Evaluating the performance of skewed prestressed concrete bridge

Cent. Eur. J. Eng. • 3(2) • 2013 • 329-347 DOI: 10.2478/s13531-012-0061-x

Central European Journal of Engineering

Evaluating the performance of skewed prestressed concrete bridge after strengthening Research Article

Ali Fadhil Naser1,2∗ , Wang Zonglin3† 1 School of Transportation Science and Engineering, Bridge and Tunnel Engineering, Harbin Institute of Technology, 150090 Harbin City, China 2 Foundation of Technical Education, Al-Mussaib Technical Collage, Iraq 3 School of Transportation Science and Engineering, Bridge and Tunnel Engineering, Harbin Institute of Technology, 150090 Harbin City, China

Received 07 July 2012; accepted 15 February 2013

Abstract: The objectives of this paper are to explain the application of repairing and strengthening methods on the damaged members of the bridge structure, to analyze the static and dynamic structural response under static and dynamic loads after strengthening, and to evaluate the structural performance after application of strengthening method. The repairing and strengthening methods which are used in this study include treatment of the cracks, thickening the web of box girder along the bridge length and adding internal pre-stressing tendons in the thickening web, and construct reinforced concrete cross beams (diaphragms) between two box girders. The results of theoretical analysis of static and dynamic structural responses after strengthening show that the tensile stresses are decreased and become less than the allowable limit values in the codes. The values of vertical deflection are decreased after strengthening. The values of natural frequencies after strengthening are increased, indicating that the strengthening method is effective to reduce the vibration of the bridge structure. Therefore, the strengthening methods are effective to improve the bearing capacity and elastic working state of the bridge structure and to increase the service life of the bridge structure. Keywords: Theoretical analysis • Box girder • Strengthening • Cross-beam • Deflection • Stress • Strain • Natural frequency © Versita sp. z o.o.

1. ∗ †

E-mail: [email protected] (Corresponding author) E-mail: [email protected]

Introduction

Skewed bridges are widely used in China and with the rapid development of urban communications; the actual bearing state of large numbers of bridges exceeded the initial design requirements due to the increasing in vehicle 329

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Evaluating the performance of skewed prestressed concrete bridge after strengthening

numbers and axle weights, which led to numerous cracks appearing on these bridges and the decline of the whole structural stiffness. In general, when the flexural loadcarrying capacities of existing bridge structures are not sufficient for the service loads, structural members of the bridge structure need to strengthen and repair [1–3]. The strengthening of prestressed concrete box girder bridge includes improvement of the strength and stiffness of structural members, and the repairing process involves re-establishing the strength and function of the damaged members. The strengthening of the bridge structural members can be carried out by replacing poor quality or flawed materials by using better quality materials, attaching additional load-bearing materials, and re-distribution of the loading actions through imposed deformation on the structure system. The selection of an appropriate method for the strengthening and repair of the bridge structural members depends on a number of factors. These factors include the type and age of structure, the importance of structure, the magnitude of the strength required which is need to increase, the type and degree of damage, available materials, cost and feasibility, and aesthetics. The strengthening and repairing of the bridge structure can be provided an effective and economic solution in appropriate situation [4–10]. Karayannis et al. studied the effectiveness of a technique for the repair of damaged reinforced concrete beam column connections due to cyclic loading by adopting experimentally investigated. They Concluded that the concerning the effectiveness of the applied repair technique, based on maximum cycle loads, loading stiffness, and hysteretic energy absorption capabilities of the tested specimens, are drawn and commented upon. Remarks concerning the influence of different design reinforcement arrangements on the behavior of the joints are also included. The examined repair technique can be considered to be satisfactory, since all repaired joints exhibited equal or higher response load values and loading stiffness compared to the virgin ones, and tended to undergo more full loading cycles without a significant loss of strength [11]. Tsonos investigated the effectiveness and suitability of shotcrete and cast-in-place concrete as means of retrofitting columns and beam–column joints in reinforced concrete frame structures, so as to improve their shear and/or flexural performance. He found that All types of concrete jackets examined were found to be equally satisfactory in their ability to strengthen existing old frame structures [12]. Karayannis and Sirkelis presented the results of an experimental investigation on the behavior of critical external beam–column joints repaired and strengthened with a combination of epoxy resin injections and carbon-fiber-

