Torsion Behavior of Strengthened Reinforced Concrete Box Girders with Openings

doi:10.21203/rs.3.rs-2338232/v2

An experimental test program consisting of eleven reinforced concrete box girders with a length of 1300 mm, a cross-section of 350 x 350 mm and 200 x 200 mm an inner cross-section was carried out. Four control specimens were tested: two as box girders, one solid beam and one box girder with an opening. Two specimens with openings were retrofitted with steel plates and CFRP around the opening and two specimens without openings were retrofitted longitudinally with steel plates and CFRP sheets. Two specimens were strengthened with U-shaped steel plates and CFRP sheets. One specimen was strengthened with longitudinal and U-shaped CFRP sheets. All the specimens were tested under pure torsion up to failure. To validate the finite element model, numerical models were used and their results were compared to experimental results. After verification, different variables were studied such as the influence of the opening location, number of openings, area of the opening, change in longitudinal and transverse steel amount, and strengthening around the opening. The comparative study revealed that the number of openings and their dimensions are the most important factors influencing the torsional moment. Also, the strengthening around the opening compensates the torsional strength that was lost due to the opening.

Torsion

Box girder

Strengthening

Steel plates

CFRP

Strengthening and rehabilitation are among the matters that have become important and necessary. They have priority like a result of some changes as increases in service load, errors in design or construction, aging, changes in the structure's use, changes to design code regulations, degradation problems, and unpredicted impacts or excessive earthquakes. There are many different materials and methods used in strengthening over time: for example, strengthening with steel strips, bonding material, or fibers of various kinds. The technical details required to complete the work differ according to the strengthening material used. The method and type of material used will also be affected by the importance of the structure, the possibility of stopping its use or not, and the suitability of the conditions surrounding the operation process [1–9].

Torsional moment is considered as a non-basic force effect on structure, but in some cases, it becomes the basic effective force, such as ring beams, spiral stairs, and curved elements in bridges. In addition, its difficulty in studying and testing it in the laboratory led to a lack of research on torsion compared with shear and bending moment forces. Salama et al. [10] studied the torsion performance of RC T-shaped beams with rectangular openings in the web. Seven samples were tested with some variables such as opening height, flange thickness and flange width with fixed depth, width, span, and opening length for all beams. The experimental results indicated that the opening height, flange height, and flange width parameters had a great influence on torsion strength of the beams. Al-Bayati et al. [11] studied an experimental program of RC beams tested in torsion using the NSM technique. Ten beams were divided into two beams as references and the eight were strengthened with CFRP laminates fully wrapped into pre-cut grooves using the NSM. The performance of RC beam strengthened with GFRP exposed to pure torsional moment was studied experimentally by Panchacharam and Belarbi [12]. Some variables were studied, such as number of strengthened beam faces (3 or 4), fiber orientation, influence of anchors in U-wrapped test beams, and the effect of the number of FRP. Soliman et al. [13] dealt with the design methods of RC structures under pure torsion by summarizing different codes of building and comparing between them. Meleka et al. [14] studied numerically the behavior of RC beams with opening under torsion. Meleka et al. [15] investigated an experimental program for beams strengthened by GFRP and subjected to combined bending and torsion. The strengthened beams included a full covering with discrete strips and continuous sheets of GFRP with the same reinforcement ratio. The results indicated that strengthening with GFRP improves the overall performance of the beams. Elkheshen et al. [16] studied torsional performance of RC beams reinforced with FRP stirrups and bars. A comparison of the results of analytical models and practical data was presented, and it demonstrated acceptable agreement in the ultimate torsion moment with a 6.5% difference.

Reinforced concrete Box Girders (BGs) are considered one of the best systems for resisting torsional moments. A substantial amount of research has been devoted to investigating the behavior of RC BGs in order to improve the torsional capacity of RC beams. Jing et al. [17] investigated experimentally RC box beam strengthened with CFRP sheets under combined loads, such as cyclic torque, shear, and bending moment. Variables studied were wrapping schemes and the number of CFRP layers. The results revealed that using CFRP improved the torsional ability of the box beams. Jing and Grünberg [18] employed a mathematical model to study the torsional performance under combined actions of shear, bending and torque influence on the RC box beams strengthened with CFRP sheets.

The objectives of the current work are to investigate the influence of pure torsion on the attitude of RC box girders with and without openings and the effect of applying different strengthening systems: CFRP sheets or steel plates to improve the performance of RC box girders with and without opening. This research was carried out using various CFRP and steel wrapping schemes throughout the span and around the opening region to study the influence of strengthening on torsion capacity and then find the most appropriate scheme that can be used to achieve this aim. The aim of using steel plates and CFRP for strengthening is to study the effects of strengthening type on torsional capacity and to compare the results with the control solid beam, box girders and box girders with opening, so that more than one method of strengthening was used.

