.5
(354)
16.1
(72)
18.1
(81)
9.9
(251) 9.2 (234) -3,519 -3,120 CF
HB-100-6-0 62.2
(277)
63.6
(283)
12.2
(54)
12.4
(55)
7.7
(196) 7.9 (201) -3,244 -3,015 CF
Exp. – Experimental, Num. – Numerical, DS - Diagonal Shear Failure, CF – Compression Flexural Failure, SC-W – 495
Shear Compression Failure due to Crushing of Web, SC-T – Shear Compression Failure due to Crushing of Top 496
Flange, ST – Shear Tension Failure due to yielding of Stirrup 497
498
499
Table 8. Ultimate Shear Capacity 500
Beam
Designation
Experimental Ultimate
Shear Capacity, kip (kN)
Ultimate Shear
Capacity as per JSCE,
kip (kN)
Ultimate Shear
Capacity as per AFGC,
kip (kN)
HB-100-3-0 118.8 (529)
81.0 (360.4) 83.5 (371.6) HB-100-4-0 106.6 (474)
HB-100-5-0 80.9 (360)
HB-100-6-0 62.2 (277)
501
25
502
503
504
505
506
507
508
509
510
511
512
513
514
(a) Typical Section for HSC Beam and
Hybrid Beam Section in Middle Flexural
Span With Steel Stirrups
(b) Hybrid Beam Section in Critical
Shear Span Without Stirrups
Figure 1. General Cross Section Detailing for tested Beams
26
515
516
517
518
519
520
521
Figure 2. Detailed Dimension for Beams along with Reinforcement Cage
Critical Shear Span
(UHPC) (8 de)
Critical Shear Span
(UHPC) (8 de) Middle Flexural Span
(c) Reinforcement Cage for Hybrid Beam
(d) Hybrid Beam
(a) Reinforcement Cage for HSC Beam Tested by Grace et al. (2014)
(b) HSC Beam Tested by Grace et al. (2014)
27
522
523
524
525
526
A) Hybrid beam reinforcement cage showing shear zone
(without stirrup) and flexural zone (with Stirrup) B) Reinforcement cage sitting on Deck with trap
door setup to facilitate concrete joint
C) Pouring of UHPC starting from beam ends
after HSC poured at mid span D) Hybrid beam concrete joint after pouring
Figure 3. Various Steps in Construction of Hybrid Beams
28
527
528
529
530
531
532
533
534
535
536
0 10 20 30 40 50 60 70 80
0
34
69
103
138
172
207
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80
Time (Days)
Com
pre
ssiv
e S
tren
gth
(M
Pa)
Com
pre
ssiv
e S
tren
gth
(k
si)
Time (Days)
UHPC Compressive Strength
HSC Compressive Strength
HSC Cylinder (6" x 12") UHPC Cylinder (3" x 12")
Figure 4. Average Concretes Compressive Strength with Time
29
537
538
539
540
541
542
543
544
545
546
547
548
LVDT’s (For measuring crack response)
LMT
(For measuring
deflection under load)
Elastomeric Neoprene
Bearing Pad
Figure 5. Shear Test Setup for Hybrid Beams
30
549
550
551
552
553
554
555
556
557
558
0 25.4 50.8 76.2 101.6 127 152.4 177.8 203.2 228.6 254
0
89
178
267
356
445
534
623
0
20
40
60
80
100
120
140
0.0 2.0 4.0 6.0 8.0 10.0
DEFLECTION (MM)
SH
EA
R F
OR
CE
(K
N)
SH
EA
R F
OR
CE
(K
IP)
DEFLECTION (IN.)