reinforced plastics (C-FRP) sheets. From the observed responses of the examined specimens it can be deduced that the technique of epoxy resin injections is appropriate for the total rehabilitation of the joints seismic capacity, since no damages have been observed at the joint area of the specimens after the repair. The combination of this technique with the use of C-FRP sheets leads to a significant improvement of the loading capacity, the energy absorption and the ductility and finally it leads to improved type of damages compared with the damage modes of the specimens during the initial loading [13]. The main damages of reinforced concrete bridge include different types of cracks, scaling, spalling, delaminating, efflorescence, stains, corrosion of steel reinforcement, deformation, and excessive deflection. Cracks play important role in the acceleration of reinforcement corrosion, deterioration of concrete, damage of bridge structure components and elements beneath of deck. Therefore, cracks can be reduced the performance and durability of bridge concrete structure. Cracks can be caused by many factors such as loads applied during construction or in-services condition, foundation movements, temperature changes and gradients, shrinkage and creep of concrete. Generally, there are two types of cracks. The first type is known as non-structural cracks which can be observed in the bridges and overpass structures. This type can be caused by thermal expansion and contraction of concrete, contraction of concrete during curing process, change in temperature, and corrosion of steel reinforcement. The second type is known as structural cracks which are caused by dead and live load stresses [14–20]. The objectives of this paper are to explain the application of repairing and strengthening methods on the damaged members of the bridge structure, to analyze the static and dynamic structural response under static and dynamic loads after strengthening, and to evaluate the structural performance after application of strengthening method.

2. Description of the bridge structure Hashuang bridge is located in Harbin City within Heilongjiang province in the east north of China. This bridge is type of pre-stressed concrete box girder oblique bridge. The total length of the bridge is 95.84 m and has total width is 17 m, including two box girders. The width of box girder web is varying from 35 cm to 70 cm along the length of the bridge. The arrangement of spans is 28 m+40 m+28 m. The transversal arrangement of the deck is 14.0 m carriageway and 2x1.5 m sidewalk, and the deck which is paved by the 8 cm waterproof concrete

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and 8 cm asphalted concrete pavement. The construction process of this bridge adopts the method of cast-in-place span-by-span method [21]. Figure 1 shows Hashuang bridge structure. Figure 2 shows the layout of box girders.

Figure 1.

3. Description of the main problems of the bridge structure Damage inspection process is carried out on the structural members of the bridge structure such as outside and inside of box girders of all the bridge spans, piers, abutments, bearings, sidewalks, and steel rails. The results of inspection process show that the web of box girder suffers from serious shear cracks. The distance between cracked area and the mid-pier No. 2 is about 10.5 m within span No.2 (39 m of bridge length). These cracks extend from the top to lower flange of box girder. There are two cracks incline 45 degree to the mid-span direction with widths are 0.5 to 2.0 mm and the widest cracks are found in the middle of web of box girder. Both of the outside web and inside web of box girders have the same crack position, but the crack degree of the box girder’s outside web is more serious than the inside web. There are six transverse bending cracks on the bottom of box girder around quartile of middle span. The spacing between these cracks rang from 20 cm to 30 cm and the width is 0.35 mm. In the span No. 3 near the pier, the web of box girder appears 12 diagonal cracks have width rang from 0.1 mm to 0.12 mm. Figure 3 shows the cracks in the box girders. The inspection process of other parts of the bridge structure shows that the state of abutments, piers, and sidewalks is good, but the bearing, drainage holes, steel rails, and expansion joints suffer from damage. The steel rails are corroded and the expansion joint loses the material which fills the joint. There are many dusts and debris which are collected on the bridge deck in the location near sidewalk. According to the inspection results, it can be noted that the state of the bridge structure is not good and the bridge structure needs to repair and strengthen.

Hashuang bridge structure

(a)

4. Repairing methods

(b)

Figure 2.