In pure torsion, a set of eleven RC box girder specimens were tested. Figures 1&2 and Table 1 give their details. The dimensions and reinforcement for all specimens were kept constant but the openings and retrofitting schemes whether using CFRP or steel plate were varied. All box girders with a length of 1300 mm and a cross-section of 350 x 350 mm were tested. The inner box cross-section of each specimen was 200 x 200 mm. One beam was a same outer dimensions and length. Reinforcement was taken as 8 bars with 8 mm diameter in the longitudinal direction. Reinforcements in a transverse direction were closed stirrups with 6 mm diameter and 150 mm spacing. For all tested specimens, the thickness of the cover is 25 mm. Figure 1 displays the box girder geometry and reinforcement arrangements of the specimens depending on the aforementioned considerations.

Table 1

Tested specimens
G. No.	Specimens Code	Description of the Tested Specimens
1	CS	Control Solid beam
	CB1	Control Box girder 1
	CB2	Control Box girder 2
	CBO	Control Box girder with Opening
2	BOS	Box girder with Opening retrofitted by Steel strips
2	BOF	Box girder with Opening retrofitted by CF strips
3	BLS	Box girder retrofitted with Longitudinal Steel strips
3	BUS	Box girder retrofitted with U shaped Steel strips
4	BLF	Box girder retrofitted with Longitudinal CF strips
	BUF	Box girder retrofitted with U shaped CF strips
	BLUF	Box girder retrofitted with Longitudinal & U shaped CF strips

Table 1 demonstrates a description of the experimental program, including retrofitting systems. Group (1) contains four specimens and is called the control group: one specimen was a solid beam, two specimens were box girders and one was box girder with an opening located in the center of the beam on the lower side with dimensions equal to 100 x 200 mm. The reinforcement details of the specimens with openings are the same as the control specimens for the longitudinal and transverse stirrups, except one bar and one stirrup were cut off. The two strengthened box girders with openings are listed in Group (2). The remaining five specimens have the same reinforcement details and dimensions of the reference box girder and strengthened with CFRP sheets and steel plates and they split into two groups (groups (3) & (4)). Group (3) contains two box girders strengthened with steel strips: BLS with Longitudinal Steel strips and BUS with U-shaped Steel strips. Group (4) contains three box girders strengthened with CF strips: BLF with Longitudinal carbon Fiber strips, BUF with U-shaped carbon and with BLUF Longitudinal & U-shaped carbon Fiber strips.

The materials used in the preparation, making, and casting of the tested specimens are manufactured locally. Fine and coarse aggregates consist of ordinary siliceous sand and dolomite, respectively. Aggregates contain good quality materials and clean from injurious materials. Ordinary Portland cement was used in all specimens as a binder material. Master Rheobuild 880 [19] is also used to decrease water content and increase the ultimate strength. Tests for the properties of these components and the resulting concrete were performed and compared with the allowable values according to the Egyptian code Standard Specifications ECP 203-09 “Annex III” [20].

The MBRACE CF 120 carbon fiber were utilized in this investigation is unidirectional black CF woven by white thermoplastic heat-set fibers as seen in Fig. 3–10. The technical details, mechanical and physical properties of the dry carbon fibers and CFRP laminate are listed in Table 2, according to the manufacturer's sheet [80]. Adhesive materials are divided into two parts: surface preparation and epoxy resins that adhesion carbon fiber to the concrete surface. MasterProtect ® 2020 was the surface preparation that is a non-slumping combination of epoxy bedding and an adhesive. There are three packs, fine aggregate pack and quick healing material suitable for a range of applications including bedding, void filling, and concrete repair with a total weight available package of 10 kg units. Steel plates of 1 mm thickness were used in strengthening reinforced concrete specimens, whether longitudinal, U-shaped, or around the opening. Table 3, shows the test results of steel specimens (average value out of three specimens) involving elongation percentage, ultimate tensile strength, yield stress, chemical analysis and impact strength test: according to EN 10025-2:2011 for Grade S275JR. MasterBrace ADH® 4000 is an epoxy adhesive for MasterBrace ADH System and was used as adhesive material for steel plates. Also, punching was done in the places of attaching bolts as an additional type to connect the steel plates with the concrete.

Table 2

Properties of CF120 [19]
Fiber Modulus	240 GPa
Fiber Density	1.7 gm/cm³
Fiber Reinforcement	Carbon – High Tensile
Fiber Weight	200 gm/m²
Thickness	0.117 mm
Sheet Width	300 mm
Ultimate Tensile Elongation	1.55%
Tensile Strength	3,800 MPa

Table 3

Test results of steel plates
Test Description	Result	Limit Required For Grade S275JR According to EN 10025-2:2011
Yield Stress (Reh)	341 MPa	Min. 275 MPa
Ultimate Tensile Strength (Rm),	527 MPa	430–580 MPa
Elongation %	19%	Min. 15%
Impact Strength	32 Joule	Min. 27 Joule
Chemical Analysis	Acceptable	Max. C 0.21%, Min 1.50%, Cu 0.55%, P 0.035%, S 0.035%, N 0.012%, CEV 0.40%

The concrete mixture was designed using the ACI318 [21] method to obtain the constituents of the concrete mix which achieved a strength of 50 N/mm². Three mixers are designed to change the mixing water ratio and Master Rh880 as Table 4. Table 5 shows the compressive strength kg/cm² of three mixtures of cubic 150x150x150 mm after 7 days and 28 days.

