Behavior of concrete beams reinforced with GFRP under transverse force

The article discusses the effect of transverse reinforcement spacing for the strength and deformation characteristics of beams with glass fibre reinforced polymer. The bending tests results of reinforced concrete specimens are presented (GFRP) with different concrete strength and reinforcement spacing. Force-deflection, force-GFRP bars deformation and force-concrete compressed zone deformation dependencies are given in the article. Based on ultimate force and beams destruction pattern it is established that increasing transverse reinforcement spacing reduces the beams strength and leads to destruction in oblique section. With narrowmashed transverse reinforcement fracture occurs in the compressed zone of concrete. A computational analysis for different types of beams fracture is presented. It is established that transverse reinforcement spacing doesn’t affect the parameters determined by service limit state: crack formation load, crack width and beam deflection. A comparative analysis of maximum permissible deflection based on test results and theoretical calculations was carried out. The numerical values of bending stiffness parameter are obtained at the loading stages with linear deformation before and after first crack formation.


Introduction
Glass-fiber reinforced polymer (GFRP) bars market in Russia has increased drastically in the last years. Currently many necessary regulatory documents for GFRP bars and instructions for reinforced with GFRP structure design have been developed and constituted in Russia [1], [2], [3], [4], [5].
Therefore, there is an increase in industrial and civil structures designed with the use of GFRP bars. However, it is not advised to use GFRP as a working reinforcement for bending structures due to lack of experimental data. Nevertheless, it is not wise to neglect tensile properties of GFRP bars. Some Russian and foreign researches of bending elements reinforced with GFRP showed good results [6], [7], [8], [9].
We can achieve economical profit by increasing overhaul period for bending elements in aggressive environments (silage, hopper, highways beams) in case of using GFRP reinforcement. Tests of beams were carried out to get experimental data of real work of concrete elements reinforced with GFRP. According to previous researches, after diagonal cracking occurs, deflection of FRP RC beams is significantly greater than the estimated according to Eurocode 2, and the component of shear crack inducted deflection can affect the serviceability [10]. Beams were tested by short-term load in order to achieve fracture from transverse force in oblique section.  Table 1 shows concrete characteristics based on cubes tests (100x100x100 mm) according to [11], prisms tests (100x100x400 mm) for compression according to [12] and prisms tests (100x100x400 mm) for bending according to [11] in order to estimate axial tension strength.  Beams have dimensions of 100x200x3200 mm.

Experimental program
Beam for short-term load were tested inside MTS equipment which consists of rearranging power frame CFM Schiller, controller FlexTest-60 and hydrocylinder MTS 201.30T.
Displacement indicators Mircon IC-50-0,01 with a range of 0-50 mm and division value of 0,01 mm were used to measure deflection.
Ultrasonic pulse method with the help of «Pulsar 1.2» and piezoelectric converters with a frequency of 65 kHz was used to estimate crack formation process.
Concrete and GFRP deformations were registered via multichannel measurement complex National Instruments based on NI PXIe-1075. Strain gages with the base of 1 mm (TML FLA-1-11) were used for GFRP, with the base of 60 mm and 120 mm (TML PL 60-11, TML PL-120-11) -for concrete.
Strain gages layout is shown on figure 2. Piezoelectric converters layout is shown on figure 3.
Concrete cubes and prisms were tested on test machine Instron 1000 HDX. Crack formation process was also controlled visually with the help of Brinell microscope MPB-2.
The beams were loaded step by step: -before crack formation -load step was 2,0 kN, loading speed was 1,0 kN/min, hold time at each step was 5 min; -after crack formation till load reaches 18,0 kN -load step was 4,0 kN, loading speed was 6,0 kN/min, hold time at each step was 5 min; -after load reaches 18,0 kN till fracture -load step was 12,0 kN, loading speed was 6,0 kN/min, hold time at each step was 5 min.
Following measurements were carried out at each step during hold time: load and displacement of hydrocylinder, -deflection of beam, deformation of strain gages; -ultrasonic speed between control points; -visual examination of the beam and crack recording ( fig. 14-15).
Four transmitter-reciever (T-R) routes for ultrasonic oscillations (USO) controlled normal and oblique crack formation and development along the beam.

Displacements and deformations measurements
Deflection charts for two deformation segments are shown on fig. 4-6. Displacements in the first segment before crack formation should correspond with theoretical deflections from bending moment. Only one beam from each test series is shown in this chapter because beams inside the series have corresponding deflection measurement data.
Strain gages data correspond with stress-strain behavior of beam according to deflection data ( fig. 7-12).

