were ground into the surface of the concrete using a rotary hand grinder. .... In the full-scale furnace testing of the beam-slab assemblies, the load was controlled.
http://irc.nrc-cnrc.gc.ca
Results of fire resistance experiments on FRP-strengthened reinforced concrete slabs and beam-slab assemblies – Report no. 2 IRC-RR-234 Bénichou, N.; Kodur, V.K.R.; Chowdhury, E.U.; Bisby, L.A.; Green, M.F. August 2007
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RESULTS OF FIRE RESISTANCE EXPERIMENTS ON FRP-STRENGTHENED REINFORCED CONCRETE SLABS AND BEAM-SLAB ASSEMBLIES – REPORT No. 2 By N. Benichou, V.K.R. Kodur, E.U. Chowdhury, L.A. Bisby and M.F. Green
ABSTRACT Demolishing and rebuilding deteriorated structures, resulting primarily from corrosion and heavy use, is not an economically viable alternative in most countries, where infrastructure is in urgent need of rehabilitation. In recent years, fibre-reinforced polymers (FRPs) have been explored as materials to prolong the lives of civil engineering structures, provide seismic upgrading, and reduce maintenance costs. However, the performance of these systems in fire remains incompletely understood. To further enable applications of FRPs in buildings, research on the behaviour of FRP-strengthened reinforced concrete slabs and beam-slab assemblies in fire has been conducted at the National Research Council of Canada (NRC) in collaboration with Intelligent Sensing for Innovative Structures (ISIS) Canada, Fyfe Co. LLC., and Degussa Building Systems. The experimental program consisted of fire tests on intermediate-scale reinforced concrete slabs and full-scale reinforced concrete beam-slab assemblies that were strengthened with externally bonded FRP materials. The slabs and beam-slabs were also provided with supplemental fire protection systems, applied to the exterior of the FRP strengthening materials. This report describes the results from these fire endurance experiments. The test data indicates that reinforced concrete slabs and beam-slabs that have been strengthened with externally-bonded FRPs can achieve a satisfactory fire endurance of 4 hours with adequate protection from fire.
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RESULTS OF FIRE RESISTANCE EXPERIMENTS ON FRP-STRENGTHENED REINFORCED CONCRETE SLABS AND BEAM-SLAB ASSEMBLIES – REPORT No. 2 By N. Benichou, V.K.R. Kodur, E.U. Chowdhury, L.A. Bisby and M.F. Green
ACKNOWLEDGEMENTS The authors are members of the Intelligent Sensing for Innovative Structures Network (ISIS Canada) and wish to acknowledge the support of the Networks of Centres of Excellence Program of the Government of Canada and the Natural Sciences and Engineering Research Council. The authors would also like to acknowledge the National Research Council of Canada, Degussa Building Systems and Fyfe Co. LLC. Finally, for this series of experiments, the authors wish to thank the technical staff of Queen’s University (Paul Thrasher, Neil Porter and Dave Tryon), National Research Council of Canada (John Latour, Joe Hum, Patrice Leroux, Jocelyn Henrie, Richard Rombough and Roch Monette) and Degussa Corporation (Richard J. Ewanko Jr. and Michael Urbas).
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RESULTS OF FIRE RESISTANCE EXPERIMENTS ON FRP-STRENGTHENED REINFORCED CONCRETE SLABS AND BEAM-SLAB ASSEMBLIES – REPORT No. 2 By N. Benichou, V.K.R. Kodur, E.U. Chowdhury, L.A. Bisby and M.F. Green INTRODUCTION Demolishing and rebuilding structures with deterioration, resulting primarily from corrosion and heavy use, is not an economically viable alternative in many countries, where infrastructure is in urgent need of rehabilitation. In recent years, fibre-reinforced polymers (FRPs) have been explored as materials to prolong the lives of civil engineering structures and to reduce maintenance costs. This is because of their various advantages, including high strength-to-weight ratios and electrochemical corrosion resistance. Fire safety is a major consideration in designing structural components for buildings, and this is satisfied by providing safety measures such as fire extinguishment using sprinklers and, by using materials in buildings that have some resistance to elevated temperature [1,2]. All structural members in buildings that require fire ratings are designed to satisfy serviceability requirements and safety limit state conditions. The basis of fire safety design is that, when other measures for containing the fire fail, structural integrity is the last line of defence for the building occupants. One of the main concerns when implementing FRP strengthening materials in buildings is their inherent combustibility and the various risks associated with fire, such as the potential for increased smoke generation, toxicity, fire growth, etc. If sufficiently heated, the polymer matrix component of the FRP material will ignite, causing the polymer binder to weaken and raising potential concerns as to the structural integrity of FRP-strengthened concrete structures during fire. Until now, FRP applications have been largely limited to the rehabilitation or construction of bridges, due partly to insufficient knowledge about the fire resistance of FRP. Therefore, the application of FRP materials in buildings requires research into their ability to endure exposure to fire. To enable applications of FRPs in buildings, research on the behaviour of FRPstrengthened reinforced concrete beam-slab assemblies in fire is currently being conducted at the National Research Council of Canada (NRC), in collaboration with ISIS Canada, Queen’s University, Fyfe Co. LLC., and Degussa Building Systems. As part of this effort, an experimental program has been conducted consisting of fire tests on intermediate-scale FRPstrengthened and insulated reinforced concrete slabs and full-scale FRP-strengthened and insulated reinforced concrete beam-slab assemblies. The intermediate-scale slabs were tested under fire exposure to evaluate the thermal effectiveness of the insulation, so that an appropriate thickness of insulation could be provided to the beam-slab assemblies in fire. The beam-slab assemblies were tested to validate numerical models (currently under development). The results of this experimental program are presented in this report. TEST SPECIMENS The experimental program consisted of fire tests on two intermediate-scale reinforced concrete slabs and two full-scale reinforced concrete beam-slab assemblies, all of which were
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strengthened with the MBrace Carbon FRP externally-bonded strengthening system 1 . The slabs were designated as Slab-3 and Slab-4 and the beam-slab assemblies were designated as Beam-3 and Beam-4. Details of the reinforced concrete slabs and reinforced concrete beamslab assemblies are shown in FIGURE-1 and FIGURE-2, respectively. Dimensions The slabs were rectangular in shape, 1331 mm (52.4 in.) by 954 mm (37.6 in.) and 150 mm (6 in.) thick. The reinforcement details were as shown in FIGURE-1. The beam-slab assemblies were T-shaped in cross-section with an overall span of 3.9 m (12.7 ft.) and overall height of 400 mm (15.7 in.). The flange was 1220 mm (48 in.) wide and 150 mm (5.9 in.) thick. The web was 300 mm (11.8 in.) wide. The reinforcement details are shown in FIGURE-2. Materials Cement Type I Portland cement, a general-purpose cement for construction of reinforced concrete structures, was used for fabricating the reinforced concrete slabs. Type III Portland cement, a high early strength cement, was used for fabricating the reinforced concrete beam-slab assemblies. Aggregates All specimens were fabricated with carbonate aggregate concrete. The maximum aggregate sizes used in the slabs and beam-slabs were 14 mm (0.55 in.) and 13.2 mm (0.52 in.), respectively. The fine aggregate used was natural sand. Reinforcement Deformed bars were used for reinforcing both the slabs and beam-slab assemblies. In the intermediate-scale slabs, four 10M steel bars were evenly distributed along the direction of the 954 mm (37.6 in.) edge and three 15M steel bars were evenly distributed along the direction of the 1331 mm (52.4 in.) edge. The 15M steel bars had a clear cover of 25 mm (0.98 in.) from the bottom and were supporting the 10M steel bars below. All reinforcements in the slabs had specified yield strengths of 400MPa. The longitudinal reinforcements in the beam-slab assemblies, which had a T-shaped cross section, consisted of fourteen 10M steel bars in the flange and two 20M steel bars in the web. For lateral reinforcements, twenty-six 10M steel ties were spaced at 150mm (5.9 in.) longitudinally. Additional lateral reinforcements were provided in the flange in two layers of 10M steel bars spaced at 150mm (5.9 in.) o/c. The steel reinforcements had a clear cover of 40mm (1.57 in.) from the exterior surface of the concrete to the steel ties. The specified yield strengths
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Certain commercial products are identified in this report in order to adequately specify the experimental procedure. In no case does such identification imply recommendations or endorsement by the National Research Council, nor does it imply that the product or material identified is the best available for the purpose.
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of the steel bars were 515 MPa (74.7 ksi) for the 10M bars and 494 MPa (71.6 ksi) for the 20M bars. Concrete Mix A single batch of concrete was used for fabricating the slabs. The concrete was supplied by Lafarge Ready-Mix, Kingston, Canada, and was delivered to the Structures Testing Laboratory at Queen’s University. The concrete for the slabs was designed to have a specified compressive strength of 28 MPa (4.1 ksi). Two different batches of concrete (with the same mix designs) were used for fabricating the beam-slabs. The concrete was supplied by PreCon, Belleville, Canada. The concrete for the beam-slabs was designed to have a specified compressive strength of 41 MPa (5.9 ksi). The batch quantities and specified properties of the concrete mix proportions are provided in TABLE-1. The 28-day cylinder compressive strength of the slab concrete was 27 MPa (3.9 ksi) and the corresponding compressive strength on the day of the slabs’ fire endurance test was 29 MPa (4.2 ksi). The average 28-day cylinder compressive strength of the beam concrete was 59 MPa (8.6 ksi) and the corresponding compressive strengths on the day of the fire endurance test were 60 MPa (8.7 ksi) for Beam-3 and 63 MPa (9.1 ksi) for Beam-4 (note that these strengths are about 50% higher than the original compressive design strength). Fabrication The intermediate-scale slabs were fabricated and cured in the Structures Testing Laboratory at Queen’s University, Kingston, Canada and then shipped to the Fire Testing Facility of the National Research Council, Ottawa, Canada. The beam-slab assemblies were fabricated and cured at PreCon, Belleville, Canada and then shipped to the National Research Council, Ottawa, Canada for full-scale fire testing. Both slabs and beam-slabs were cast in plywood formwork. Reinforcing Bars The 15M longitudinal reinforcing bars were placed into holes drilled into the plywood to maintain a consistent concrete clear cover of 25 mm (1.0 in.). The longitudinal reinforcements were subsequently tied together using steel ties. FIGURE-3 shows the formwork and reinforcement layout during fabrication of the slabs. The reinforcing bars and stirrups for the beam-slab assemblies were spot-welded together to form the steel cage. The cage was lifted and placed into the formwork on plastic chairs to maintain a consistent concrete clear of 40 mm (1.6 in.) to the steel ties. FIGURE-4 shows the steel cage for the beam-slabs during fabrication. Instrumentation To record the temperatures during the fire endurance tests, Chromel-alumel (Type K) thermocouples were secured to the reinforcing steel and at various locations within the concrete of the slabs and beam-slabs. A steel drill-rod of 3.1mm diameter was tack welded to the steel reinforcement cage for securing thermocouples to the rod so that temperature at various depths in the concrete slabs and beam-slabs could be recorded. FIGURE-5 shows the locations of the thermocouples within the slabs. FIGURE-6 and FIGURE-7 show the location of the
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thermocouples within the beam-slab assemblies and on the unexposed surfaces of the beamslab assemblies, respectively. Displacement gauges were also used during the fire tests to monitor beam deflection, as shown in FIGURE-8. To install the thermocouples at the FRP/concrete bondline, shallow vertical grooves were ground into the surface of the concrete using a rotary hand grinder. The thermocouple wires were then placed inside the grooves, run down the length of the slabs and beam-slabs, and out of the side of the specimen. The thermocouple wires were kept in the grooves by filling the grooves with glue at intervals of about 15 mm and taping the wires in place. Wooden supports were also used to hold the thermocouple wires in the grooves until the glue had set, at which time the tape was carefully peeled off the cured glue. The thermocouples at the FRP/insulation bondline were installed in a similar manner, although grooves were not used in this case and the thermocouple wires were bonded directly to the exterior surface of the FRP wraps, and five-minute epoxy was used as the adhesive. FIGURE-11 illustrates the thermocouple instrumentation installed at the FRP/concrete bondline and FRP/insulation bondline. Concrete Placement The slabs were poured in two lifts. The concrete was placed in the formwork using shovels and was then hand-vibrated during each lift to ensure adequate consolidation. The beam-slab assemblies were poured using a large overhead hopper in two lifts. After each lift, the concrete was vibrated to ensure adequate consolidation. In addition, twelve 152.4mm (6 in.) diameter by 304.8mm (12 in.) high concrete cylinders were cast from each batch for conducting concrete compressive strength tests. Curing The slabs were cured under wet burlap and plastic sheets at 21°C (69.8°F) to 24°C (75.2°F) and 100% humidity for four days, after which the formwork was removed and the slabs were allowed to cure in the Structures Testing Laboratory at Queen’s University at ambient temperature and relative humidity for approximately six months, until the slabs were ready to be transported to the National Research Council of Canada, Ottawa. The beam-slabs were cured in a plastic enclosure for 24 hours, after which point the formwork was removed. The beam-slabs were allowed to cure in the PreCon precast plant at ambient temperature and relative humidity for 12 months and then transported to the National Research Council. FRP Strengthening For the intermediate-scale slabs, the strengthening system consisted of a single layer of the MBrace CF130 unidirectional carbon/epoxy FRP strengthening system. The FRP was bonded to the tension face of both slabs along the direction of the 1330mm edge by staff at Degussa Building Systems, Cleveland, Ohio. For the beam-slab assemblies, the strengthening system consisted of a single layer of 200mm (7.9 in.) wide MBrace CF130 unidirectional carbon/epoxy FRP sheet bonded to the tension faces (soffits) of the beams’ webs. In addition, to provide anchorage to this flexural CFRP strip, two layers of 650mm (25.6 in.) wide MBrace CF130 U-wrap was bonded over the flexural strip at the ends of the beam-slabs. The U-wraps were provided to prevent a debonding