Table 4

Concrete mix design
Material			Volume m³
Cement	3.15	450	0.143
Sand	2.56	667	0.260
Coarse Aggregate 19 mm.	2.68	1135	0.423
Free Water	1.00	166–176	0.166–0.176
Total Water	1.00	180–190	0.180–0.190
Admixture	1.17	7–9	0.006–0.007
Total Volume			1.027–1.018

Table 5

Test results for hardened concrete for Mix 3
Age	Compressive Strength kg/cm2											F_cu kg/cm²
	The beams are in order as mentioned in the Table 1
	1	2	3	4	5	6	7	8	9	10	11
7	337	342	338	345	378	374	381	344	358	371	369	358
28	538	544	535	552	587	563	592	547	551	560	558	557

The specimens were tested with a 3000 kN hydraulic Jack system. Every specimen was tested under pure torsion using two steel frame load arms: one on side and the second on the other side, but in the reverse direction. All specimens were tested using a concentrated load on a stiff steel I-beam, which distributed the load on two stiff cantilevers steel at the beam's ends. The technique of producing a torsional moment on reinforced concrete beams using a rigid I-beam and loading frame arm were used after studying several methods used in previous studies. The supports used for each specimen were restrained in the vertical direction at mid-width and free to rotate about the three main axes. The applied torque on the beam and an LVDT placed vertically and on the upper edge of the steel frame were used to calculate the angle of twist. The average value of the LVDT records was taken as a further confirmation of the results. One LVDT was placed to measure the specimen's horizontal displacement. Strain gauges (Table 6) for longitudinal internal steel bars, steel plates and fiber sheets were placed and measured. The width of the crack was measured after the collapsing of the face of the main facade of the beam. Specimens subjected to pure torsion testing using the test setup depicted in Fig. 3.

Table 6

Properties of strain gauge
Properties	Electrical Strain Gauge
Properties	CFRP	Steel
Company	KYOWA	TOKYO
Type	KC-60-120-Al-11	FLA-6-11-1LJC
Gauge Factor (24^o C, 50% RH)	2.08 ± 1.0%	2.11 ± 1.0%
Gauge Length	60 mm	6 mm
Gauge Resistance (24^o C, 50% RH)	120 + .4 Ω	120 + .5 Ω

SOLID65 was used for modeling concrete and resin without or with reinforcing bars. SOLID65 is able to cracking in tension and crush in compression. Eight nodes constitute the element, each with 3 DOFs, translations at every node in the all directions. One of this element's most important characteristics is its ability to represent material non-linearity. This element can also account for creep and plastic deformation. Link180 was used for modeling reinforcement. It is a three-dimensional spar that can be used in a variety of engineering implementations, such as springs, trusses, links, sagging cables, and so on. It is a uniaxial compression - tension element consisting of 2 nodes with 3 DOFs: translation at every node in all directions. Link180 is eligible to large deflection, rotation, creep, and plastic deformation strain, but with no bending. SOLID185 is a 3-D element solid structure used for simulating the steel cantilever and FRP. It consists of eight nodes having 3 DOFs: translations in all directions at each node. The element is capable of plasticity, large strain, creep, large deflection, stress stiffening, and hyper-elasticity. SOLID186 was used to express the steel plates. It has large strain and deflection, stress stiffening, hyper-elasticity, creep, and plasticity capabilities. It is a 3-D modeling and represented by twenty nodes. Every node has three DOFs: translations in z, y and x directions [22–29]. Figure 4 presents the geometry of the used elements.

Stress-strain relationship is very important for the representation of concrete in ANSYS program. It was introduced numerically from Eq. 1 to Eq. 4 (ECP 203-09, [20]). Where:\({\epsilon }_{0}\)is a strain at the ultimate compressive strength f_c, \(f\) is a stress at any strain ε, \(\epsilon\) is a strain at stress\(f\), and f_cu is the characteristic strength of concrete that f_cu ≈ 1.25 f_c. Shear transfer coefficients defined as 0.0 to 1.0 and it simulates appropriate for open and closed cracks. The coefficient was defined 0.2 and o.6 for the open and closed cracks, respectively. The ultimate compressive and uniaxial tensile is also needed to define cracking and crushing failure modes for the concrete. Many studies suggest that the uniaxial crushing stress in the concrete model entered − 1.0 to turn off the crushing to overcome convergence problems. The steel material properties were assumed to be bilinear isotropic elastic-perfectly plastic material as presented in the experimental section. Properties of resin used in the model are assumed according to MasterBrace 4500 and MasterBrace 4000 data sheets, which the Poisson's Ratio is 0.3 and Modulus of Elasticity is 4500. CFRP is defined in ANSYS as orthogonal material properties whose properties are different in all directions.