HB-100-3-0
HB-100-4-0
HB-100-5-0
HB-100-6-0
Figure 6. Shear Force - Deflection Response for Hybrid Beams
31
559
560
561
562
563
564
565
566
567
568
-4000-3500-3000-2500-2000-1500-1000-5000
0
89
178
267
356
445
534
623
-4000-3500-3000-2500-2000-1500-1000-5000
0
20
40
60
80
100
120
140
TOP FLANGE CONCRETE STRAIN (MIRCO-STRAIN)
SH
EA
R F
OR
CE
(K
N)
TOP FLANGE CONCRETE STRAIN (MICRO-STRAIN)
SH
EA
R F
OR
CE
(K
IP)
HB-100-3-0(UHPC at Load) HB-100-3-0(UHPC at Joint) HB-100-3-0(HSC at Joint)HB-100-4-0 (UHPC at load) HB-100-4-0(UHPC at Joint) HB-100-4-0(HSC at Joint)HB-100-5-0(UHPC at Load) HB-100-5-0(UHPC at Joint) HB-100-5-0(HSC at Joint)HB-100-6-0(UHPC at Load) HB-100-6-0(UHPC at Joint) HB-100-6-0(HSC at Joint)
Figure 7. Shear Force - Compressive Strains at Top Flange at Various Location for
Hybrid Beams
32
569
570
571
572
573
574
575
576
577
0 1000 2000 3000 4000 5000 6000 7000
0
89
178
267
356
445
534
623
0 1000 2000 3000 4000 5000 6000 7000
0
20
40
60
80
100
120
140
BOTTOM FLANGE CONCRETE STRAIN (MICRO-STRAIN)
SH
EA
R F
OR
CE
(K
N)
BOTTOM FLANGE CONCRETE STRAIN
SH
EA
R F
OR
CE
(K
IP)
HB-100-3-0
HB-100-4-0
HB-100-5-0
HB-100-6-0
Figure 8. Shear Force - Bottom Flange Concrete Strain Response for Hybrid Beams
33
578
(B) Crack Pattern at a/d of 4
(C) Crack Pattern at a/d of 5
Figure 9. Crack Patterns Observed in Hybrid Beams at Various loading point (a/d)
(A)Crack Pattern at a/d of 3
(D) Crack Pattern at a/d of 6
34
579
580
581
582
583
584
585
586
587
588
0.000 0.051 0.102 0.153 0.204 0.255 0.306 0.357 0.408
0
89
178
267
356
445
534
623
0
20
40
60
80
100
120
140
0.000 0.002 0.004 0.006 0.008 0.010
CRACK WIDTH (MM)
SH
EA
R F
OR
CE
(K
N)
SH
EA
R F
OR
CE
(K
IP)
CRACK WIDTH (IN.)
HB-100-3-0(UHPC)
HB-100-4-0(UHPC)
HB-100-5-0(UHPC)
HB-100-6-0(UHPC)
Figure 10. Shear Force - Crack Width Response for Hybrid Beams
35
589
590
591
592
593
594
595
596
597
598
0.000 0.051 0.102 0.153 0.204 0.255 0.306 0.357 0.408
0
89
178
267
356
445
534
623
0
20
40
60
80
100
120
0.000 0.005 0.010 0.015 0.020
CRACK WIDTH (MM)
SH
EA
R F
OR
CE
(K
N)
SH
EA
R F
OR
CE
(K
IP)
CRACK WIDTH (IN.)