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failure mode of the flexural strengthening sheet. Installations specialists from Degussa Building Systems and graduate students from Queen’s University installed the strengthening system to the beam-slab assemblies at the National Research Council of Canada. The strengthening system increased the ultimate design capacity by 33% based on ACI 440 [3], 11% based on CSA-S806 [4] and 37% based on ISIS Canada guidelines. Details of the load calculations are provided in Appendix A. The sheets were installed on the slabs and beam-slabs in accordance with Degussa Corporation installation procedure. FIGURE-9 and FIGURE-10 provide details of the strengthening for the slabs and beam-slabs. The application process for the beam-slabs was as follows: 1. The concrete substrate was checked for any defects or protrusions that could affect the ability of the FRP to bond to the concrete. However, no defects were found on the specimens. 2. Since the beam specimens were cast in a high quality formwork, the surface of the beamslabs was extremely smooth. The concrete substrate was prepared using hand grinders and sandblasting, to achieve a minimum surface texture prescribed by the International Concrete Repair Institute (ICRI). The surface was lightly brushed using a heavy-duty scrub brush to remove any dust or loose debris after the mechanical abrasion. 3. MBrace primer was applied to the concrete surface using a small nap roller (FIGURE-11j). 4. MBrace putty was applied to the primed surface with a trowel to fill any surface defects (FIGURE-11k). 5. MBrace saturant was applied to the primed and puttied surface with a medium nap roller to a thickness of 0.46mm (18 mils) to 0.56mm (22 mils). 6. A 200mm wide resin-saturated FRP sheet was placed onto the concrete surface of the beam’s soffit and gently pressed into the saturant (FIGURE-11m). A roller was used to roll in the direction of the fibres to facilitate impregnation and remove any air bubbles. 7. A second coat of saturant was applied with a medium nap roller. 8. Immediately after installing the flexural strip, the U-wrap was installed on top of the flexural FRP sheet at the ends of the beam-slabs (FIGURE-11n). 9. The FRP was allowed to cure for at least 12 hours at ambient temperature (approximately 15°C). Fire Protection Two different types of fire protection systems, both developed by Degussa Corporation, were used to provide supplemental fire insulation over the FRP on the slabs and beam-slabs. The fire protection scheme included MBrace Insulation Systems 1 and 2. Details of the insulation systems are provided in FIGURE-9 and FIGURE-10. MBrace Insulation System 1 is a spray-applied cementitious-based mortar that was developed for fire-resistant tunnel linings and which prevents any mechanical deterioration to concrete structures above 300°C (572°F) and also prevents explosive spalling when concrete is exposed to a high heating rate. MBrace Insulation System 2 is an experimental cementitious fire protection material. Since MBrace Insulation System 2 is an experimental product, additional mechanical and thermal properties were not available at the time of testing, other than those approximated from observations made during the fire tests. For the slabs, the fire protection scheme consisted of MBrace Insulation System 1 on Slab-3 and of MBrace Insulation System 2 on Slab-4. Both slabs were protected with 38mm
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(1.5 in.) of insulation applied by trowel to the exterior of the FRP strengthening material. Based on the observations made during the testing of the slabs, both the beam-slabs were protected with MBrace Insulation System 1, which was thought to be the superior system. Beam-3 and Beam-4 were protected with an average insulation thickness of 38mm (1.5 in.) and 25mm (1.0 in.), respectively. Since the underside of the beam-slabs was exposed to the fire, the underside of the flanges and webs of the beam-slab assemblies were protected with the fire protection system (refer to Figure 11q). The insulation was installed on the slabs and beam-slabs in accordance with Degussa Building Systems installation procedures. FIGURE-9 and FIGURE-10 provide details of the insulation layout for the slabs and beam-slabs. The application process for the beam-slabs was as follows (refer to FIGURE-11): 1. A thin layer of MBrace Primer was applied to the underside of the beam-slabs, using a roller, and was allowed to become tacky. 2. Once the MBrace Primer coat was tacky, MBrace Insulation System 1 was spray-applied on the soffit of the beam, using an industrial-scale shotcreting rig, until the beam was fireprotected with the desired thickness. 3. The MBrace Insulation System 1 was allowed to cure in the Fire Testing Laboratory at the National Research Council of Canada (NRC) until the date of the test. TEST APPARATUS During the fire endurance tests, the specimens were exposed to elevated temperatures on their soffits. The two slabs were tested in the intermediate-scale furnace at NRC, and the two beam-slabs were tested in the full-scale floor furnace, also at NRC. These furnaces were designed to produce temperature and loading conditions as prescribed in ASTM E119 and CAN/ULC S101 [6,7]. The NRC Intermediate-Scale Furnace has a small chamber where specimens up to a maximum size of 1.35m (4.43 ft.) × 1.98m (6.5 ft.) can be tested. While it is capable of testing both loaded and unloaded specimens, no load was applied to the slabs tested in the current study. The full-scale floor furnace has a chamber that can test 4.87m (16 ft.) × 3.96m (13 ft.) specimens. There are small view ports along the walls of both furnaces that allow viewing of the exposed side of the specimens during testing. Loading Device No load was applied to the intermediate-scale slabs during fire exposure. The beamslabs were subjected to sustained vertical applied load from above using a loading system with 30 distributed hydraulic jacks with the loading spread over three circular loading pads. Each hydraulic jack had a load capacity of 13 kN (2910 lb.) (refer to Figures 11r and 14). Furnace Chamber The interior of both furnace chambers are lined with ceramic insulating blankets that efficiently transfer heat to the specimen through radiation. Layers of ceramic insulation were provided between the two slabs and two beam specimens to ensure that each acted thermally independent of the other as shown in FIGURE-15. It should be noted that only the underside of the slabs, and only the web and underside of the beam-slab assemblies were exposed to the fire.
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Heat in the intermediate-scale furnace is supplied by four propane gas burners in the walls of the furnace chamber, with a total capacity of 300 kW (284 Btu/s). Heat in the full-scale furnace is supplied by two banks of 15 burners located along the base of the furnace walls. The total capacity of the burners is 4700 kW (4455 Btu/s). In both furnaces, each burner can be adjusted individually, which allows for a high degree of temperature uniformity within the furnace chamber. Furnace Instrumentation The temperatures in the intermediate-scale furnace were measured using four Type K chromel-alumel thermocouples, while temperatures within the furnace were measured by nine of the same type of thermocouples. The temperatures measured by the furnace thermocouples were averaged and the average temperature was used to automatically control the furnace temperature. In the full-scale furnace testing of the beam-slab assemblies, the load was controlled using servocontrollers and was measured using pressure transducers. The accuracy of controlling and measuring loads in this testing apparatus is about ±4 kN (900 lbf) at lower load levels and relatively better at higher loads. TEST CONDITIONS AND PROCEDURES Both the intermediate-scale and full-scale furnaces can produce the conditions described in ASTM E119, which are similar to those prescribed by CAN/ULC S101. The two slabs were placed in the intermediate-scale furnace at the same time and were tested concurrently. Each slab was thus supported on three sides. As mentioned earlier, no load was applied to the slabs during the fire exposure. The full-scale beam-slabs were placed in a movable frame that is used to transfer the beam-slabs in and out of the furnace opening (refer to FIGURE-11a). The specimens were fixed to the frame by steel mounts at both ends (FIGURE-11c). Once the beam-slabs were secured in the frame, the frame was lowered onto the opening of the floor furnace and any openings were filled with ceramic-insulated panels. Prior to the fire endurance test, the moisture content of the test specimens were measured using a Vaisala moisture sensor. A hole was drilled into the concrete at the centre of the slab and beam specimens (from the unexposed side). The relative humidity and moisture contents of each specimen at the time of testing are given in TABLE-3. End Conditions The intermediate-scale slabs were not subjected to applied load during fire exposure and therefore their end conditions are not discussed here. The beam-slabs were axially restrained during the fire test by placing steel shims at their ends prior to testing (FIGURE-11c). The support conditions were selected to meet the conditions described in ASTM E119 and CAN/ULC S101 corresponding to an axially-restrained flexural assembly.
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Loading The purpose of fire testing the intermediate-scale slabs was to evaluate the thermal performance of the two insulation systems. Thus, the slab experienced no load other than its self-weight during the fire endurance test. During the full-scale beam-slab fire tests, the assemblies were tested under a sustained uniformly distributed load. The sustained applied load was 35kN/m (2.33kip/ft), which represents 47% of the ultimate strengthened capacity according to ACI 440.2R-02 [3], 34% according to CSA S806-02 [4] and 46% according to ISIS Design Manual No. 4 [5]. The ultimate design capacity and the applied load during the fire endurance tests are given in TABLE-3. Details of the load calculations are presented in Appendix A. The preloading of the beam-slab specimens began 46 minutes prior to the start of the fire exposure. Upon reaching the required load level, the fire in the furnace was initiated. The required load level was maintained at a constant value throughout the fire endurance test. Fire Exposure As mentioned previously, fire exposure of all assemblies was from below. The ambient temperature at the start of each of the slab tests was approximately 18° C (64.4° F). The beamslabs were tested during the winter season, so the ambient temperature at the beginning of the tests was 5° C (41° F). During the fire endurance tests of the slabs and beam-slabs, the furnace temperature was controlled to follow the standard time-temperature curve described in ASTM E119, which is equivalent to CAN/ULC S101 standard fire curve. This standard fire curve can be approximately expressed using the following equation:
(
)
T f = 20 + 750 1 − e −3.79533t + 170.41 t where, t
Tf
= time in hours = temperature of furnace in °C
Recording of Results As mentioned previously, both the slab and beam-slab specimens were instrumented with thermocouples as shown in FIGURE-6 and FIGURE-7 to measure the temperature of concrete, steel, FRP and insulation during the fire test. In addition, displacement gauges were instrumented as shown in FIGURE-8 to measure deflection at one-minute intervals throughout the tests. Visual observations of crack propagation in the insulation, and spalling of insulation and concrete was recorded during the fire endurance test through the small view ports around the walls of the furnace. Failure Criteria In standard fire endurance tests, a structural element must carry the applied load for the required duration of the fire test without structural failure under its sustained service load. In addition, depending on the restraint condition, a structural element must satisfy additional criteria to ensure that it will perform its required load-bearing and fire-separating properties. For instance, the temperatures should not exceed a specified temperature at the unexposed side
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and in the tension steel reinforcement. Because there was no load applied to the slabs, no load-bearing failure criteria was applicable. Since the purpose of the slab tests was to investigate the performance of the thermal insulation, the temperatures during the slab fire endurance were compared with the thermal criteria stated in ASTM E119 and ULC S101. Thus, the slab specimens were assumed to have failed if any of the following limits were reached: • • •
Slab Criterion 1: Steel temperature Slab Criterion 2: Average unexposed face temperature Slab Criterion 3: Point unexposed face temperature
The beam-slabs were subjected to their service load during fire testing. Thus, the beamslabs were assumed to have failed if any of the following criteria were exceeded: • • • •
Beam-Slab Criterion 1: Steel temperature Beam-Slab Criterion 2: Average unexposed face temperature Beam-Slab Criterion 3: Point unexposed face temperature Beam-Slab Criterion 4: Load-bearing capacity
Both beam-slabs successfully resisted the sustained applied load of 35kN/m for more than four hours of fire exposure without structural failure. Near the end of the fire endurance test, the applied load was increased to 75 kN/m but the beam-slabs did not fail. After 4.5 hrs the fire test was stopped to prevent any damage to the floor furnace. Since the beam-slabs were restrained axially, the beam-slabs were not required to satisfy the specified temperature limits stated in ASTM E119 to achieve a fire endurance rating. Thus, the beam-slabs achieved a 4-hour fire endurance rating, satisfying the structural stability criterion for over four hours. Although the temperature criteria set by ASTM E119 was not required to be satisfied, maintaining the specified temperature limits stated in ASTM E119 during fire exposure would allow the beamslabs to have a significant post-fire residual strength. RESULTS AND DISCUSSION The results of the fire endurance tests are given in TABLE-3. The temperatures of the furnace, concrete, steel, FRP and insulation, and the vertical deflections were recorded during the fire endurance tests. The recorded temperatures and deflections for the slabs are given in Appendix-B. The recorded temperatures and deflections for the beam-slabs are given in Appendix-C. Performance of the Insulation The performance of the insulation depends very heavily on its overall thickness. From previous studies [12], it was determined that a layer greater or equal to 25mm (1.0 in.) should provide a suitable thickness of insulation to protect the reinforced concrete elements and the FRP-strengthening systems for the required duration. However, it should be noted that providing excess insulating material on the underside of a member may not be beneficial since the insulating material is being bonded to the concrete substrate with a tack coat of the primer, and without any mechanical anchorage. This bond may not be able to hold the excess weight of the insulation and may result in debonding of the insulation off of the substrate concrete prematurely during a fire endurance test. Also, to ensure the effectiveness of the insulation, overhead insulation installation must be performed in several lifts, and a significant amount of time must elapse between lifts, thus decreasing the cost-effectiveness of thick fire insulation systems due to increased installation costs.