f = \(\frac{Ec \epsilon }{1+{\left(\frac{\epsilon }{\epsilon o}\right)}^{2} }\) Eq. 1

ε _o = \(\frac{2fc}{Ec}\)Eq. 2

E _c = 4400\(\sqrt{fcu }\) N/mm² Eq. 3

f ₁ = 0.3 f_c Eq. 4

To solve nonlinear problems in ANSYS program, Newton-Raphson method was used. In this method, the load is split into a sequence of load increments called load steps. Load steps can be divided into several load sub-steps. The stiffness matrix of the model is recalculated after each load step and sub-step solution to account for nonlinear variations in structural stiffness. After that, the program solves the next stage, whether it is step or sub-step until the solution reaches the total load. Direct contact and perfect bond were assumed between concrete, steel rebar, steel frame, resin, FRP and steel plate.

In FEM analysis, every component is divided into relatively small elements in the so-called meshing process. The results were obtained at the integration points of elements. So the smaller these elements are, the more good results and convergence are obtained, but at the same time, the solution requires longer time and more storage space. In this study, meshing dimensions for all elements don't exceed 25 x 25 mm, which meshing will coincide with the actual elements, location and preserving of aspect ratio. Nodes displacement was used to model the boundary conditions in this ANSYS model. The roller support was represented by putting the value of displacement of Y and X directions to be zero. The steel arm was allowed to translate in Z direction and rotate in Z, Y, and X directions. The anti-symmetry boundary condition was used to obstruct the beam to translate in Z direction. A vertical displacement in Y direction was applied instead of the forcing load to get acceptable representation of the curves after the peak point. Simulated models are plotted in Fig. 8.

Figure 9 illustrates the relation between torsional moments and angles of twist and Fig. 10 represents the crack pattern of the tested beams. In this comparison, it was shown that the results of the first control box girder CB1 are very close to that of the second control one CB2, whether in terms of the angle of rotation or the value of resistance to torsion. For the control specimen that had an opening, the value of the maximum torsion was decreased by about 39% compared to the CB1. The solid beam showed the highest value of torque resistance. The maximum load of this beam was 213.49 kN which resulted in a torsional torque of 43.76 kN.m at a twisting angle of 0.0149 rad/m. Then the load suddenly decreased from 225 kN to 76 kN. The solid beam has the ability to demonstrate the torsion torque by a greater percentage than the box beams up to a 50% percentage. The maximum load of the control beam was 142.63 kN which causes a torsional torque of 29.24 kN.m at an angle of twist 0.0107 rad/m. The maximum load of the beam with opening reached 87.16 kN and caused torsional torque of 17.87 kN.m and an angle of rotation of 0.0054 rad/m as shown in Fig. 9. In this sample, a collapse occurred at a lower value than the control specimens due to the presence of the opening. The presence of the aperture caused the sample to lose 39% of the torsional resistance, compared to the control box girder without an opening.

From Fig. 10, it can be seen that for solid beam, some cracks extended under the loading frame until crushed were occurred and a part of the concrete crushed until it reached the reinforcing main steel. The size of the crack caused was within 4 mm. In the test of the control box beam, one crack occurred until it reached the steel rebar. The crack was diagonally at an angle of around 45 degrees and it extended until it reached the bottom of the loading frame. There were some slight cracks around the main crack with the same angle of inclination. The main crack almost occurred in the middle of the face, facing the load. The main crack extended in the form of a V shape at two faces of the specimen. For CBO, at first, one crack occurred around the specimen, and with increasing load, the cracks increased around the opening. The crack size was about 1.0 mm on the opposite side when taking readings. A portion of the concrete around the opening was crushed as shown in Fig. 10. In Fig. 10, comparing box girders containing openings with (BOS and BOF specimens) and without strengthening (CBO specimen) through the relationship between torsion and twisting angle, which shows that strengthened specimens’ failure torque was obtained with a value close to the failure value of the control specimen CB1. This indicates the efficiency of the strengthening in restoring the reduction of torsional stiffness due to the opening. In addition, the collapse of specimen BOF was a result of the separation of the fiber. The beam with steel strip: BOS reached 141.19 kN ultimate load and caused 28.94 kN.m torsional moment of and 0.0088 rad/m twisting angle. The maximum load of BOF was 114.1 kN at a torsional torque of 23.39 kN.m and a twisting angle of 0.0105 rad/m. Cracks occurred around the opening in the two beams BOS and BOF which were strengthened by steel and CFRP, respectively, as an angle of inclination of 45 degrees and it started at the end of the strengthening strips as shown in Fig. 10. Due to the use of a resin material and the anchor bolts, a higher control and resistance to cracks occurred. The size of the cracks in BOS was about 0.85 mm around the hole. On the other hand a de-bonding and separation of the CFRP strips was observed at the end of the test of the BOF specimen. The size of the cracks around the opening is approximately 1.6 mm for BOF.