The layout of transverse section of the bridge. (a) half section of mid-span box girder, (b) half section of pier box girder (dimension in cm)

and

strengthening

In order to ensure the safety application, improve the structural performance, increase the bearing capacity, to reduce the vibration of the bridge, and extend the service life of the bridge structure, there is a need to repair and strengthen of the bridge structure. The repairing and strengthening methods include treatment of the cracks, thickening the web of box girder along the bridge length and adding internal pre-stressing tendons in the thickening web, and construct reinforced concrete cross beams (diaphragms) between two box girders. 331



control stress is 1395 MPa. Two tendons are installed in each side of the additional webs. Figure 4 shows the layout of new additional webs reinforcement. Figure 5 shows the transverse layout of box girder after finish the thickening of the outside of the webs. Figure 6 shows the longitudinal layout of prestressing tendons of thickening webs. The connection between the new additional webs with the original web of box girder by using implanted steel bars which have diameter is equal to 16 mm. Outside of the original box girders webs needs to roughen by picking the concrete surface and the depth of roughening is ranged from 1 to 2 cm. Stirrups (diameter 16 mm) are installed and welded with the implanted steel reinforcements. When concrete of the widening part of the web is casted and the pouring process is started, there is a need to drill holes in the deck and then pour from the deck. Grouting the holes can be reserved in the part where the web connects with the top of box girders and the incompact parts are filled with structure paste. Anchoring parts of abutments could be anchored into side diaphragms with reinforcements which have diameters are equal to 20 mm because of there is greater shear in this location of the bridge structure. Figure 3.

4.1.

The cracks in the box girders of Hashuang bridge

Treatment of the cracks

The method of grouting repair is adopted to repair the cracks in the parts of box girders web in the quarter and center of middle span of the bridge structure. For cracks width less than 0.15 mm, the grouting method stages include clean and remove the laitance and dust, dig a Vshape groove by using chisel adhesive, and sealing the cracks by using the mixed epoxy resin No. 6101. The surface of cracks is leveled by using scraper. For cracks width more than 0.15 mm, the grouting method is used to repair the cracks by using the grouting machine.

4.2.

Thickening the web of box girders

The outside of box girders webs of two sides of the bridge structure are thickened by using reinforced concrete with internal pre-stressed tendons to increase the resistance of shear and to improve the compressive stress reserve of box girders. The additional thickness of outside webs is equal to 25 cm in the location of abutment and spans, and 50 cm in the location of pier box girders. 12Φ15.24 steel strands are adopted as prestressing tendons. The standard strength is equal to 1860 MPa and the tension

4.3. Construction of reinforced concrete cross beams Reinforced concrete cross beams (diaphragms) are constructed between two box girders in the location of piers, quarters of middle span, center of middle span (span No.2), center of side spans (span No.1 and No.3), and near the abutment. The thickness of cross beams was equal to 0.5 m. The object of these cross beams is to reduce the vibration of the bridge structure and to strengthen the connection between the two sides of the bridge (two box girders). Figure 7 shows the layout of cross beams between two box girders.

5. Theoretical analysis of internal forces after strengthening According to Chinese code (JTJ023-85) [22], the original design of the Hashuang pre-stressed concrete box girder bridge was carried out. In this analysis, SAP200 software Ver. 14.2.0 is used to analyze the internal forces of the bridge structure after strengthening due to dead load, live load, prestressed load, temperature load, and crowded load.

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Figure 4.

The layout of new additional webs reinforcement

1. Concrete density = 26 kN/m3 , Poisson ratio (µ) = 0.2, concrete compressive strength = 40 MPa (C40). 2. Deck loads: Deck weigh + sidewalk weight + railings weight = 40 N/m, crowded load = 2.9 kN/m. The total weight per square meter = 40/17 (width of bridge) = 2.35 kN/m2 . 3. Anchorage set slip (∆l) = 6 mm. 4. For prestressed losses, friction coefficient between steel beam and rubber tube (k) = 0.003 m−1 , µ = 0.35. 5. For concrete creep, efficiency coefficient of elasticity (K ) = 0.3, creep factor (γ) = 0.021, creep ultimate value = 2.3. 6. Temperature load: according to Chinese code (JTGD60-2004), positive T1 = +14, negative T1 = -7, positive T2 = +5, negative T2 = -2.5. 7. Load combination: • Combination I (COMB I) = Dead load (structure weight) + Deck load + Prestressed load. Figure 5.

5.1.

The transverse layout of box girder after finish the strengthening of the outside of the webs and outside floor

Requirements of analysis

The requirements are used in the analysis of the bridge structure include:

• Combination II (COMB II) = COMB1 + Moving load (vehicle load) + Crowded load + Temperature load. 8. Pre-stressed tendons: longitudinal prestressing tendons made of 1×7 wire 15.24-1860II-GB/T5224-1995. Tendon area is equal to 1656 mm2 . The standard strength and controlled 333



(a)

(b)

Figure 6.