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Both slabs were exposed to fire for four hours without failure. However, there was some development of minor cracks in both of the insulation materials within the first two hours of the tests. These cracks appeared to very gradually widen as the test progressed, likely due to thermally-induced shrinkage of the insulation. Nonetheless, the fire protection/insulation on both slabs remained intact for the full duration of the test. The most significant visual observations from these slab fire tests were that flames were observed emerging from cracks in the MBrace Insulation System 2 protected Slab-4. Late in the fire exposure, a minimal amount of flaming was observed emanating from a crack in the MBrace Insulation System 2. This flaming was thought to be associated with localized burning of the polymer adhesive/matrix beneath the insulation at the location of a crack. Both beam-slabs were exposed to fire for more than four hours without failure. During the beam fire test debonding of the insulation from the web of the beam-slab specimens was observed that exposed the FRP to elevated temperature. The flexural FRP material, which was anchored by FRP U-wraps at the ends of the specimens, was observed hanging at midspan from exposure to elevated temperature. Also, due to the loss of insulation (due to delamination) from the soffits of the concrete flanges, some spalling was observed from the underside of the flanges, thus exposing the tension steel reinforcement in the slab to elevated temperature. The overall timeline and general observations recorded during the beam-slab tests are provided below: Beam-3 Time hr:min 0:00 0:45 1:06 1:16 1:25 1:29 2:47 4:10 4:50
Observations Beam loaded to 35kN/m; initiated the fire in the furnace Flaming observed at the corners of the web on the surface of the insulation Insulation started debonding from the surface of the beam Moisture and emission of steam noted from unexposed surface of beam Insulation from the web soffit started spalling; delamination of fibres in the FRP was noted Concrete started spalling from the web at midspan Insulation from the slab started spalling Initiated increase in load from 35 kN/m to 75 kN/m Load was increased to the maximum capacity of the loading system (75 kN/m); structural failure not imminent, hence test was stopped
Beam-4 Time hr:min 0:00 0:25 0:40 0:55 1:07 1:13
Observations Beam loaded to 35kN/m; initiated the fire in the furnace Flaming observed at the corners of the web on the surface of the insulation Vigorous flaming observed around the U-wrap anchorage region; moderate flaming at midspan Insulation debonded around the U-wrap anchorage region; cracks visible on the surface of the insulation. Insulation started spalling from the underside of the flange Concrete from the flange region started spalling.
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1:16 1:21 1:23 1:34 1:37 1:40 1:43 3:42 4:10 4:50
Moisture and emission of steam noted from unexposed surface of beam Vigorous flaming from the insulation on the web soffit was observed Insulation on the web soffit started spalling; delamination of fibres in the FRP was noted; the U-wrap anchorage was still holding the fibres from the flexural FRP strip Wide cracks visible around the flange Concrete spalling from the flange Fibres from the FRP composite have delaminated Steel bars in the flange visible The unexposed side at the flange reached 200°C Initiated increase in load from 35 kN/m to 75 kN/m Load was increased to the maximum capacity of the loading system (75 kN/m); structural failure not imminent, hence test was stopped
Temperatures A comparison of the recorded temperatures at various locations in the MBrace Insulation System 1 protected Slab-3 and MBrace Insulation System 2 protected Slab-4 are given in APPENDIX-B. The data demonstrate that there were no significant differences in recorded temperatures within the insulated slabs until about 230 minutes, when the temperature at the insulation-FRP interface abruptly increased in the MBrace Insulation System 1 protected slab due to localized loss of insulation from the soffit of the beam-slab specimens. However, in the MBrace Insulation System 2 protected slab, the rate of temperature increase at the insulationFRP interface remained fairly constant. The test data indicate that it will be difficult to maintain the FRP temperature below the glass transition temperature of the matrix for prolonged periods of time during fire exposure. However, the data also indicated that the insulation will remain intact at FRP bondline temperatures up to and exceeding 200° C. The two materials behaved similarly, and either can be considered as a potential option for fire protection of FRPstrengthened reinforced concrete members. Hence, the decision as to which materials will be used in full-scale tests was based on the availability and cost of the two options. Figures in APPENDIX-C show a comparison of the recorded temperatures at various locations in the MBrace Insulation System 1 protected Beam-3 and Beam-4. The data shows that the recorded temperatures within Beam-4 are higher than Beam-3. This variation of temperature is likely due to the difference in thickness, which was 13mm (0.51in.), of the insulating material. The temperature at the FRP/concrete interface reached the glass transition temperature of the FRP system at around 30 minutes of exposure and the rate of increase of temperature remained steady until 84 minutes after which point an abrupt increase in the rate of temperature change was observed. This abrupt increase is thought to be due to the development of cracks within the insulation that caused the debonding of the insulation early in the fire test. The recorded average temperatures of the exposed concrete and the steel reinforcement in the web of the beam specimens were below the temperature limits, which are 140°C (284°F) for the unexposed concrete and 593°C (1099°F) for tension steel reinforcement, as stated in ASTM E119 and ULC S101. The recorded average temperatures in Beam-3 were within the tolerances set by the aforementioned standards. However, a sharp increase in the rate of temperature change was recorded for the steel reinforcement in the flange of Beam-4 about 70 minutes, at which point spalling of concrete from a section of the flange of Beam-4 exposed the reinforcement to the fire in the furnace. After 90 minutes, the average temperature of the steel reinforcement in the flange of Beam-4 reached 593°C (284°F). Regardless, both beam specimens were able to withstand the load applied during the fire test.
13
Load Capacity and Fire Endurance Fire endurance of a building component or assembly is the length of time it can fulfill its load-bearing function or its fire separating function or both when exposed to the standard fire, as previously discussed [6]. ASTM E119 and ULC S101 define failure for loaded unrestrained reinforced concrete beam-slabs and slabs in terms of load carrying-capacity, steel reinforcement temperature, and unexposed surface temperature. The steel reinforcement temperature must be less than 593°C (1099°F). The average temperature of the unexposed face of the specimen must not increase more than 139°C (282°F) and at any individual point the increase in temperature shall be below 180°C (356°F). For loaded restrained reinforced concrete beam-slabs and slabs, the temperature criteria are not required to achieve a fire endurance rating according to ASTM E119. However, maintaining the steel and unexposed concrete temperature below the temperature stated in ASTM E119 would allow the specimen to retain most of its unstrengthened capacity. As mentioned earlier, the slabs did not experience any externally applied load during the fire exposure. The intermediate-scale fire tests of these slabs are beneficial to evaluate the thermal performance of the insulating material. During the fire endurance test, the reinforcement and the unexposed surface of the two slabs satisfied the temperature criteria in ASTM E119. Therefore, both slabs, which were protected with 38mm (1.5 in.) thick insulation, achieved a fire endurance rating of four hours. The beam-slabs successfully resisted the applied load through the duration of the fire endurance test, and therefore achieved a 4 hour fire endurance rating. During the fire endurance test, the steel and the unexposed surface temperature were below the prescribed temperature as in the standard, however, Beam-4 failed the steel temperature criteria prescribed by ASTM E119 after 1.5 hours. Comparison APPENDIX-B and APPENDIX-C provide comparisons of recorded temperatures at various locations in the slabs and beam-slabs, respectively. Shown in the figures are the average temperatures within the insulation, at the FRP sheet interface, at the bottom of the steel reinforcement, and at the unexposed surface of the specimens. SUMMARY This phase of the experimental program consists of fire endurance tests on two intermediate-scale slabs and two full-scale beam-slab assemblies. Both types of members were strengthened with externally-bonded FRP strengthening systems and both were protected with one of two types of supplemental fire insulation materials. From the experimental program, the following conclusions can be drawn: 1. Reinforced concrete beam-slabs that are strengthened with externally-bonded FRP strengthening systems can achieve satisfactory fire endurance ratings of more than four hours with adequate protection from fire. 2. Slabs and beam-slabs with 25mm or greater thickness of the insulation systems described herein satisfied the thermal criteria stated in the ASTM E119 and ULC-S101 standards for more than four hours. However, excess insulation may not be beneficial and proper installation techniques should be adopted for successful fire endurance tests.
14
3. The thermal performances of the two insulating materials used in this study, MBrace Insulation System 1 and 2, were comparable. Thus, the decision as to which materials are used to protect structural building elements should be based on the availability and cost of the two insulating materials. REFERENCES 1. NRC 1995. National Building Code of Canada 1995. National Research Council of Canada. Ottawa 2. Kodur, V.K.R. 1999. Fire Resistance Requirement of FRP Structural Members. Proceedings of the Annual Conference of the Canadian Society for Civil Engineering, Regina, Saskatchewan, pp. 83-95. 3. ACI 2002. ACI 440.2R-02: Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American Concrete Institute, Farmington Hills, MI. 4. CSA 2002. S806: Design and construction of building components with fibre-reinforced polymers. Canadian Standards Association. 177pp. 5. ISIS 2001. Strengthening reinforced concrete structures with externally bonded fibre reinforced polymers. Intelligent Sensing for Innovative Structures Canada, Winnipeg, Manitoba. 6. ASTM 2001. Test Method E119-01: Standard Methods of Fire Test of Building Construction and Materials. American Society for Testing and Materials, West Conshohocken, PA. 7. CAN/ULC 2004. Standard Methods of Fire Endurance Tests of Building Construction and Materials. CAN/ULC-S101-M04, Underwriters’ Laboratories of Canada, Scarborough, ON 8. CSA, 1994. CAN/CSA A23.3-94: Design of Concrete Structures. Canadian Standards Association, Ottawa, Ontario. 9. ACI 2002. Building Code Requirements for Structural Concrete (ACI 318-02/318R-02). American Concrete Institute, Farmington Hills, MI. 10. ACI 1995. Building Code Requirements for Structural Concrete (ACI 318-95). American Concrete Institute, Farmington Hills, Michigan, 369 pgs. 11. ISIS Canada 2001. Reinforcing Concrete Structures with Fibre Reinforced Polymers, ISIS Canada Corporation, Winnipeg, Manitoba. 12. Williams, B.K. 2004. Fire Performance of FRP-Strengthened Reinforced Concrete Flexural Members. Phd thesis, Department of Civil Engineering, Queen’s University, Kingston, Ontario.
15
TABLE-1: Batch quantities and measured properties of concrete for slabs and beam-slabs. Mix Parameter Slabs Specified 28-day Strength 28 Aggregate Type Crushed Limestone Maximum Aggregate Size 14 Type 1 Cement (kg/m3) 280 Type 3 Cement (kg/m3) Coarse Aggregate (kg/m3) 1020 Fine Aggregate (kg/m3) 980 Water (kg/m3) 152 Superplasticizer Mid-range Water Reducer As per MBTa specifications Slump (mm) Max 90 Water-cement Ratio 0.54 a MBT = Master Builders Technologies Inc.