Figure 9 represents the relationship between the torsional moment and the twisting angle for comparison between the control specimen (CB1) and the strengthened box girders, whether with longitudinal or U-shaped steel strips of 1 mm thickness: beams of group (3). The use of longitudinal strengthening resisted the propagation of cracks, which led to a reduction in the bitch and led to a change in the direction of the cracks laterally as shown Fig. 10 and it was in the range of 1.1 mm. Steel strips resisted the occurrence of adjacent cracks and pitch of the BUS specimen that was strengthened with steel plates as U-shaped as shown in Fig. 10. The size of the crack at the opposite side of the load was about 5.0 mm and no separation of steel strips from the concrete was observed. It was found that the torsional resistances increased by values of 32% and 16% in the strengthened specimens in a longitudinal and U-shaped, respectively.

Figure 9 shows the comparison between the control specimen and box girders strengthened with CFRP as a relationship between the torsional moments versus the twisting angle. It is shown that the box girder strengthened by longitudinal or longitudinal with U-shaped strips has better behavior than strengthened with only U-shaped strips. The maximum load was 170.50 kN at a twisting angle of 0.0128 rad/m and the maximum torsion torque was 34.95 kN.m. The use of longitudinal sheets of CF led to an increase in the number of cracks and it did not allow cracks to continue as plotted in Fig. 10. The bond between the concrete and the fiber was good even after the collapse so that a separation was taken place for only one strip. A concentration of stress occurred at the bottom of the loading frame, and this coincided with the separation of the fiber strip. Also, cracks occurred on the face that was not strengthened with the carbon fiber due to the resistance of the fiber in the other sides. The size of the crack at the destination corresponding to the loading was 0.45 mm. For specimen BUF, which was strengthened with U-shaped form, the fiber slice was separated from the reinforced concrete as shown in Fig. 10. The separation of the fiber strips led to a single crack, and its width increased by increasing loads. on the opposite sides of taking readings, the fibers resisted the continuation of the crack and therefore their number increased, and this also occurred in the strengthened lower face. By measuring the width of the cracks on the side opposite the readings, it was from 0.3 mm to 0.9 mm. The highest load was 185.42 kN at a twisting angle of 0.0073 rad/m and torsional torque 38.01 kN.m.

The maximum load of the BLUF sample was 212.23 kN producing a torque of 43.51 kN.m and a twisting angle of 0.0231 rad/m as shown in Fig. 9. After reaching the ultimate load, the load decreased by small values by increasing the angle of rotation. The sample loading process was stopped and did not continued until the load reached significantly lower values, where a large rotation angle occurred, and there was a fear that the sample fell due to the occurrence of rotations from one direction to the other direction. The presence of fiber strips in both directions on the three sides of the specimen led to a higher control. It also led to an increase in cracks in the un-strengthened face, which includes a large crack as shown in Fig. 10. A separation occurred between the bonding material of the fiber and the concrete for a small part in the top layer corresponding to the un-strengthened face, and this occurred as a result of the widening of the crack. The size of the cracks ranged from 0.25 mm to 1.0 mm.

Figure 11 and Fig. 12 compare the control specimens and the strengthened box girders by U-shaped and longitudinal strips, whether steel or CFRP, respectively. It is shown that torsional moment values were obtained with lower rotation angle values compared with the values of the reference specimens and the retrofitted box girders provided higher torsional resistance than the control specimens. Also, applying longitudinal steel strips gave higher structural performance for BGs than FRP Strips under torsional loads.

Figure 13 plots the relevance between the angle of rotation and the torsional moment of specimens as a comparison between the numerical (NU) and experimental (EX) results. This figure presents that the CB1 specimen remained in the elastic phase until the value of the torsional moment for EX results was equal to 26.5 kN.m and the value equal to 25 kN.m for NU. In this part, EX results were very close to NU results. After that, the sample moved to the phase of plasticity in which the sample reached the ultimate torsional moment equal to 28.10 kN.m with a twisting angle = 0.01171 rad/m for NU result and for EX result equals 29.24 kN.m with a twisting angle equals to 0.01072 rad/m. The value of the ultimate torsional moment in NU is less than the EX by 3.9%. After reaching the ultimate stage, the value of the torsional moment begins to decrease as the value of the angle of rotation increases until the collapse occurs. Figure 14 shows the crack pattern for FEM results, which shows a high level of agreement with experimental findings. Significantly the same results when comparing the second experimental specimen CB2 results with FEM. The comparison revealed that the experimental and FEM results were in good agreement.