Ultrasonic measurements
Crack formation in beams B3.14.50.1-B3.14.50.3 was detected by short routes (T1-R2, T2-R1, T2-R2) on the loading step from 4 to 6 kN. Crack developing in concrete through the GFRP bars and active formation of oblique cracks was seen on chart for oblique routes with load changing from 8 to 30 kN. Increase in crack width in the pure bending zone with the slowdown of oblique crack growth was registered with load changing from 42 to 90 kN.
The beam B3.14.100.3 was characteristic in the beam series B3.14.100.1-B3.14.100.3 based on USO data. Microcracks formation in the pure bending zone was registered on the loading step from 2 to 4 kN. After that, active hair cracks formation was seen that slowed down when the load reached 30 kN. Active oblique cracks formation started at 8 kN based on USO data from routes T1-R2 and T2-R1.
For beams B3.14.150.1-B3.14.150.3 there was a unified crack formation and developing image based on USO data. Microcracks formation was registered on the loading step from 4 to 6 kN and continued till the load reached 20 kN. After that there was a slowdown in developing of hair and mainstream cracks ( fig. 13).

Comparison of the mid-span deflection
Theoretical deflection for beam B3.14.50.1 from bending moment per 1 kN of external force: where: = 2563,1 · 2 -concrete modulus of elasticity for beam B3.14.50.1; Bending stiffness is 3,7 times less than on the first segment of linear deformation. Concrete modulus of elasticity for beams B.3.14.100.2 and B.3.14.100.3 is higher compared to beam series B3.14.50. For beam B3.14.100.3 on the first linear deformation segment with loading up to 6 kN deflection was ƒe = 0,8 mm (excluding deflection on holds), which corresponds with deflection per 1 kN of ƒ , = 0,13 . In the load range from 14 to 78 kN deflection increased from 7,3 to 54,3 mm For beams with 50 and 100 mm spacing in transverse reinforcement fracture occurred in the pure bending zone from bending moment. For beams with 150 mm spacing in transverse reinforcement fracture occurred from shear force in the oblique section.
With the small increase in modulus of elasticity comparing to beam B3.14.50.1, difference in deflection can be explained by methodical error in measurements on small load values.
In the segment of linear deformation with cracks in the load range from 10,0 to 90,0 kN deflection increased by 67,7 mm, which corresponds with deflection per 1 kN of ƒe,II = 0,85 mm.

Bending moment calculation results
It was established that for beams with transverse reinforcement spacing of 50 and 100 mm tension deformations in the longitudal GFRP bars in the limit state is almost equal. (fig. 7, 9). Internal moments in the normal section for beams B3.14.50.1 and B3.14.100.1 calculated using GFRP bars deformation and ultimate compression stress in concrete differ negligibly (5%) from moments from external load. Herewith, load margin in GFRP bars by 50% predetermined fracture of these beams in compressed concrete zone.

Shear force calculation
Elastic and strength characteristics of concrete and GFRP bars were acquired during specimens tests (table 1).
Calculation of shear force taken by concrete and transverse reinforcement is made for beam B3.14.100.1 with the lowest concrete strength.
Concrete  for beams with longitudal GFRP Ø14 with 50 mm spacing in transverse reinfocement P cr = 0,10·P u ;  for beams with longitudal GFRP Ø14 with 100 mm spacing in transverse reinfocement P cr = 0,08·P u ;  for beams with longitudal GFRP Ø14 with 150 mm spacing in transverse reinfocement P cr = 0,09·P u ; 5. Crack formation was gradual based on USO and visual control data: at first there was abrupt increase in cracks length with a corresponding increase in cracks width and then there was only increase in crack width (with stable length of cracks) in the load range from 0,3-0,5 P u to P u . 6. Theoretical deflection calculated using initial geometric section characteristic and concrete and GFRP modulus of elasticity is lower than experimental by 10% average based on deflection measurement in the initial linear loading stages. 7. Main work of beam during loading was during crack developing, elastic tension of GFRP bars and almost linear increase in deflection. On this stage bending stiffness compared to initial is :  3,7 times lower for beam with 50 mm spacing in transverse reinfocement and equals = 462 · 10 4 · 2 ;  5,6 times lower for beam with 100 mm spacing in t ransverse reinfocement and equals = 389 · 10 4 · 2 ;  4,7 times lower for beam with 150 mm spacing in transverse reinfocement and equals = 366 · 10 4 · 2 .