The longitudinal layout of prestressing tendons of thickening webs: (a) elevation view of span No.1, (b) elevation view of span No.2

tension force of steel strands is equal to MPa and 2310 kN, respectively. Figure 6 shows the layout of longitudinal pre-stressed tendons. 9. Live load: according to Chinese code (JTG D622004) [23], the live load is used shown in Figure 8. Pk = 180 kN, if the length of span ≤ 5 m, Pk = 360 kN, if the length of span ranges from 5 m to 50 m. Uniform load (qk ) = 10.5 kN/m. The bridge consists of four lanes. Therefore, the reduction factor is equal to 0.67. The maximum span length is equal to 40 m. Therefore, the pk is equal to 320 kN.

5.2.

Description of bridge model

strengthening methods which are used in the bridge model include thickening the web of box girder along the bridge length and adding internal prestressing tendons in the thickening web, and construct reinforced concrete cross beams (diaphragms) between two box girders. Figure 9 shows the bridge model. This study will be considered the load combination I and II in the analysis to recognize the amount of improvements in the structural responses of the bridge structure after strengthening.

5.3. Analysis of internal forces due to load combination I 5.3.1.

The bridge model consists of two shell element objects. The first object represents the right side of the bridge (forward side) and the second object is the left side of bridge (backward side). Each object includes three spans. The first left span has length which is equal to 28 m. The second span is a middle span of the bridge which has length equal to 40 m, and the third right span has length equal to 28 m. The bridge structure is type of skewed bridge. The angle of skew is equal to N33oW. The

Analysis of stress

Figure 10 shows the values of stresses before and after strengthening due to load combination I for object No.1 (forward side). From this figure it can be shown that the values of compressive stresses of object No.1 are increased after strengthening. For box girder top, the maximum compressive stress is equal to -6.5 MPa which is more than the values before strengthening -5.2 MPa and less than the allowable values in Chinese codes, JTJ02385 and JTG D62-04, which are equal to -19.6 MPa and

334



(a)

(b)

Figure 7.

The layout of cross beams between two box girders: (a) The view of cross beam after finished, (b) The longitudinal view of cross beams

nese codes (JTJ023-85 and JTG D62-04) which are equal to 2.99 MPa and 1.68 MPa respectively. Figure 11 shows the values of stresses before and after strengthening due to load combination I for object No.2 (backward side). From this figure it can be noted that the maximum compressive stress of box girder top is equal to -6.6 MPa which is more than the values before strengthening -5.0 MPa and less than the allowable values in Chinese codes (JTJ023-85 and JTG D62-04) which are equal to -19.6 MPa and -18.78 MPa respectively. There are small tensile stresses appear in the top of box girders. The maximum value is equal to 0.2 MPa which is less than the allowable values in Chinese codes (JTJ02385 and JTG D62-04) which are equal to 2.99 MPa and 1.68 MPa respectively. For box girder bottom, the values of compressive stresses are increased after strengthening, but the values at the pier box girder are decreased. The maximum compressive stress before strengthening is equal to -7.1 MPa and decreased to -6.6 MPa after strengthening. The value after strengthening is less than the allowable values in Chinese codes (JTJ023-85 and JTG D62-04) which are equal to -19.6 MPa and -18.78 MPa respectively. From the above comparison it can be concluded that the strengthening program is effective to improve the structural performance of the bridge structure by decreasing the tensile stresses approximately by 50% and increasing the compressive stresses. For JTJ023-85: Allowable compressive stress = 0.7 × 28 = -19.6 MPa Allowable tensile stress = 1.15 × 2.6 = 2.99 MPa For JTG D62-04: Allowable compressive stress = -0.7 × 26.8 = -18.78 MPa Allowable tensile stress = 0.7 × 2.4 = 1.68 MPa

5.3.2.

Figure 8.