The CBO specimen remained in the elastic phase until the EX torsion moment reached 15 kN.m and the NU torsion moment reached 13.8 kN.m, as plotted in Fig. 13. The practice and NU outcomes were fairly similar in this section. The sample next entered the plasticity phase, where it reached an ultimate torsional moment that was equal to 17.66 kN.m at a twisting angle of 0.01200 rad/m as the NU result and 17.87 kN.m at a twisting angle of 0.00544 rad/m as the EX result. The ultimate torsional moment from the NU was lower than the EX results by 1.2%. After reaching the last stage, the torsional moment starts to decrease as the angle of rotation increases, until the specimen collapses. Figure 14 shows the experimental and FEM crack patterns. The solid beam is one of the tested beams in group 1 as control beams. The angle of rotation versus the torsional moment curves of CS is shown in Fig. 13. The specimen remained in the elastic phase until the torsional moment was equivalent to 41.5 kN.m as the EX results and 37.5 kN.m in the NU. The EX and NU results were extremely similar in this section. The sample then entered the phase of plasticity, where it reached an ultimate torsional moment of 41.77 kN.m with a twist angle of 0.01400 rad/m from the NU curve, and 43.76 kN.m with a twist angle of 0.01065 rad/m from the EX curve. The NU value of the torsional moment is less by 4.5 percent than the EX value in this stage. The crack pattern for this specimen from the EX and NU is closed and it was not listed to prevent elongation.

Group (2) contains the box girders with an opening, which were strengthened by applying the strengthening material around the opening. It consists of two specimens; BOS and BOF. The first box girder was strengthened with CFRP and the second box girder was strengthened with steel plate strips. The relationship between the angle of rotation and the torsional moment of BOS and BOF is shown in Fig. 13. The specimen remained in the elastic phase until the torsion moment was equal to 25 kN.m for EX and equal to 28 kN.m for NU. The NU results were fairly close to the experimental results in this section. After that, the sample started the phase of plasticity, where it attained 35.77 kN.m an ultimate torsional moment with 0.01143 rad/m a corresponding angle of rotation from NU curve, and 28.94 kN.m with a rotation angle of 0.00884 rad/m from the EX curve. The Numerical results are greater by 23.6% than the EX in this stage. After reaching the last stage of loading, the torsional moment begins to reduce as the angle of rotation increases, until the girder collapses. The BOF sample remained in the elastic phase until the torsional moment for the EX results was equal to 20.5 kN.m and equal to 18 kN.m for NU, as shown in Fig. 13. Then, the plasticity stage was begun, where it lasted until the ultimate torsional moment reached 24.32 kN.m at a twisting angle of 0.01343 rad/m as NU, and 23.39 kN.m at a twisting angle of 0.01051 rad/m as the EX results. The NU results of this sample were fairly close to the EX results. The crack pattern of the specimens of this group from the EX and NU is closed that it simulated as a concentrated crack round the opening and it was sufficient to list one sample; BOF, as an example in Fig. 14 to prevent elongation.

In group (3), the results of box girders strengthened with steel plate strips are reviewed. The set consists of two girders, one of which was strengthened with longitudinal steel strips (BLS) and the other was strengthened with U-shaped steel strips (BUS). Figure 13 plots the relevance between the angle of rotation and the torsional moment of BLS. This figure shows that the sample remained in the elastic phase until the value of the torsion moments for EX and NU were approximately 37 kN.m. After that, the sample moved to the phase of plasticity in which the sample reached the ultimate torsional moments equal 42.76 kN.m and 38.69 kN.m with corresponding 0.00914 rad/m and 0.01167 rad/m angles of rotation for NU and EX outputs, respectively. The value of the torsional moment of the NU is more than the EX by 10.5%. After reaching the ultimate stage, the value of the torsional moment begins to decrease as the value of the angle of rotation increases until the collapse occurs. For the BLS sample, the ultimate torsional moment for NU is larger by 2.3% than the experimental value. Figure 14 shows the crack pattern of a BLS specimen as an example of this group and it shows good agreement for NU result.

Group (4) contains the box girders that were strengthened by CFRP. It consists of three specimens; BLF, BUF and BLUF. The first specimen was strengthened with longitudinal CFRP sheets, the second specimen was strengthened with U-shaped sheets and the third box specimen was strengthened with longitudinal U-shaped sheets. The BLF sample remained in elastic stage until the torsion moment was equivalent to 32 kN.m for EX and 28 kN.m for NU. The sample then entered the phase of plasticity, where it reached an ultimate torsional moment 37.27 kN.m with a rotation angle 0.01429 rad/m for the NU outcomes, and moment 34.95 kN.m with a rotation angle 0.01282 rad/m for EX outcome. The ultimate value of the torsional moment as NU is 6.6 percent larger than the EX value. The BUF sample remained in the elastic phase until the torsion moment became 22.5 kN.m and 25 kN.m as EX and NU results, respectively. After that, the moment increased to be 35.85 kN.m and 38.01 kN.m with corresponding twisting angles of 0.01314 rad/m and 0.00728 rad/m as EX and NU results, respectively. The ultimate value of torsional moment for FEM is less than the experimental by 5.7%. The torsional moment begins to decrease as the angle of rotation increases after reaching the ultimate moment, until the structure collapses. For the BULF sample, the value of the ultimate torsional moment for NU is less than the EX by 6.3%. A good agreement in the NU result of this group was observed as Fig. 14 that contains the crack pattern of a BLUF specimen as an example of this group from both EX and NU outcomes.