Beam-slabs 41 Crushed Limestone 14 440 1100 632 151 As per MBTa specifications Max 200 0.34
TABLE-2: Summary of test program Specimen Date Cast Date Tested Aggregate FRP (DD/MM/YY) (DD/MM/YY) Type Wrap Slab 3 05/12/02 11/02/04 Carbonate CF 130 Slab 4
05/12/02
11/02/04
Carbonate CF 130
Beam 3
23/09/03
10/11/04
Carbonate CF 130
Beam 4
24/09/03
10/11/04
Carbonate CF 130
Insulation 38mm MBrace Insulation System 1 38mm MBrace Insulation System 2 25 to 38 mm MBrace Insulation System 1 25 to 38 mm MBrace Insulation System 1
TABLE-3: Summary of results of fire endurance tests on slabs and beam-slabs Relative Ambient Moisture Ultimate Applied Failure Fire Failure Humidity Temp. Contenta Load Load Endurance Mode Loadc (%) (kN) (min.) (% vol.) Capacityb (kN/m) (° C) (kN-m) Slab-3 54 18 3.59 > 240 N/A Slab-4 54 18 3.58 > 240 N/A Beam-3 61 5 5.12 123 35 N/A > 270 N/A Beam-4 61 5 5.12 123 35 N/A > 270 N/A a Determined in accordance with ULC S101 [7] b Determined in accordance with ACI 440.2R-02. Refer to Appendix A. c The applied load represents the full unfactored service load, assuming a live-to-dead load ration of 1:1 Specimen
16
NTS
954 305
208
172
305
172
A
208
305
305
1331
305
A
SECTION A-A: 15M steel rebar
10M steel rebar
25
152
NTS
No. of specimens: 8 Reinforcement: 15M (longitudinal) 10M (transverse)
Concrete: 28MPa Aggregate: Carbonate 25mm concrete cover *All dimensions in mm
FIGURE-1: Dimensions and Reinforcement details of Slab-3 and Slab-4
17
ELEVATION:
CROSS SECTION:
26-10M stirrups at 150 o/c 209 wide by 309 high (measured at CL)
400
250 150
1220
3806 47
300 47
3900
CROSS SECTION: Detail
1220
40
All bars 10M unless otherwise specified
40
Clear concrete cover 40 mm to stirrups
100
Spaced at 150 mm o/c along beam
150
150
40 20
40
20M bars
All dimensions in millimeters
40
FIGURE-2: Dimensions and Reinforcement details of Beam-3 and Beam-4
18
Lift hooks 10M bar
15M bar
FIGURE-3: Formwork and nd reinforcement layout for intermediate-scale slabs
FIGURE-4: Steel reinforcement for beam-slab assemblies
19
Internal thermocouple locations
51
A
B 51
LOCATION A
LOCATION B
NTS
NTS CL
CL
29 30
75 100 125
15
31 32
27
33 34 43
28 CL
30 50
26
44
Prime coat MBrace Carbon FRP sheets Insulation primer
45 CL
Insulation
FIGURE-5: Location of thermocouples in slab specimens (all dimensions in mm)
20
ELEVATION:
A
B
C
400
Thermocouple
951.5
951.5
951.5 3806
SECTIONS A & C:
All thermocouples bonded to longitudinal reinforcements
Thermocouples measuring temperature within the exterior layers 16&10: Concrete/FRP, 17&11: FRP/Insulation, 18&12: Insulation/Fire Exposed Surface
94
SECTION B:
156
150
150
60
34
35
36
37
38
29
30
31
32
33
61 (Beam 4)
60 (Beam 3) 27
28
13 (Beam 4)
125
24 22 43 44 45
230
23
51
25 21
35 35 35
15 (Beam 3) 26
Thermocouples measuring temperature within the exterior layers 43: Concrete/FRP, 44: FRP/Insulation, 45: Insulation/Fire Exposed Surface
FIGURE-6: Location of internal thermocouples in beam-slab assemblies (all dimensions in mm)
21
51
17 (A), 11 (C) 18 (A), 12 (C)
47
41 (A) 16 (A), 10 (C)
80
40 (A)
ELEVATION:
D
E
B
F
G
400
Thermocouple
475.8
951.5
475.8
475.8
951.5
3806 1 (D), 2 (E), 9 (G)
SECTIONS D, E & G:
SECTIONS B & F:
3 (B), 6 (F)
4 (B), 7 (F)
320
5 (B), 8 (F)
320
FIGURE-7: Location of thermocouples on the unexposed surface of the beam-slab assemblies (all dimensions in mm)
22
ELEVATION:
A
B
C
400
Displacement Gauge
951.5
951.5
951.5 3806 1 (A), 3 (C)
SECTIONS A & C:
SECTION B:
4
2
320
FIGURE-8: Location of displacement gauges (all dimensions in mm)
23
Concrete Prime coat Insulation Primer
1 layer MBrace CF130 (carbon) composite
Insulation(see table)
Slab-3
Slab-4
Insulation Type
MBrace System 1
MBrace System 2
Thickness
38mm
38mm
FIGURE-9: Strengthening and insulation details for slabs
24
Total Length available= 3900mm (153.5 in.)
1220mm (48 in.)
Shims
Shims 2 layers MBrace CF130 U-Wrap
650mm (25.5")
650mm (25.5")
150mm (6 in.)
MBrace Insulation System 1 25 to 38 mm (1.0/ 1.5 in.) thick
250mm (10 in.) Chamfer: 25mm (1 in.)
Wabo® MBrace CF130
1 layer MBrace CF130 Flexural Strip
Chamfer: 25mm (1 in.)
200mm (8 in.)
C LSupport
C LSupport
300mm (12 in.)
150mm
150mm
Section A
Beam Elevation
N.T.S.
N.T.S.
1220mm (48 in.)
150mm (6 in.)
MBrace Insulation System 1 25 to 38 mm (1.0 to 1.5 in.) thick
250mm (10 in.)
MBrace CF130 U-Wrap MBrace CF130
Material MBrace CF130 Flex-Strip No. of Layers MBrace CF130 U-Wrap No. of Layers MBrace Insulation System 1 (Thickness)
200mm (8 in.) 300mm (12 in.)
Section B N.T.S.
FIGURE-10: Strengthening and insulation details for the beam-slab assemblies
25
BEAM-3 1 2 38 mm (1.5 in.)
BEAM-4 1 2 25 mm (1.0 in.)
(a)
(b)
(c)
(d)
(e)
(f)
FIGURE-11: (a) Movable frame that transfers the beams in and out of the furnace opening; (b) Beam-slab assemblies in the movable frame; (c) End condition – axially restraint; (d) Making grooves for thermocouples using hand grinder; (e) Grooves for thermocouples; (f) Making round edges for the U-wraps.
26
(g)
(h)
(i)
(j)
(k)
(l)
FIGURE-11 (continued): (g) Sand blasting the soffit of beams to have texture for the FRP installation; (h) Thermocouples in the grooves; (i) Installing thermocouples at the concrete/FRP interface with hot glue; (j) Applied primer on the underside of the beams; (k); Tack coat for the installation of FRP-strengthening system (l) Wooden supports to hold the thermocouples in the grooves
27
(m)
(n)
(o)
(p)
(q)
(r)
FIGURE-11 (continued): (m) Installing the flexural FRP strip on the beam web; (n) Installing the FRP U-wraps for anchorage of the flexural strip; (o) Installing thermocouples at the FRP/insulation interface; (p) Spray-applying insulation; (q) Insulated test specimens; (r) Loading frame
28
FIGURE-12: Curing of beams
FIGURE-13: Intermediate-scale furnace for slab slabs and beams
29
FIGURE-14: Full-scale floor furnace for beams and slabs
30
APPENDIX A: LOAD CALCULATIONS FOR FRP-STRENGTHENED REINFORCED CONCRETE BEAM-SLAB ASSEMBLIES This appendix presents detailed load calculations for the beam-slab assemblies tested at the National Research Council, Ottawa, Canada. The load calculations for the unstrengthened specimens were determined according to CSA A23.3-94 [8] and ACI 318-02/318R-02 [9]. Load calculations for the specimens in the strengthened state were determined using ISIS Canada Manual No. 4 [5], ACI 440.2R-02 design guide [3] and CSA S806-02 [4]. Since ULC-S101 [7] is considered equivalent to ASTM E119 [6], the fire endurance tests were conducted according to ULC-S101 [7]. A1. Material Specifications and Properties A summary of the material properties used for calculating the loads are as follows: Table A1: Summary of Material Properties Specimens Materials Beam 3 Concrete & Beam 4
Steel Rebar: 10M (from Mill Report)
Steel Rebar: 20M (from Mill Report)
Carbon FRP, MBrace® CF130 (from Manufacturer)
Properties Density of Concrete, γc : 2350 kg/m3 ’ Compressive Strength, fc : 59 MPa Tensile Strength: Negligible Ultimate Strain: 0.0035 (Can) 0.0030 (U.S.) Yield Strength: 515 MPa Ultimate Strength: 630 MPa Elastic Modulus: 200 MPa Yield Strain: 0.00257 Yield Strength: 494 MPa Ultimate Strength: 659 MPa Elastic Modulus: 200 MPa Yield Strain: 0.00247 Ultimate Strength: 3800 MPa Elastic Modulus: 227 GPa Yield Strain: 0.0167
A2. Dimensions of the beam-slab assemblies The dimensions of the test specimens are shown in Figure A1. These dimensions were chosen, in accordance with CSA A23.3-94 [8] and ACI 318M-99 (ACI, 1999). The overall beam length is 3900 mm. The test span was estimated to be 3860 mm, as shown in Figure A2. A3. Specified Dead and Live Load The National Building Code of Canada (NRC, 1995) requires the weight of all construction materials supported by a structural member be included in the specified dead load. So, to consider the weight of the slabs placed on either side of the beam specimens, a tributary width of 3 m is being used to determine the self weight of the test specimens. Thus, the selfweight of the test specimen is:
31
⎤ ⎛ γ specimen ⋅ 9.81 ⎞ ⎡{(tributary width of slab + beff )× h f } ⎟⎟ ⋅ ⎢ ⎥ 1000 +(hw × bw )⎦ ⎠ ⎣ ⎝
ωself − weight = ⎜⎜
Eqn. A1
⎤ ⎛ 2350 ⋅ 9.81 ⎞ ⎡{( 0.89 × 2 + 1.220 ) × 0.15} =⎜ ⎟⋅⎢ ⎥ +(0.25 × 0.3)⎦ ⎝ 1000 ⎠ ⎣ = 12.10 kN/m
1220 57
150 250
93 339
10M bars 20M bars 300
Figure A1: Dimensions of the beam-slab specimens
Shims
Shims
Total length available = 3962mm
CL support
CL support
Chamfer: 25
Chamfer: 25
150
150
Note: All dimensions in mm
Figure A2: Profile of specimen resting on concrete sills in furnace
32
250mm
150mm
890mm
1220mm
890mm
Fireshield 1350 34 to 25mm thick.
Slab
Slab
MBrace CF130 200mm 300mm
Figure A3: FRP-Insulation System In Eqn. A1, γspecimen is the density of the specimen in kg/m3, beff is the effective width of the beam-slab assembly in m, hf is the thickness of the flange in m, hw is the width of the web in m and bw is the width of the web in m. An additional tributary width of 0.89 m on each side of the beam-slab assembly was considered to account for width of slabs, which would be placed on either side of the beam-slab assembly in a building as shown in Figure A3. According to the National Building Code of Canada (NRC, 1995), a minimum of 1 kPa, due to walls and partitions, must be considered when estimating the specified dead load for a structural member. Therefore, the weight of the partitions is:
ω partitions = 1 kPa ⋅ (Tributary width of 3 m ) = 3.00 kN/m
Eqn. A2
The weight of the insulation system (MBrace Insulation System 1) as shown in Figure A3 is also included in the specified dead load. Two test beam-slab assemblies designated as Beam 3 and Beam 4 had an insulation thickness of 38 mm and 25 mm, respectively. To account for the worst-case scenario, the weight of the insulation was calculated with the lower value among the two thicknesses, which is 25 mm because it would produce a higher superimposed live load from the load calculations.