The static live load

-18.78 MPa respectively. There are not tensile stresses appear. For box girder bottom, the values of compressive stresses are increased after strengthening, but the values at the pier box girder are decreased. The maximum compressive stress before strengthening is equal to -6.9 MPa and decreased to -6.7 MPa after strengthening. The value after strengthening is less than the allowable values in Chinese codes (JTJ023-85 and JTG D62-04) which are equal to -19.6 MPa and -18.78 MPa respectively. The tensile stresses are decreased after strengthening. The maximum value of tensile stress is decreased from 2.5 MPa to 0.6 MPa which is less than the allowable values in Chi-

Analysis of vertical deflection

The values of vertical deflection before and after strengthening due to load combination I are shown in Figure 12. From this figure it can be seen that the maximum vertical deflection is decreased from -19 mm to -17 mm after strengthening, indicating that the strengthening program is effective to improve the stiffness of the bridge structure.

5.4. Analysis of internal forces due to load combination II 5.4.1.

Analysis of stress

Figure 13 shows the values of stresses before and after strengthening due to load combination II of object No.1. For maximum stress values of box girder top, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 2.7 MPa to 0.7 MPa. The value after strengthening is less than the 335



Figure 9.

The bridge model after strengthening

allowable value in Code-JTJ023-85 (2.34 MPa) and CodeJTG D62-04 (1.68 MPa). The higher value of compressive stress is increased from -4.7 MPa to -6.1 MPa which is less than allowable value in Code-JTJ023-85 (-14 MPa) and Code-JTG D62-04 (-13.4 MPa). For maximum stress values of box girder bottom, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 3.8 MPa to 2.0 MPa. The value after strengthening is less than the allowable value in Code-JTJ023-85 (2.34 MPa) and more than the value in Code-JTG D62-04 (1.68 MPa), because of the original design of the bridge using Code-JTJ023-85 and the model used live load of Code-JTG D62-04 which is heavier than live load in Code-JTJ023-85. Therefore, the original design is not suitable to carry the additional heavy traffic load. For minimum stress values of box girder top of object No.1, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 1.3 MPa to -0.3 MPa. The value after strengthening is less than the allowable value in CodeJTJ023-85 (2.34 MPa) and Code-JTG D62-04 (1.68 MPa). The higher value of compressive stress is increased from -6.6 MPa to -7.4 MPa which is less than allowable value in Code-JTJ023-85 (-14 MPa) and Code-JTG D62-04 (13.4 MPa). For minimum stress values of box girder bottom, the higher value of tensile stress is decreased from 1.6 MPa to 0.6 MPa. The value after strengthening is less

than the allowable value in Code-JTJ023-85 (2.34 MPa) and Code-JTG D62-04 (1.68 MPa). The higher value of compressive stress is increased from -10.0 MPa to 7.2 MPa which is less than allowable value in CodeJTJ023-85 (-14 MPa) and Code-JTG D62-04 (-13.4 MPa). The values of stresses before and after strengthening due to load combination II of object No.2 are shown in Figure 14. For maximum stress values of box girder top, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 3.4 MPa to 1.1 MPa. The value after strengthening is less than the allowable value in Code-JTJ023-85 (2.34 MPa) and Code-JTG D62-04 (1.68 MPa). The higher value of compressive stress is increased from -4.5 MPa to -6.5 MPa which is less than allowable value in Code-JTJ023-85 (14 MPa) and Code-JTG D62-04 (-13.4 MPa). For maximum stress values of box girder bottom, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 3.7 MPa to 2.2 MPa. The value after strengthening is less than the allowable value in Code-JTJ023-85 (2.34 MPa) and more than the value in Code-JTG D62-04 (1.68 MPa), because of the original design of the bridge using Code-JTJ023-85 and the model used live load of Code-JTG D62-04 which is heavier than live load in Code-JTJ023-85. Therefore, the original design is not suitable to carry the additional heavy traffic load.

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(a)

(b)

Figure 10.