HB-100-4-0(UHPC)
HB-100-4-0(HSC)
HB-100-6-0(UHPC)
HB-100-6-0(HSC)
Figure 11. Shear Force - Crack Width Response for Hybrid Beam at a/d of 4
36
599
Figure 5(a) Diagonal Shear Failure of HB-100-3-0
Figure 5(b) Diagonal Shear Failure of HB-100-4-0
Figure 5(c) Compression Flexural Failure of HB-100-5-0
Figure 5(d) Compression Flexural Failure of HB-100-6-0
Figure 12 Modes of Failure of Hybrid Beams (HB) at various a/d ratios
37
600
601
602
603
604
605
606
607
608
609
610
2 3 4 5 6 7
0.4
0.6
0.8
1.0
1.2
1.4
0.4
0.6
0.8
1.0
1.2
1.4
2 3 4 5 6 7
a/d
Mu
/Mn
Mu
/Mn
a/d
Hybrid Beam (HSC Section at Joint) Hybrid Beam (UHPC Section under Load)
Steel Stirrup Beam CFCC Stirrup Beam
FLEXURE FAILURE
SHEAR FAILURE
Figure 13. Variation of Mu/Mn of various tested Beams with a/d
38
611
612
613
614
615
616
617
618
619
620
621
34.20
27.20
22.80 21.9019.70
16.30 16.10 14.80 15.5012.20 12.40
14.20
118.80
61.2058.60
100.60
53.60 52.20
80.90
49.70 49.10
62.20
44.2046.30
0
89
178
267
356
445
534
623
0
20
40
60
80
100
120
140
HB-100-3-0 SS-100-3-6 SC-100-3-6 HB-100-4-0 SS-100-4-6 SC-100-4-6 HB-100-5-0 SS-100-5-6 SC-100-5-6 HB-100-6-0 SS-100-6-6 SC-100-6-6
SH
EA
R F
OR
CE
(K
N)
SH
EA
R F
OR
CE
(K
IP)
BEAMS
Cracking Shear Force
Ultimate Shear Force
Figure 14 Cracking Force and Ultimate Shear capacity for all Tested Beams
39
6
22
6
23
6
24
6
25
6
26
6
27
6
28
6
29
6
30
6
31
6
32
HB-100-3-0
HB-100-3-0
HB-100-3-0
SS-100-3-6
SS-100-3-6
SS-100-3-6
SC-100-3-6
SC-100-3-6
SC-100-3-6
HB-100-4-0
HB-100-4-0
HB-100-4-0
SS-100-4-6
SS-100-4-6
SS-100-4-6
SC-100-4-6
SC-100-4-6
SC-100-4-6
HB-100-5-0
HB-100-5-0
HB-100-5-0
SS-100-5-6
SS-100-5-6
SS-100-5-6
SC-100-5-6
SC-100-5-6
SC-100-5-6
HB-100-6-0
HB-100-6-0
27.15
SS-100-6-6
SS-100-6-6
37.55
SC-100-6-6
SC-100-6-6
37.16
0 6 11
17
23
28
34
40
45
51
57
0
10
0
20
0
30
0
40
0
50
0
Ine
lastic E
ne
rgy
Ab
sorb
tion
(Ei)
Ela
stic En
erg
y
Ab
sorp
tion
(Ee
)
Du
ctility R
atio
(%) =
[Ei/(E
i+E
e)]
Energy Absorption (kN-m)
Energy Absoption (kip-in)
Fig
ure 1
5. E
nerg
y A
bso
rptio
n o
f vario
us tested
Beam
s
40
633
634
635
636
637
638
639
640
641
642
643
(B) Observed FEA Diagonal Shear Failure of HB-100-4-0
(A) Observed Experimental Diagonal Shear Failure of HB-100-4-0
Figure 16. Comparison Between Experimental and FEA Model Failure
41
644
645
646
647
648
649
650
651
0 25.4 50.8 76.2 101.6 127 152.4 177.8 203.2 228.6 254
0
89
178
267
356
445
534
623
0
20
40
60
80
100
120
140
0.0 2.0 4.0 6.0 8.0 10.0
DEFLECTION (MM)
SH
EA
R F
OR
CE
(K
N)
SH
EA
R F
OR
CE
(K
IP)
DEFLECTION (IN.)
HB-100-3-0(Exp) HB-100-3-0(Num)
HB-100-4-0(Exp) HB-100-4-0(Num)
HB-100-5-0(Exp) HB-100-5-0(Num)
HB-100-6-0(Exp) HB-100-6-0(Num)
Figure 17. Comparison between FEA and Experimental Force - Deflection Response