⎛ γ insulation ⋅ 9.81 ⎞ ⎛ Cross Section Area of ⎟ ⋅ ⎜⎜ 1000 ⎝ ⎠ ⎝ Insulation Material
ωinsulation = ⎜
33
⎞ ⎟⎟ ⎠
Eqn. A3
⎡⎛ Cross Section ⎞ ⎤ ⎟ ⎛ Cross Section ⎞⎥ ⎛ γ insulation ⋅ 9.81 ⎞ ⎢⎜ ⎟⎟⎥ =⎜ ⎟ ⋅ ⎢⎜ Area of Beam ⎟ − ⎜⎜ Area of B eam 1000 ⎝ ⎠ ⎢⎜ ⎠⎥ ⎟ ⎝ ⎣⎝ and Insulation ⎠ ⎦ ⎛ 1335 ⋅ 9.81 ⎞ =⎜ ⎟ ⋅ [(3 ⋅ 0.175 + 0.250 ⋅ 0.35) − (3 ⋅ 0.150 + 0.25 ⋅ 0.3)] ⎝ 1000 ⎠ = 1.15 kN/m where, γinsulation is the density of the insulation in kg/m3, Therefore, the specified dead load is:
ωD = ωself − weight + ω partitions + ωinsulation ω D = 12.10 + 3.00 + 1.15 ω D = 16.25 kN/m
Eqn. A4
Also stated in the National Building Code of Canada (NRC, 1995), the minimum specified uniformly distributed live loads on an area ranges from 1.4 kPa to 4.8 kPa. The required shear force and bending moment for the design of the reinforced concrete beam-slab assemblies was calculated using a uniformly distributed live load of 2.4 kPa. The FRP strengthening system for the reinforced concrete beam-slab assemblies was designed to resist an increased live load of 4.8 kPa. Therefore the required specified live load for the reinforced concrete beam-slab assemblies is:
(ω L )RC
⎛ Specified distributed = ⎜⎜ ⎝ live load of 2.4 kPa = 7.2 kN/m
⎞ ⎟⎟ ⋅ (Tributary width of 3 m ) ⎠
Eqn. A5
And, the required specified live load for the FRP-strengthened reinforced concrete beam-slab assemblies is
(ω L )Strengthend = 14.4 kN/m
⎛ Specified distributed = ⎜⎜ ⎝ live load of 4.8 kPa
⎞ ⎟⎟ ⋅ (Tributary width of 3 m ) ⎠
Eqn. A6
A3.1 Shear Force and Bending Moment according to CSA A23.3-94 [8] Based on CSA A23.3-94 [8], the maximum shear force and bending moment due to specified dead and live load are calculated with load factors stated in Clause 8.3.2.1:
α D = 1.25 α L = 1.50 (ω f )2.4kPa = (α D ⋅ ω D ) + (α L ⋅ ω L )
Eqn. A7
(ω )
Eqn. A8
f
4.8 kPa
= (1.25 × 16.25) + (1.50 × 7.2 ) = 31.11 kN/m = (α D ⋅ ω D ) + (α L ⋅ ω L )
= (1.25 × 16.25) + (1.50 × 14.4) = 41.91 kN/m
34
Therefore, the required shear force and moment capacity of the reinforced concrete beam-slab assemblies is:
(V ) f
2.4 kPa
=
(ω ) f
2.4 kPa
⋅ (Test Span )
2 31.11 × 3.806 = = 59.20 kN 2 (ω f )2.4kPa ⋅ (Test Span)2 (M f )2.4kPa = 8 31.11 × 3.806 2 = = 56.33 kN·m 8
Eqn. A9
Eqn. A10
Therefore, the required moment capacity of the FRP-strengthened reinforced concrete beamslab assemblies is:
(M ) f
4.8 kPa
=
(ω ) f
4.8 kPa
⋅ (Test Span )
2
8 41.91 × 3.806 2 = = 75.89 kN·m 8
Eqn. A11
A3.2 Shear Force and Bending Moment according to ACI 318-02/318R-02 [9] Based on ACI 318-02/318R-02 [9], the maximum shear force and bending moment due to specified dead and live load are calculated using the load resistance factors in Clause C.2.1:
α D = 1.4 α L = 1.7 (ω f )2.4kPa = (α D ⋅ ω D ) + (α L ⋅ ω L )
(ω ) f
4.8 kPa
= (1.4 × 16.25) + (1.7 × 7.2 ) = 34.99 kN/m = (α D ⋅ ω D ) + (α L ⋅ ω L )
= (1.4 × 16.25) + (1.7 × 14.4) = 47.23 kN/m
Therefore, the required shear force and moment capacity of the reinforced concrete beam-slab assemblies is:
(V ) f
2.4 kPa
(M ) f
=
(ω ) f
2.4 kPa
⋅ (Test Span )
2 34.99 × 3.806 = = 66.59 kN 2
2.4 kPa
=
(ω ) f
2.4 kPa
⋅ (Test Span )
2
8 34.99 × 3.806 2 = = 63.36 kN·m 8
35
Therefore, the required moment capacity of the FRP-strenghened reinforced concrete beamslab assemblies is:
(M ) f
4.8 kPa
=
(ω ) f
4.8 kPa
⋅ (Test Span )
2
8 47.23 × 3.806 2 = = 85.52 kN·m 8
Summary of the required shear and flexural strength of the reinforced concrete beamslab assemblies according to Canadian and American codes are given in Table A2 and Table A3. A4. Design Flexural Strength of Reinforced Concrete Beam The reinforced concrete specimens had three layers of flexural reinforcements: 8 No. 10M bars, 6 No. 10M bars and 2 No. 20M bars, as shown in Figure A1. Based on the required reinforcement area for a 2.4 kPa live load, 2 No. 20M bars were adequate to provide the necessary flexural resistance. However, as per Clause 10.5.3, minimum reinforcement was provided in the slab portion so that cracks could be adequately controlled in the tension zone of the slab adjacent to the web. However, a typical designer would consider the flexural strength contribution from the primary steel reinforcement, which in this case is the 2 No. 20M bars [19.5mm diameter and 600mm2 total areas] in the web of the specimen. The effective depth of the primary steel reinforcement is thus:
d = h − cover − diameter of 10M rebar − ( 12 of diameter of 20M rebar ) 19.5 d = 400 − 40 − 11.3 − ≅ 339 mm 2
Eqn. A12
The following assumptions were used in calculating the flexural design strength of the beamslab assemblies: The neutral axis of the beam is within the flange The flexural steel reinforcement have yielded A4.1 Design Flexural Strength according to CSA A23.3-94 [8] According to Clause 10.3.3, the effective flange width is the lesser of:
(b)
Span ⎞ 3806 ⎞ ⎛ ⎛ ⎜2 × ⎟ + bw = ⎜ 2 × ⎟ + 300 = 1822.4 mm > 1220 mm 5 ⎠ 5 ⎠ ⎝ ⎝ 12 × h f = 12 × 150 = 1800 mm > 1220 mm
(c )
1220 mm
(a)
When calculating the design flexural strength according to CSA A23.3-94 [8], the effective width of the flange (beff) was taken to be 1220mm. As dictated in Clauses 8.4.2, 8.4.3, and 10.1.7 of the CSA A23.3-94 [8] design code, the following factors were used in determining the internal forces in concrete and steel.
36
φc = 0.60 φS = 0.85 f c' = 59 MPa
α1 = 0.85 − 0.0015 f c' = 0.76 ≥ 0.67 β1 = 0.97 − 0.0025 f c' = 0.82 ≥ 0.67
Eqn. A13 Eqn. A14
The internal compressive forces in the concrete, C, and tensile forces in the steel, T, are:
(
)
C = φ c ⋅ α 1 f c' ⋅ (β 1 c ) ⋅ b = 0.60 ⋅ (0.76 ⋅ 59) ⋅ (0.82 ⋅ c ) ⋅ 1220 = 26915c T = φ s ⋅ As ⋅ f y = 0.85 ⋅ 600 ⋅ 494 = 251940
Eqn. A15 Eqn. A16
α1fc’ εcu β1 c c
C
d
εs
T
Strain Profile
Stress-block Profile
Figure A4: Stress-Strain Distribution for the reinforced concrete T-beam Equating the compressive and tensile forces for equilibrium, the neutral axis, c, is: C =T Eqn. A17
26915c = 251940 c = 9.36 mm
To verify the assumption that the steels have yielded, the strains of the tensile steels were calculated using c:
37
⎛d −c⎞ ⎟ ⎝ c ⎠ ⎛ 339 − 9.36 ⎞ = 0.0035 ⋅ ⎜ ⎟ = 0.1232 > ε y = 0.0025 As assumed ⎝ 9.36 ⎠
ε s = ε cu ⋅ ⎜
Eqn. A18
where, εcu is the maximum compression strain of concrete which is taken to be 0.0035 as stated in Clause 10.1.3. Taking moments about the compressive force, C, the sectional moment resistance was calculated as:
β c⎞ ⎛ M r = T ⋅ ⎜d − 1 ⎟ 2 ⎠ ⎝ ⎛ ⎛ 0.82 ⋅ 9.36 ⎞ ⎞ M r = 251940 ⋅ ⎜⎜ 339 − ⎜ ⎟ ⎟⎟ 2 ⎝ ⎠⎠ ⎝ M r = 251940 ⋅ (339 − 3.84 )
Eqn. A19
M r = 84.44 × 10 6 N·mm = 84.44 kN·m > M f = 56.33 kN·m A4.2 Design Flexural Strength according to ACI 318-02/318R-02 [9] According to Clause 8.10.2, the effective flange width shall not exceed
(a) (b)
1 4
× Span = 14 × 3806 = 951.5 mm < 1220 mm
2 ⋅ (8 × h f ) + bw = 2 ⋅ (8 × 150 ) + 300 = 2700 mm > 1220 mm
Therefore, the effective flange width (beff) is 951.5mm as it is the lesser of the values stated above. As stated in Clauses 10.2.7.3 and 9.3.2.1 of ACI 318-02/318R-02 [9] code, the following factors were used in determining the internal forces in concrete and steel.
β 1 = 0.65 φ = 0.90
The internal compressive forces in the concrete, C, and tensile forces in the steel, T, are: C = 0.85 f c' ⋅ b ⋅ (β 1 c ) = 0.85 ⋅ 59 ⋅ 951.5 ⋅ (0.65 ⋅ c ) = 31017c Eqn. A20
T = As ⋅ f y = 600 ⋅ 494 = 296400
Eqn. A21
Equating the compressive and tensile forces for equilibrium, the neutral axis depth, c, is:
C =T 31017c = 296400
c = 9.55 mm To verify the assumption that the steels have yielded, the strains of the tensile steels were calculated using ‘c’:
⎛d −c⎞ ⎟ ⎝ c ⎠
ε s = ε cu ⋅ ⎜
38
⎛ 339 − 9.55 ⎞ ⎟ = 0.1035 > ε y = 0.0025 ⎝ 9.55 ⎠
ε s = 0.0030 ⋅ ⎜
As assumed
where, εcu is the maximum compression strain of concrete which is taken to be 0.0030 as stated in Clause 10.2.3. Taking moments about the compressive force, C, the sectional moment resistance was calculated as:
⎡ ⎛ β c ⎞⎤ M r = φ ⋅ M n = 0.90 ⋅ ⎢T ⋅ ⎜ d − 1 ⎟⎥ 2 ⎠⎦ ⎣ ⎝ ⎡ ⎛ ⎛ 0.65 ⋅ 9.55 ⎞ ⎞⎤ M r = 0.90 ⋅ ⎢296400 ⋅ ⎜⎜ 339 − ⎜ ⎟ ⎟⎟⎥ 2 ⎝ ⎠ ⎠⎦ ⎝ ⎣
Eqn. A22
M r = 0.90 ⋅ [296400(339 − 3.10)]
M n = 89.60 × 106 N·mm = 89.60 kN·m > 63.36 kN·m Summary of the design flexural strength of the reinforced concrete beam-slab assemblies according to Canadian and American codes are given in Table A2. A5. Flexural Capacity of FRP-Strengthened Reinforced Concrete Beam As before, this section provides detailed calculations for the strengthened reinforced concrete beam. A5.1 FRP-Strengthening System The flexural strengthening scheme includes a CFRP sheet of 200 mm width applied to the bottom of the web. Only one layer of CFRP sheet, having a thickness of 0.165 mm, was applied. A5.2 Design Flexural Strength according to ISIS Canada Guidelines Based on ISIS Canada Manual No. 4 [5], the material resistance factor for FRP material is:
φ frp = 0.75
The following strain relationships were derived:
⎛d −c⎞ ⎛ 339 − c ⎞ ⎟ = 0.0167 ⋅ ⎜ ⎟ ⎝h−c⎠ ⎝ 400 − c ⎠ ⎛ c ⎞ ⎛ c ⎞ ⋅⎜ ⎟ = 0.0167 ⋅ ⎜ ⎟ ⎝h −c⎠ ⎝ 400 − c ⎠
ε s = ε fu ⋅ ⎜
Eqn. A23
ε c = ε fu
Eqn. A24
where, εfu is the ultimate strain of FRP stated by the manufacturer and h is the total height of the beam. At ultimate condition, the concrete compressive strain is less than the ultimate concrete strain, εcu, when failure is assumed through FRP rupture. So, the depth of neutral axis, c, was
39
assumed and using an iterative process described in ISIS Design Manual No.3 (ISIS Canada, 2001a), the coefficients α and β were determined as shown below. The elastic modulus of concrete was determined as stated in Clause 8.6.2.2 in CSA A23.2-94.
α1fc’ εcu β1 c c
d
C
400
εs
T εfrp
Tfrp
Strain Profile
Stress-block Profile
Figure A5: Stress-Strain Distribution of FRP-strengthened RC beam
(
)
⎛ γ ⎞ E c = 3300 f + 6900 ⎜ c ⎟ ⎝ 2300 ⎠ ' c
1.5
Eqn. A25
where, γc is the density of concrete in kg/m3
(
)
⎛ 2350 ⎞ E c = 3300 59 + 6900 ⎜ ⎟ ⎝ 2300 ⎠ E c = 33305 MPa
1.5
Assuming c = 25 mm, the strain of concrete was determined using Eqn. A24:
⎛ 25 ⎞ −3 ⎟ = 1.113 × 10 < ε cu 400 − 25 ⎝ ⎠
ε c = 0.0167 ⋅ ⎜
Using Figures 6.4 and 6.5 in the ISIS Design Manual No.3 (ISIS Canada, 2001a), the following values were estimated for the stress-block coefficients ‘α’ and ‘β’.
α = 0.48 β = 0.67
40
Therefore, the internal compressive and tensile forces are as follows:
( )
C = φ c ⋅ αf c' ⋅ (βc ) ⋅ b = 0.60 ⋅ (0.48 ⋅ 59) ⋅ (0.67 ⋅ 25) ⋅ 1220 = 347232 T = φ s ⋅ As ⋅ f y = 0.85 ⋅ 600 ⋅ 494 = 251940 T frp = φ frp ⋅ A frp ⋅ f fu = 0.75 ⋅ (0.165 × 200 ) ⋅ 3800 = 94050
Eqn. A26 Eqn. A27 Eqn. A28
Since C ≈ Σ T, c equals 25 mm as assumed. The strains in the steel are calculated using Eqn. A23.