A total of twenty-nine RC box girders were tested. The specimen’s configurations were the same for all tested specimens but different in opening location, area of opening, the retrofitted schemes around the opening and amount of longitudinal and transverse steel. All box girders have a length of 2100 mm and a cross-section of 350 x 350 mm. The inner box cross-section of these girders is 200 x 200 mm. The main dimensions for all specimens are shown in Fig. 15. Cover thickness for all tested box girders is 25 mm and the width of the opening is 100 mm. Table 7 demonstrates the specification of the specimens in the parametric study. Group (1) continues box girds with openings. In the case of the samples with one side opening or two mid openings, the openings have 200 mm length and 600 mm distance from the end of the beam. The sample with one side or two mid openings and the openings have 400 mm length have 500 mm distance from the end of the beam and the samples with one opening or two mid opening and the openings have 600 mm length have 400 mm distance from the end of the beam. The specimens of Group (2) were the same as in Group 1 with a difference in amount of steel amount. Longitudinal reinforcements were taken as 8 bars of 16 mm diameter in longitudinal direction distributed on the perimeter of the specimen (Al = 1608 mm²). Reinforcements in a transverse direction were closed stirrups with a spacing and diameter of 100 mm and 10 mm, respectively. The aim of Group (3) specimens is to investigate the validity of applying CFRP as strengthening materials to box girders with opening under torsional loads and illustrate the influence of strengthening for different opening locations and dimensions, so that this group is the same as the specimens of Group (1) except that CFRP sheet was applied around the opening. Figure 15 plots BSTO20 as an example.

Table 7

Parametric analysis program
Group No.	Description	Specimens Symbol	Description of the tested specimens
1	Different Opening Dimensions	CB	Control Box girder
		CBSO20	Control Box girder with Side Opening, 200 mm length
		CBSO40	Control Box girder with Side Opening, 400 mm length
		CBSO60	Control Box girder with Side Opening, 600 mm length
		CBMO20	Control Box girder with Middle Opening, 200 mm length
		CBMO40	Control Box girder with Middle Opening, 400 mm length
		CBMO60	Control Box girder with Middle Opening, 600 mm length
		CBTO20	Control Box girder with Two Opening, 200 mm length
		CBTO40	Control Box girder with Two Opening, 400 mm length
		CBTO60	Control Box girder with Two Opening, 600 mm length
2	Different Reinforcement	BR	Box girder Reinforcement
		BRSO20	Box girder Reinforcement with Side Opening, 200 mm length
		BRSO40	Box girder Reinforcement with Side Opening, 400 mm length
		BRSO60	Box girder Reinforcement with Side Opening, 600 mm length
		BRMO20	Box girder Reinforcement with Middle Opening, 200 mm length
		BRMO40	Box girder Reinforcement with Middle Opening, 400 mm length
		BRMO60	Box girder Reinforcement with Middle Opening, 600 mm length
		BRTO20	Box girder Reinforcement with Two Opening, 200 mm length
		BRTO40	Box girder Reinforcement with Two Opening, 400 mm length
		BRTO60	Box girder Reinforcement with Two Opening, 600 mm length
3	Strengthening Around Opening	BSSO20	Box girder Strengthened around Side Opening, 200 mm length
		BSSO40	Box girder Strengthened around Side Opening, 400 mm length
		BSSO60	Box girder Strengthened around Side Opening, 600 mm length
		BSMO20	Box girder Strengthened around Middle Opening, 200 mm length
		BSMO40	Box girder Strengthened around Middle Opening, 400 mm length
		BSMO60	Box girder Strengthened around Middle Opening, 600 mm length
		BSTO20	Box girder Strengthened around Two Opening, 200 mm length
		BSTO40	Box girder Strengthened around Two Opening, 400 mm length
		BSTO60	Box girder Strengthened around Two Opening, 600 mm length