⎛ 339 − 25 ⎞ ⎟ = 0.0140 > ε y ⎝ 400 − 25 ⎠
ε s = 0.0167 ⋅ ⎜
As assumed
Therefore, taking moments about the compressive force, C, the design flexural resistance of the strengthened section is:
βc ⎞ βc ⎞ ⎛ ⎛ M r = T ⋅ ⎜d − ⎟ + T frp ⋅ ⎜ h − ⎟ 2 ⎠ 2 ⎠ ⎝ ⎝ ⎛ ⎛ ⎛ 0.67 ⋅ 25 ⎞ ⎞ ⎛ 0.67 ⋅ 25 ⎞ ⎞ M r = 251940 ⋅ ⎜⎜ 339 − ⎜ ⎟ ⎟⎟ + 94050 ⋅ ⎜⎜ 400 − ⎜ ⎟ ⎟⎟ 2 2 ⎝ ⎠⎠ ⎝ ⎠⎠ ⎝ ⎝
Eqn. A29
M r = 251940 ⋅ (339 − 8.38) + 94050 ⋅ (400 − 8.38)
M r = 120.13 × 10 6 N·mm = 120.13 kN·m > 75.89 kN·m A5.3 Flexural Capacity according to ACI 440.2R-02 [3] When calculating the design flexural strength of the FRP-strengthened beam specimens, based on ACI 440.2R-02 [3], flexural reduction factor was taken as dictated in Clause 9.6.1 of ACI 440.2R-02 [3].
ψ frp = 0.85
Since the test specimens were not exposed to any severe environmental conditions prior to testing, the manufacturer specified material properties were used in calculating the design flexural strength. Furthermore, a bond-dependent coefficient, κm, is used to limit the strain in the laminate at failure as stated in Clause 9.2 of ACI 440.2R-02 [3]. nE f t f = 1 ⋅ 227 × 10 3 ⋅ 0.165 = 37455 < 180000 Eqn. A30 where, n is the number of layers of laminates, Ef is the elastic modulus of the FRP laminate and tf is the thickness of each layer of FRP laminate. The bond-dependent coefficient is calculated as stated in Clause 9.2 of ACI 440.2R-02 [3] design code.
nE f t f ⎞ ⎛ ⎜1 − ⎟ ⎜ 360000 ⎟ ⎝ ⎠ 1 37455 ⎞ ⎛ = ⎜1 − ⎟ = 0.894 ≤ 0.90 60 ⋅ 0.0167 ⎝ 360000 ⎠
κm =
1 60ε fu
Eqn. A31
Therefore, the effective strain εfe in the FRP laminate at ultimate is:
ε fe = κ m ⋅ ε fu = 0.894 ⋅ 0.0167 = 0.0149
Eqn. A32
41
Using the effective strain in the FRP laminate, the strain relationships for the steel and concrete were derived as follows:
⎛d −c⎞ ⎛ 339 − c ⎞ ⎟ = 0.0149 ⋅ ⎜ ⎟ ⎝h−c⎠ ⎝ 400 − c ⎠ ⎛ c ⎞ ⎛ c ⎞ ⋅⎜ ⎟ = 0.0149 ⋅ ⎜ ⎟ ⎝h −c⎠ ⎝ 400 − c ⎠
ε s = ε fe ⋅ ⎜
Eqn. A33
ε c = ε fe
Eqn. A34
Thus, the internal compressive and tensile forces are as follows:
C = 0.85 f c' ⋅ (β 1 c ) ⋅ b = 0.85 ⋅ 59 ⋅ (0.65 ⋅ c ) ⋅ 951.5 = 31017c T = As ⋅ f y = 600 ⋅ 494 = 296400
Eqn. A35 Eqn. A36
T frp = A frp ⋅ ε fe ⋅ E f = (0.165 × 200 ) ⋅ 0.0149 ⋅ 227 × 10 3 = 111616
Eqn. A37
Equating the compressive and tensile forces for equilibrium, the neutral axis depth c from the extreme compression fibre is: C = T + T frp Eqn. A38
31017c = 296400 + 111616 c = 13.15 mm Therefore, the strains in the concrete and steel are calculated using Eqn. A33.
⎛ 339 − 13.15 ⎞ ⎟ = 0.0126 > ε y ⎝ 400 − 13.15 ⎠ ⎛ 13.15 ⎞ ε c = 0.0149 ⋅ ⎜ ⎟ = 0.0005 < ε cu ⎝ 400 − 13.15 ⎠
ε s = 0.0149 ⋅ ⎜
As assumed As assumed
Therefore, the ultimate flexural resistance of the strengthened section is:
⎡ ⎛ β c⎞ β c ⎞⎤ ⎛ Eqn. A39 M r = φ ⋅ ⎢T ⋅ ⎜ d − 1 ⎟ + ψ frp ⋅ T frp ⋅ ⎜ h − 1 ⎟⎥ 2 ⎠ 2 ⎠⎦ ⎝ ⎣ ⎝ ⎡ ⎛ ⎛ ⎛ 0.65 ⋅ 13.15 ⎞ ⎞ ⎛ 0.65 ⋅ 13.15 ⎞ ⎞⎤ M r = 0.90 ⋅ ⎢296400 ⋅ ⎜⎜ 339 − ⎜ ⎟ ⎟⎟ + 0.85 ⋅ 111616 ⋅ ⎜⎜ 400 − ⎜ ⎟ ⎟⎟⎥ 2 2 ⎝ ⎠⎠ ⎝ ⎠ ⎠⎦ ⎝ ⎝ ⎣
M r = 0.90 ⋅ [296400 ⋅ (339 − 4.27 ) + 0.85 ⋅ 111616 ⋅ (400 − 4.27 )] M r = 123.08 × 10 6 N·mm = 123.08 kN·m > 85.52 kN·m
A5.4 Flexural Capacity according to CSA S806-02 [4] Based on CSA S806-02 [4], the material resistance factor for FRP material is:
φ frp = 0.75
The maximum tensile strain, according to CSA S806-02 [4], in the FRP laminate is limited to 0.007, that is, ε frp = 0.007 .
42
⎛d −c⎞ ⎛ 339 − c ⎞ ⎟ = 0.007 ⋅ ⎜ ⎟ ⎝h−c⎠ ⎝ 400 − c ⎠ ⎛ c ⎞ ⎛ c ⎞ ⋅⎜ ⎟ = 0.007 ⋅ ⎜ ⎟ ⎝h−c⎠ ⎝ 400 − c ⎠
ε s = ε frp ⋅ ⎜
Eqn. A40
ε c = ε frp
Eqn. A41
As before at ultimate, the concrete compressive strain is less than εcu, so the depth of neutral axis, c, is assumed and using an iterative process described in ISIS design guidelines, the stress-block coefficients α and β were determined. Assuming c = 34.8 mm, the concrete strain was determined using Eqn. A41
⎛ 34.8 ⎞ −3 ⎟ = 0.67 × 10 ⎝ 400 − 34.8 ⎠
ε c = 0.007 ⋅ ⎜
Using Figures 6.4 and 6.5 in the ISIS Canada Design Manual No. 3 (ISIS, 2001a), the following values were determined for the coefficients α and β.
α = 0.29 β = 0.67
Therefore, the internal compressive and tensile forces are as follows:
( )
C = φ c ⋅ αf c' ⋅ (βc ) ⋅ b = 0.60 ⋅ (0.29 ⋅ 59) ⋅ (0.67 ⋅ 34.8) ⋅ 1220 = 292022 T = φ s ⋅ As ⋅ f y = 0.85 ⋅ 600 ⋅ 494 = 251940
T frp = φ frp ⋅ A frp ⋅ ε frp ⋅ E f = 0.75 ⋅ (0.165 × 200 ) ⋅ 0.007 ⋅ 227 × 10 3 = 39328
Eqn. A42
Since C ≈ Σ T, c is 34.8 mm as assumed. The strains in the concrete and steel are:
⎛ 339 − 34.8 ⎞ ⎟ = 0.0058 > ε y ⎝ 400 − 34.8 ⎠ ⎛ 23 ⎞ ε c = 0.007 ⋅ ⎜ ⎟ = 0.0004 < ε cu ⎝ 400 − 23 ⎠
ε s = 0.007 ⋅ ⎜
As assumed As assumed
Therefore, the ultimate flexural resistance of the strengthened section is:
βc ⎞ βc ⎞ ⎛ ⎛ M r = T ⋅ ⎜d − ⎟ + T frp ⋅ ⎜ h − ⎟ 2 ⎠ 2 ⎠ ⎝ ⎝ ⎛ ⎛ ⎛ 0.67 ⋅ 34.8 ⎞ ⎞ ⎛ 0.67 ⋅ 34.8 ⎞ ⎞ M r = 251940 ⋅ ⎜⎜ 339 − ⎜ ⎟ ⎟⎟ + 39328 ⋅ ⎜⎜ 400 − ⎜ ⎟ ⎟⎟ 2 2 ⎝ ⎠⎠ ⎝ ⎠⎠ ⎝ ⎝ M r = 251940 ⋅ (339 − 11.66 ) + 39328 ⋅ (400 − 11.67 ) M r = 97.74 × 10 6 N·mm = 97.74 kN·m > 75.89 kN·m Summary of the design flexural strength of the FRP-strengthened concrete beam-slab assemblies according to Canadian and American codes are given in Table A2.
43
A6. Service Capacity of FRP-Strengthened Reinforced Concrete Beam As per Clause 9.4 in ACI 440.2R-02 [3] and Clause 4.8.1 in ISIS Canada Design Manual No.4 [5], the stress in the steel under service load conditions should be limited to 80% of the yield strength. The flexural capacity at service is thus determined by taking the material resistance factor to be 1.0. A6.1 Service Load Capacity according to ISIS Canada Guidelines The strain relationships for this case are as follows:
⎛h−c⎞ ⎛ 400 − c ⎞ ⎟ = 0.80 ⋅ 0.0025 ⋅ ⎜ ⎟ ⎝d −c⎠ ⎝ 339 − c ⎠ ⎛ 400 − c ⎞ = 0.002 ⋅ ⎜ ⎟ ⎝ 339 − c ⎠
ε frp = 0.80ε y ⋅ ⎜ ε frp
Eqn. A43
⎛ c ⎞ ⎛ c ⎞ ⎟ = 0.80 ⋅ 0.0025 ⋅ ⎜ ⎟ ⎝d −c⎠ ⎝ 339 − c ⎠ ⎛ c ⎞ ε c = 0.002 ⋅ ⎜ ⎟ ⎝ 339 − c ⎠
ε c = 0.80ε y ⋅ ⎜
Eqn. A44
The elastic modulus of concrete E c is 33305 MPa as calculated in Eqn. A25. Therefore, the compressive and tensile forces become:
⎡ ⎤ ⎛ c ⎞ C = φc ⋅ 0.5 ⋅ (ε c ⋅ Ec ) ⋅ c ⋅ b = 1.0 ⋅ 0.5 ⋅ ⎢0.002 ⋅ ⎜ ⎟ ⋅ 33305⎥ ⋅ c ⋅ 1220 ⎝ 339 − c ⎠ ⎣ ⎦ 2 ⎛ c ⎞ ⎟⎟ C = 40632 ⋅ ⎜⎜ − c 339 ⎝ ⎠ T = φ s ⋅ As ⋅ 0.80 f y = 1.0 ⋅ 600 ⋅ 0.80 ⋅ 494 = 237120
Eqn. A45 Eqn. A46
⎛ 400 − c ⎞ 3 T frp = φ frp ⋅ A frp ⋅ ε frp ⋅ E frp = 1.0 ⋅ (0.165 × 200) ⋅ 0.002 ⋅ ⎜ ⎟ ⋅ 227 × 10 ⎝ 339 − c ⎠ ⎛ 400 − c ⎞ T frp = 14982 ⋅ ⎜ ⎟ ⎝ 339 − c ⎠
Eqn. A47
The neutral axis depth was determined using Eqn. A38 is:
C = T + T frp ⎛ c2 ⎞ ⎛ 400 − c ⎞ ⎟⎟ = 237120 + 14982 ⋅ ⎜ 40632 ⋅ ⎜⎜ ⎟ ⎝ 339 − c ⎠ ⎝ 339 − c ⎠ c = 43.11 mm The strains in the FRP and concrete are calculated using Eqn. A43 to Eqn. A44.
⎛ 400 − 43.11 ⎞ ⎟ = 0.00241 < ε frp ⎝ 339 − 43.11 ⎠
ε frp = 0.002 ⋅ ⎜
As assumed
44
⎛ 43.11 ⎞ ⎟ = 0.000291 < ε cu ⎝ 339 − 43.11 ⎠
ε c = 0.002 ⋅ ⎜
As assumed
Therefore, the maximum allowable service moment of the strengthened section is:
c⎞ c⎞ ⎛ ⎛ M r = T ⋅ ⎜ d − ⎟ + T frp ⋅ ⎜ h − ⎟ 3⎠ 3⎠ ⎝ ⎝ 43.11 ⎞ 43.11 ⎞ ⎛ ⎛ M r = 237120 ⋅ ⎜ 339 − ⎟ + 18071 ⋅ ⎜ 400 − ⎟ 3 ⎠ 3 ⎠ ⎝ ⎝ M r = 237120 ⋅ (339 − 14.37 ) + 18071 ⋅ (400 − 14.37 )
Eqn. A48
M r = 83.94 × 10 6 N·mm = 83.94 kN·m A6.2 Service Load Capacity according ACI 440.2R-02 [3] The concrete elastic modulus, Ec, as stated in Clause 8.5.1 of ACI 318/318R-02 [3]:
γ c = 2350 kg/m 3 (147 lb/ft 3 ) f c' = 59 MPa (8557 psi)
Ec = γ c ⋅ 33 f c' = (147 ) ⋅ 33 8557 = 5440649 psi 1.5
1.5
Eqn. A49
Ec = 37512 MPa In Eqn. A31 and Eqn. A32, the bond-dependent coefficient ( κ m ) and effective strain in the FRP laminate ( ε fe ) was calculated to be as follows:
κ m = 0.894 ≤ 0.90
&
ε fe = 0.0149
The strain of FRP and concrete can be expressed as Eqn. A43 and Eqn. A44.
⎛ 400 − c ⎞ ⎟ ⎝ 339 − c ⎠ ⎛ c ⎞ ε c = 0.002 ⋅ ⎜ ⎟ ⎝ 339 − c ⎠
ε frp = 0.002 ⋅ ⎜
Using Eqn. A43 and Eqn. A44, the compressive and tensile forces become:
⎡ ⎤ ⎛ c ⎞ C = 0.5 ⋅ (ε c ⋅ Ec ) ⋅ c ⋅ b = 0.5 ⋅ ⎢0.002 ⋅ ⎜ ⎟ ⋅ 37512⎥ ⋅ c ⋅ 951.5 ⎝ 339 − c ⎠ ⎣ ⎦ 2 ⎞ ⎛ c ⎟⎟ C = 35693 ⋅ ⎜⎜ ⎝ 339 − c ⎠ T = As ⋅ 0.80 f y = 600 ⋅ 0.80 ⋅ 494 = 237120 ⎛ 400 − c ⎞ 3 T frp = A frp ⋅ ε frp ⋅ E frp = (0.165 × 200) ⋅ 0.002 ⋅ ⎜ ⎟ ⋅ 227 × 10 339 − c ⎝ ⎠
45
Eqn. A50
⎛ 400 − c ⎞ T frp = 14982 ⋅ ⎜ ⎟ ⎝ 339 − c ⎠ Equating the compressive and tensile forces for equilibrium, the neutral axis depth c is:
C = T + T frp ⎛ c2 ⎞ ⎛ 400 − c ⎞ ⎟⎟ = 237120 + 14982 ⋅ ⎜ 35693 ⋅ ⎜⎜ ⎟ ⎝ 339 − c ⎠ ⎝ 339 − c ⎠ c = 45.79 mm The strains in the FRP and concrete are:
⎛ 400 − 45.79 ⎞ ⎟ = 0.00242 < ε frp ⎝ 339 − 45.79 ⎠ ⎛ 45.79 ⎞ ε c = 0.002 ⋅ ⎜ ⎟ = 0.000312 < ε cu ⎝ 339 − 45.79 ⎠
ε frp = 0.002 ⋅ ⎜
As assumed As assumed
Therefore, the maximum allowable service moment of the strengthened section is:
c⎞ c⎞ ⎛ ⎛ M r = T ⋅ ⎜ d − ⎟ + ψ frp ⋅ T frp ⋅ ⎜ h − ⎟ 3⎠ 3⎠ ⎝ ⎝ 45.79 ⎞ 45.79 ⎞ ⎛ ⎛ M r = 237120 ⋅ ⎜ 339 − ⎟ + 0.85 ⋅ 18099 ⋅ ⎜ 400 − ⎟ 3 ⎠ 3 ⎠ ⎝ ⎝ M r = 237120 ⋅ (339 − 15.26) + 0.85 ⋅ 18099 ⋅ (400 − 15.26)
Eqn. A51
M r = 82.68 × 10 6 N·mm = 82.68 kN·m A7. Superimposed Fire Test Loads As stated in ULC-S101 [7], a superimposed load must be applied to the test specimens to simulate the stress level under full specified service load or maximum working load during a fire endurance test. Using the ultimate and service moment capacities of the specimens, the uniformly distributed load for the tests can be calculated. A summary of the relationships used to derive the equations that will calculate the superimposed load is provided in this section of the Appendix. A7.1 Equations for determining the superimposed load Factoring the specified load gives the following relationship in Eqn. A52
ω f = α Dω D + α Lω L Eqn. A52 where, ω f is the factored total load, α D and α L are the dead and live load factors, and ω D and ω L are the dead and live dead loads. The dead to live load ratio is expressed as in Eqn. A53:
46
r=
ωD ωL
Eqn. A53
Rearranging Eqn. A53,
ω D = rω L
Eqn. A54
According to ULC-S101 [7], a dead to live load ratio of 1.0 may be used to reflect the actual inservice conditions. Rearranging Eqn. A54,
ωD = ωL
Eqn. A55
Substituting Eqn. A55 in Eqn.A52,
ω f = α Dω D + α Lω D ω f = (α D + α L ) ⋅ ω D ωf ωD = (α D + α L )
Similarly,
ωL =
Eqn. A56 Eqn. A57 Eqn. A58
ωf
Eqn. A58
(α D + α L )
A7.1.1 ISIS Canada Guidelines [5] and CSA S806-02 [4] According to ULC-S101, the total specified load in fire ( ω fire ) should be expressed as Eqn. A59.
ω fire = ω D + ω L ωf ωf + ω fire = (α D + α L ) (α D + α L ) Therefore,
ω fire = But,
Eqn. A59 Eqn. A60
2ω f
Eqn. A61
(α D + α L )
ω fire = ω super + ω s.w Eqn. A62 where, ω super is the superimposed load during the fire test and ω s.w the self-weight of the beam and insulation.
ω super = ω fire − ω s.w
Eqn. A63
Substituting Eqn. A61 in Eqn. A63,
ω super =
2ω f
(α D + α L )
− ω s.w
Eqn. A64
47
But,
ωf =
8M r L2
Eqn. A65
Substituting Eqn. A65 in A64, the superimposed load from the ultimate strengthened capacity based on ISIS Canada Manual No. 4 [5] and CSA S806-02 [4] can be determined using Eqn. A66.
⎛
2
⎞ 8M
⎟⎟ ⋅ 2 R − ω s.w ω super = ⎜⎜ α α + L L ⎠ ⎝ D
Eqn. A66
Modifying Eqn. A66, where the load factors are takes as 1.0, the superimposed from the service capacity based on ISIS Canada Manual No. 4 [5] and CSA S806-02 [4] can be determined using Eqn. A67.
2 ⎛ ⎞ 8M s ⎟ ⋅ 2 − ω s.w ⎝ 1.0 + 1.0 ⎠ L 8M = 2 s − ω s.w L
ω super = ⎜
Eqn. A66
ω super
Eqn. A67
A7.1.2 ACI 440.2R-02 [3] In Section C2.5 of ASCE 7-02 standard (ASCE, 2002), the total specified load in an extraordinary event such as fire should be expressed as shown in Eqn. A68. ω fire = 1.2ω D + 0.5ω L Eqn. A68 Therefore,
ω fire =
1.2ω f
+
0.5ω f
Eqn. A69
(α D + α L ) (α D + α L )
Using similar derivation procedure demonstrated in Section A7.1.2 of this thesis, the following equations were derived.
ω fire =
1.7ω f
Eqn. A70
(α D + α L )
ω super =
1.7ω f
(α D + α L )
− ω s.w
Eqn. A71
⎞ 8M R ⎟⎟ ⋅ 2 − ω s.w ⎠ L ⎛ 1.7 ⎞ 8M s =⎜ ⎟ ⋅ 2 − ω s.w ⎝ 1.0 + 1.0 ⎠ L 6.8M s = − ω s.w L2 ⎛
1.7
ω super = ⎜⎜ ⎝αD + αL
Eqn. A72
ω super
Eqn. A73
ω super
Eqn. A74
A7.1.2 Self-weight of the insulated FRP-Strengthened Beam-Slab Assemblies To determine the self-weight of the T-beam specimens, the weight of the slabs placed on either side of the beam specimens were not considered as demonstrated in Section A3 of this thesis.
48
⎛ γ specimen ⋅ 9.81 ⎞ ⎟ ⋅ (beff × h f ) + (hw × bw ) ⎟ 1000 ⎠ ⎝ ⎛ 2350 ⋅ 9.81 ⎞ =⎜ ⎟ ⋅ [(1.220 × 0.15) + (0.25 × 0.3)] ⎝ 1000 ⎠ = 5.95 kN/m
[
ω T −beam = ⎜⎜
]
⎛ γ insulation ⋅ 9.81 ⎞ ⎛ Cross Section Area of ⎞ ⎟⎟ ⎟ ⋅ ⎜⎜ 1000 ⎠ ⎝ Insulation Material ⎠ ⎝ ⎡⎛ Cross Section ⎞ ⎤ ⎟ ⎛ Cross Section ⎞⎥ ⎛ γ insulation ⋅ 9.81 ⎞ ⎢⎜ ⎟⎟⎥ =⎜ ⎟ ⋅ ⎢⎜ Area of Beam ⎟ − ⎜⎜ Area of B eam 1000 ⎠ ⎢⎜ ⎝ ⎠⎥ ⎝ ⎟ ⎣⎝ and Insulation ⎠ ⎦
ωinsulation = ⎜
Eqn. A75
Eqn. A76
⎛ 1335 ⋅ 9.81 ⎞ =⎜ ⎟ ⋅ [(1.220 ⋅ 0.175 + 0.250 ⋅ 0.35) − (1.220 ⋅ 0.150 + 0.25 ⋅ 0.3)] ⎝ 1000 ⎠ = 0.56 kN/m Therefore, the self-weight is:
ω s.w = ω T −beam + ω insulation ω s.w = 5.95 + 0.56 ω s.w = 6.51 kN/m
Eqn. A77
A7.2 Superimposed Test Load from ISIS Canada Guidelines [5] The design flexure strength using the ISIS Canada guidelines [5] was calculated to be 120.13 kN·m at ultimate condition and 83.94 kN·m at service condition. As per CSA codes, the dead load factor (αD) and live load factor (αL) are 1.25 and 1.5, respectively. The superimposed test load from ultimate condition using Eqn. A65, where ω s .w kN/m:
⎛
2
is
6.51
⎞ 8M
⎟⎟ ⋅ 2 R − 6.51 ω super = ⎜⎜ ⎝αD + αL ⎠ L
2 ⎞ 8 ⋅ 120.13 ⎛ − 6.51 = 41.74 kN/m ⎟⋅ 2 ⎝ 1.25 + 1.5 ⎠ 3.806
ω super = ⎜
The superimposed test load from service condition using Eqn. A67 where ω s .w is kN/m:
ω super = ω super
8M s
− ω s.w L2 8 ⋅ 83.94 = − 6.51 = 39.83 kN/m 3.806 2
49
6.51
A7.2 Superimposed Test Load from ACI 440.2R-02 [3] The design flexure strength using the ACI 440.2R-02 [3] was calculated to be 123.08 kN·m at ultimate condition and 82.68 kN·m at service condition. As per ACI 440.2R-02 [3], the dead load factor (αD) and live load factor (αL) are 1.4 and 1.7, respectively. The superimposed test load from ultimate condition using Eqn. A72, where ω s .w kN/m:
⎛
1.7
is
6.51
⎞ 8M
⎟⎟ ⋅ 2 R − 6.51 ω super = ⎜⎜ α α + L L ⎠ ⎝ D
⎛ 1.7 ⎞ 8 ⋅ 123.08 − 6.51 = 30.77 kN/m ⎟⋅ 2 ⎝ 1.4 + 1.7 ⎠ 3.806
ω super = ⎜
The superimposed test load from service condition using Eqn. A74, where ω s .w is kN/m:
ω super = ω super
6.51
6.8M s
− 6.51 L2 6.8 ⋅ 82.68 = − 6.51 = 32.30 kN/m 3.806 2
A7.3 Superimposed Test Load from CSA S806-02 [4] The design flexure strength using the CSA S806-02 standard [4] was calculated to be 97.74 kN·m. As per CSA codes, the dead load factor (αD) and live load factor (αL) are 1.25 and 1.5, respectively. Using the derived Eqn. A65, the superimposed load was calculated as below.
⎞ 8M R ⎟⎟ ⋅ 2 − 6.51 ⎠ L 2 ⎞ 8 ⋅ 97.74 ⎛ − 6.51 = 32.75 kN/m =⎜ ⎟⋅ 2 ⎝ 1.25 + 1.5 ⎠ 3.806 ⎛
2
ω super = ⎜⎜ ⎝αD + αL
ω super
A8. Strengthening Limits As stated in Clause 8.2 of ACI 440.2R-02 [3], limits must be imposed to safeguard against collapse of the structure for bond or other failure of the FRP system due to fire, vandalism or any other causes. In the case that the FRP system fails, it is recommended in ACI 440.2R-02 [3] that the existing strength of the structure should be sufficient to resist a load level as described by the following equation:
(φRn )existing ≥ (1.2ω DL + 0.85ω LL )new
Eqn. A78
where, ωDL is the strengthened dead load effects and ωLL is the strengthened live load effects. To check the strengthening limits, the superimposed loads from the ultimate conditions were calculated.