In this comparison, the effect of the opening location on the torque was studied. A comparison was made between the different box girders in the form of a relationship between the angle of rotation and the torsional moment, as shown in Fig. 16 to 18. It was found from the results that the changing of the openings location does not affect the shape of failure or value of the torsional moments, as the girders are exposed to pure torsional moments. The effect of opening dimensions on torsional moment was plotted in Figs. 19&20. The results showed that the dimensions of the aperture are one of the factors affecting the torsional moments. It was noticed that the greater the length of the aperture, the lower the torsional moment at the same angle of rotation. The decrease in the torsional moment for a box girder with an opening length of 200 mm compared to the control specimen was in proportion to 3% or 4%. In the case of the opening length of 400 mm, the decrease was from 14.7–17.6% compared to an opening length of 200 mm. In the case of the opening length of 600 mm, the decrease was from 15.4–18.4% compared with box girder with opening length of 400 mm. One of the variables in this parametric part was the effect of the number of openings. The effect of changing from one opening to two openings was studied where the length of the opening varies (20 cm, 40 cm and 60 cm). The results were reviewed and compared with the torsional moment versus angle of rotation curve, and it was found that the torsional torque values decreased by a percentage ranging from 9.2–23.3% as shown in Fig. 20 to Fig. 22. Also, whenever the opening length increases, the decrease in torsional moment increases.

In this part, the box girders in Group 2 were compared with the box girders in Group 1, in which the diameters of the longitudinal reinforcement were increased by maintaining the number of bars, as well as the number and diameter of the stirrups were increased. The effect of this on the torsional moment and behavior of the specimens was studied, and the comparison was made with the torsion versus the angle of the rotation curve, as indicated in Fig. 23. From the results, it was found that the in the transverse and longitudinal steel led to an enhancement in the torsional strength by a rate ranging between 104% and 149.5% as well as it changes the failure mode from the collapse in steel reinforcement in Group 1 to the collapse in concrete.

The strengthened girders were compared with the un-strengthened specimens by torsional moment versus angle of twist curve as illustrated in Fig. 24. The results showed that in the case of box girders with an opening length of 200 mm, the effect of strength was noted and it was able to restore the torsional moment in proportions very closely to the control specimens without opening. In cases of an opening with lengths of 400 and 600 mm, the torsional strength increased and improved the torsional stiffness in proportions ranging from 5.6–24.6%. Finally, from studies of the various variables and the comparisons between them, it is clear that one of the main factors affecting the torsional strength is the number of openings and their length. Also, the strengthening around the opening helps to recover part of the torsional stiffness that was lost as a background of the presence of the opening.

This research was concerned with investigating the influence of pure torsional moment on box girders with and without opening. In addition, studying the effectiveness of strengthening with external steel plates or CFRP strips along the span or around the opening was investigated in the current research. Eleven RC box girders with and without openings were tested experimentally. Experimental results were compared by a finite element model (FEM). After the validation of the suggested models, a numerical analysis was done using some different variables that may be affected on the behavior of the box girders subjected to torsion, such as the dimensions of the opening, amount of transverse and longitudinal steel reinforcement and the strengthening around the opening. The following main conclusions can be drawn from this investigation's experimental work and numerical analysis:

The ultimate failure load of the control solid beam was increased more than the reference box girder by about 49%.

Strengthening using the longitudinal steel plates increased the torsional capacity of the box girder by about 33% compared to the control box girder.

By applying U-shaped steel plates to the box girder, torsional capacity increased by approximately 16% over the control box specimen.

Strengthening the box girder using longitudinal CFRP strips increased the torsional capacity by about 20% compared to the control specimen.

Using U-shaped CFRP strips for specimens enhanced the torsional capacity by about 30% compared to the reference specimen. In contrast, attaching longitudinal and U-shaped CFRP strips to the box girder increased the torsional capacity by about 48% compared to the control specimen.

The box girder strengthened with longitudinal steel strips has a larger angle of twist at the failure than the box girder BUS strengthened with U-shaped strips by about 172%.

The angle of twist at the failure of the girders retrofitted with longitudinal CFRP strips is larger than the box girder strengthened with U-shaped strips by about 176%.

Strengthening the box girder with U-shaped CFRP strips exposed to a sudden failure as opposed to using longitudinal strips.

Changing the position of the opening along the box girder does not affect the pure torsional capacity.

Changing the reinforcing for box girders from the under reinforced section to the over reinforced section increases the torsional stiffness significantly, but at the same time, it leads to a sudden collapse.

Strengthening by CFRP around the opening of the box girder greatly improves the value of the torsional capacity. The percentage increase in torsional stiffness is commensurate to the opening length.

Conflict of interest

The author declares that there are no known conflicts of interest related to this publication and that no substantial financial support has been provided for this work that would have affected its conclusion.

Funding declaration

There are not funding declaration

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No competing interests reported.

Torsion Behavior of Strengthened Reinforced Concrete Box Girders with Openings

Status:

Version 2

Abstract

Figures

1. Introduction

2. Experimental Work

3. Finite Element Model

4. Experimental Results

5. Parametric Study

6. Conclusion

Declarations

References

Additional Declarations

Status:

Version 2