50
ω DL = 6.51 kN/m ω LL = 30.77 kN/m 1.2 ⋅ ω DL ⋅ L2 1.2 ⋅ 6.51 ⋅ 3.806 2 = = 14.14 kN·m 8 8 0.85 ⋅ ω LL ⋅ L2 0.85 ⋅ 30.77 ⋅ 3.806 2 (0.85M LL ) new = = = 47.36 kN·m 8 8 (φM n )existing = 89.60 kN·m
(1.2 M DL ) new =
Therefore,
(1.2M DL + 0.85M LL ) = (14.14 + 47.36) = 61.5 kN·m ≤ 89.66 kN·m
A9. Required Jack Stress during Fire Test The fire test will be conducted at the Institute for Research in Construction of the National Research Council Laboratory in Ottawa. The test furnace is equipped with a loading system of 30 hydraulic jacks. A set of 6 jacks delivers the load to the beam. Each of these jacks has a jack head diameter of 63.5mm and a maximum stress of approximately 24 MPa. Thus, the required jack stress during the fire test has been determined using the superimposed live load at ultimate condition (33 kN/m) from CSA-S806 design codes
Total Load Needed
= 33 kN/m × Test Span = 33 kN/m × 3.806 m
= 125.6 kN = 125600 N Force Needed in each Jack = 1 6 of Total Load = 1 6 × 125600 = 20933 N 2
Eqn. A79
Eqn. A80
2
⎛ 63.5 ⎞ ⎛ diameter ⎞ 2 Jack Area = π ⋅ ⎜ ⎟ = 3167 mm ⎟ =π ⋅⎜ 2 2 ⎠ ⎝ ⎠ ⎝ 1 of Total Load Needed Therfore, Jack Stress Needed = 6 Jack Area 1 × 125600 = 6 3167 = 6.6 MPa = 957 psi
Eqn. A81 Eqn. A82
Thus, the required jack stress needed for applying the test load of 33 kN/m, which was calculated for ACI design code, is 6.6 MPa (957 psi).
51
A10. Shear Resistance of the Reinforced Concrete Beam Detailed calculations for estimating the shear capacity of the beam-slab assemblies are shown in this section of the appendix. The beam-slab assemblies were fabricated with 10M bars spaced at 150 mm on centre to resist the shear force that will be produced by any applied loads. The mechanical properties of the shear reinforcements in the beam-slab assemblies are shown in Table A1. Similar to flexural resistance calculations, both Canadian and American standards and codes were used in determining the shear capacity of the test specimens. A10.1 Shear Resistance according to CSA A23.3-94 [8] As stated in Clauses 11.3 and 8.6.5 of CSA A23.3-94 [8], the shear resistance of a nonprestressed concrete beam is: Vr = Vc + Vs Eqn. A83
Vc = 0.2λφc f c' bw d ,
Eqn. A84
where λ = 1.0
Vc = 0.2 ⋅ 1 ⋅ 0.6 ⋅ 59 ⋅ 300 ⋅ 339 = 93741 N φ s Av f y d 0.85 ⋅ 200 ⋅ 515 ⋅ 339 = = 197863 N Vs = s 150
Eqn. A85
Therefore,
V r = 93714 + 197863 = 291577 N = 291.58 kN > V f = 59.20 kN A10.2 Shear Resistance according to ACI 318M-99 (ACI, 1999) As stated in Clauses 11.1.1, 11.3.1.1 and 11.5.6.1 of ACI 318M-99 (ACI, 1999), the shear resistance of a non-prestressed concrete beam is as stated: φVn = φ ⋅ (Vc + Vs ) Eqn. A86
f c'
59 ⋅ 300 ⋅ 339 = 130195 N 6 6 Av f y d 200 ⋅ 515 ⋅ 339 = = 232780 N Vs = s 150
Vc =
bw d =
Eqn. A87 Eqn. A88
Therefore,
V r = 130195 + 232780 = 362975 N = 362.98 kN > V f = 66.59 kN Summary of the shear resistance of the unstrengthened concrete beam-slab assemblies according to Canadian and American codes are given in Table A3.
52
Table A2: Summary of Design Flexure Strength of Strengthened and FRP-Strengthened Beam Specimens Design Code
Required Factored Flexural Strength (kN·m)
Design Flexural Capacity (kN·m)
Increase in flexural capacity (%)
CSA 56.33 84.44 -A23.3-94 ACI 63.36 89.60 -318-02/ 318R-02 75.89 120.13 42.63 ISIS Canada Guidelines ACI 85.52 123.08 37.27 440.2R-02 CSA 75.89 97.74 10.29 S806-02 1 Superimposed load applied during the fire test
Maximum Allowable Service Flexural Capacity (kN.m) --
Applied load1 from Ultimate condition (kN/m) --
Applied load1 from Service condition (kN/m) --
--
--
--
83.94
41.74
39.83
82.68
30.77
32.30
--
32.75
--
Table A3: Summary of Design Shear Resistance of Unstrengthened Beam Specimens Design Code
CSA A23.394 ACI 318-02/ 318R-02
Required Factored Shear Strength (kN) 59.20
Design Shear Strength (kN)
66.59
362.95
291.58
53
APPENDIX B: TEMPERATURE OF SLABS DURING FIRE ENDURANCE TEST (a) Slab-3
1200
o Temperature ( C)
1000
800
ASTM E119 standard fire Furnace Average Exposed/insulation bondline (TC-45) Insulation/FRP bondline (TC-44) FRP/concrete bondline (TC-43)
600
400
200
0 0
60
120
180
240
300
Time (min.)
(b) Slab-4
1200
800
ASTM E119 standard fire Furnace average Exposed/insulation bondline (TC-45) Insulation/FRP bondline(TC-44) FRP/concrete bondline (TC-43)
o
Temperature ( C)
1000
600
400
200
0 0
50
100
150
Time (min.)
FIGURE B.1: Insulation and FRP temperatures
54
200
250
300
(a) Slab-3
180 Avg. unexposed 125mm (TC-29) 100mm (TC-30) 75mm (TC-31) 50mm (TC-32) 30mm (TC33) 15mm (TC-34)
160
120
o
Temperature ( C)
140
100 80 60 40 20 0 0
60
120
180
240
300
240
300
Time (min.)
(b) Slab-4
250 Avg. unexposed 125mm (TC-29) 100mm (TC-30) 75mm (TC-31) 50mm (TC-32) 30mm (TC-33) 15mm (TC-34)
o
Temperature ( C)
200
150
100
50
0 0
60
120
180
Time (min.)
FIGURE B.2: Interior concrete temperatures
55
(a) Slab-3
160 140
o
Temperature ( C)
120 100 80 60 40 Top of bars (TC-26) Middle of bars (TC-27) Base of bars(TC-28)
20 0 0
60
120
180
240
300
Time (min.)
(b) Slab-4
200 180
140
o
Temperature ( C)
160
120 100 80 60 40
Top of bars (TC-26) Middle of bars (TC-27) Base of bars(TC-28)
20 0 0
60
120
180
Time (min.)
FIGURE B.3: Steel rebar temperatures
56
240
300
APPENDIX C: TEMPERATURE AND DEFLECTIONS OF BEAM-SLAB ASSEMBLIES DURING FIRE ENDURANCE TEST (a) Beam-3
1200
800
o
Temperature ( C)
1000
600
400 ASTM E119 standard fire Furnace average Exposed/insulation bond (TC-18) Insulation/FRP bond (TC-17) FRP/concrete bond (TC-16)
200
0 0
60
120
180
240
300
Time (min.)
(b) Beam-4
1400
1200
o
Temperature ( C)
1000
800
600
400
ASTM E119 standard fire Furnace average Exposed/insulation bond (TC-18) Insulation/FRP bond (TC-17) FRP/concrete bond (TC-16)
200
0 0
60
120
180
Time (min.)
FIGURE C.1: Insulation and FRP temperatures (Section-A)
57
240
300
(a) Beam-3
1200
800
o
Temperature ( C)
1000
600
400 ASTM E119 standard fire Furnace average Exposed/Insulation bond (TC-45) Insulation/FRP bond (TC-44) FRP/concrete bond (TC-43) Insulation/concrete bond (TC-15)
200
0 0
60
120
180
240
300
Time (min.)
(b) Beam-4
1200
800
o
Temperature ( C)
1000
600
400 ASTM E119 standard fire Furnace average Exposed/Insulation bond (TC-45) Insulation/FRP bond (TC-44) FRP/concrete bond (TC-43) Insulation/concrete bond (TC-13)
200
0 0
60
120
180
Time (min.)
FIGURE C.2: Insulation and FRP temperatures (Midspan)
58
240
300
(a) Beam-3
1400
1200
o
Temperature ( C)
1000
800
600
400
ASTM E119 standard fire Furnace average Exposed/insulation bond (TC-12) Insulation/FRP bond (TC-11) FRP/concrete bond (TC-10)
200
0 0
60
120
180
240
300
Time (min.)
(b) Beam-4
1200
800
o
Temperature ( C)
1000
600
400 ASTM E119 standard fire Furnace average Exposed/insulation bond (TC-12) Insulation/FRP bond (TC-11) FRP/concrete bond (TC-10)
200
0 0
60
120
180
Time (min.)
FIGURE C.3: Insulation and FRP temperatures (Section-C)
59
240
300
(a) Beam-3
1200
0mm (TC-43) 51mm (TC-22) 86mm (TC-24) 121mm (TC-25) 156mm (TC-26) 400mm (TC-4)
800
o
Temperature ( C)
1000
600
400
200
0 0
60
120
180
240
300
Time (min.)
(b) Beam-4
1200
0mm (TC-43) 51mm (TC-22) 86mm (TC-24) 121mm (TC-25) 156mm (TC-26) 400mm (TC-4)
800
o
Temperature ( C)
1000
600
400
200
0 0
60
120
180
Time (min.)
FIGURE C.4: Interior concrete temperatures (Midspan)
60
240
300
(a) Beam-3
600 Rebar bottom (TC-40) Rebar bottom (TC-41) Rebar top (TC-21) Rebar top (TC-23)
400
o
Temperature ( C)
500
300
200
100
0 0
60
120
180
240
300
240
300
Time (min.)
(b) Beam-4
700 Rebar bottom (TC-40) Rebar bottom (TC-41) Rebar top (TC-21) Rebar top (TC-23)
600
o
Temperature ( C)
500
400
300
200
100
0 0
60
120
180
Time (min.)
FIGURE C.5: Steel reinforcement temperatures (web)
61
(a) Beam-3
600 Lower rebar (TC-31) Lower rebar (TC-32) Lower rebar (TC-33) Upper rebar (TC-36) Upper rebar (TC-37) Upper rebar (TC-38)
400
o
Temperature ( C)
500
300
200
100
0 0
60
120
180
240
300
240
300
Time (min.)
(b) Beam-4 Lower rebar (TC-31) Lower rebar (TC-32) Lower rebar (TC-33) Upper rebar (TC-36) Upper rebar (TC-37) Upper rebar (TC-38)
1200
800
o
Temperature ( C)
1000
600
400
200
0 0
60
120
180
Time (min.)
FIGURE C.6: Steel reinforcement temperatures (flange)
62
(a) Beam-3
60 Section D (TC-1) Section E (TC-2) Section B (TC-4) Section F (TC-7) Section G (TC-9)
40
o
Temperature ( C)
50
30
20
10
0 0
60
120
180
240
300
Time (min.)
(b) Beam-4
120 Section D (TC-1) Section E (TC-2) Section B (TC-4) Section F (TC-7) Section G (TC-9)
80
o
Temperature ( C)
100
60
40
20
0 0
60
120
180
Time (min.)
FIGURE C.7: Unexposed surface temperature (centerline)
63
240
300
(a) Beam-3
120 Section B (TC-3) Section B (TC-5) Section F (TC-6) Section F (TC-8)
80
o
Temperature ( C)
100
60
40
20
0 0
60
120
180
240
300
240
300
Time (min.)
(b) Beam-4
400 Section B (TC-3) Section B (TC-5) Section F (TC-6) Section F (TC-8)
350
o
Temperature ( C)
300 250 200 150 100 50 0 0
60
120
180
Time (min.)
FIGURE C.8: Unexposed surface temperature (flange)
64
(a) Beam-3 50
100 Section-A at L/4 Section-B at midspan Section-C at 3L/4 UDL on beam
80
30
60
20
40
10
20
0 0
100
200
300
Total UDL (kN/m)
Deflection (mm)
40
0 400
Time (min.)
(b) Beam-4
50
100 Section-A at L/4 span Section-B at midspan Section-C at 3L/4 span UDL on beam
80
30
60
20
40
10
20
0 0
100
200
Time (min.)
FIGURE C.8: Deflections in beams
65
300
0 400
Total UDL (kN/m)
Deflection (mm)
40