The values of stresses before and after strengthening due to load combination I for object No.1, (a) top of box girder, (b) bottom of box girder

For minimum stress values of box girder top of object No.2, the values of tensile stresses are decreased after strengthening. The higher value of tensile stress is decreased from 1.6 MPa to 0.0 MPa. The value after strengthening is less than the allowable value in Code-JTJ023-85 (2.34 MPa) and Code-JTG D62-04 (1.68 MPa). The higher value of compressive stress is increased from -6.3 MPa to -8.0 MPa which is less than allowable value in Code-JTJ023-85 (14 MPa) and Code-JTG D62-04 (-13.4 MPa). For minimum stress values of box girder bottom, the higher value of tensile stress is decreased from 1.1 MPa to 0.2 MPa. The value after strengthening is less than the allowable

value in Code-JTJ023-85 (2.34 MPa) and Code-JTG D6204 (1.68 MPa). The values of compressive stresses are increased after strengthening, but the values at the pier box girder are decreased. The higher value of compressive stress is decreased from -10.4 MPa to -7.6 MPa which is less than allowable value in Code-JTJ023-85 (-14 MPa) and Code-JTG D62-04 (-13.4 MPa). From the above comparison it can be concluded that the strengthening program is effective to improve the structural performance of the bridge structure by decreasing the tensile stresses and increasing the compressive stresses.

337



(a)

(b)

Figure 11.

The values of stresses before and after strengthening due to load combination I for object No.2, (a) top of box girder, (b) bottom of box girder

For JTJ023-85: Allowable compressive stress = 0.5 × 28 = -14 MPa Allowable tensile stress = 0.9 × 2.6 = 2.34 MPa For JTG D62-04: Allowable compressive stress = -0.5 × 26.8 = -13.4 MPa Allowable tensile stress = 0.7 × 2.4 = 1.68 MPa

5.4.2.

Analysis of vertical deflection

Figure 15 shows the values of vertical deflection due to load combination II before and after strengthening. From this figure it can be noted that the values of maximum

vertical deflection are decreased from -29 mm to -24 mm, indicating that the strengthening program is effective to improve the stiffness of the bridge structure.

5.5.

Analysis of dynamic responses

The strengthening method which is used to reduce the vibration effects is using concrete cross beams between two box girders. Figure 16 shows the natural frequency before and after strengthening of the bridge modes. From this figure it can be noted that the natural frequencies af-

338



Figure 12.

The values of vertical deflection before and after strengthening due to load combination I

ter strengthening is increased and the natural frequency is equal to 5.60 Hz which is more than the natural frequency before strengthening which is equal to 4.963 Hz, indicating that the strengthening method is effective to reduce the vibration of the bridge structure. Figure 17 shows the mode shapes of modal after strengthening.

5.6.

Evaluation of strengthening methods

According to the results of theoretical analysis of static and dynamic structural responses, the tensile stresses are decreased and become less than the allowable limit values in the codes. The compressive stresses are increased and meet the allowable limit values in the codes. The values of vertical deflection are decreased after strengthening The values of natural frequencies after strengthening are increased and the natural frequency is equal to 5.60 Hz which is more than the natural frequency before strengthening which is equal to 4.963 Hz, indicating that the strengthening method is effective to reduce the vibration of the bridge structure. Therefore, this study concluded that the strengthening methods are effective to improve the structural performance of the bridge structure.

6.

Conclusions

The main conclusions of this study are: 1. Field investigation process of the bridge appearance shown that the bridge suffers from serious damages. The web of box girder of the second span near pier No.2 (in the quarter of middle span at 39 m on the bridge length) suffers from serious shear cracks. 2. There is a need to repair and strengthen of the bridge structure to ensure the safety application, improve the structural performance, increase the bearing capacity, to reduce the vibration of the bridge, and extend the service life of the bridge structure. The repairing and strengthening methods include treatment of the cracks, thickening the web of box girder along the bridge length and adding internal pre-stressing tendons in the thickening web, and construct reinforced concrete cross beams (diaphragms) between two box girders.

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(a)

(b)

Figure 12.

The values of stresses before and after strengthening due to load combination II for object No.1, (a) Max. top value of box girder, (b) Max. bottom value of box girder (cont)

340



(c)

(d)

Figure 13.

(continued) The values of stresses before and after strengthening due to load combination II for object No.1, (c) Min. top value of box girder, (d) Min. bottom value of box girder

341



(a)

(b)

Figure 13.

The values of stresses before and after strengthening due to load combination II for object No.2, (a) Max. top value of box girder, (b) Max. bottom value of box girder (cont)

342



(c)

(d)

Figure 14.

(continued) The values of stresses before and after strengthening due to load combination II for object No.2, (c) Min. top value of box girder, (d) Min. bottom value of box girder

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Figure 15.

The values of vertical deflection due to load combination II before and after strengthening

Figure 16.

The natural frequency of the bridge structure before and after strengthening

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(a)

(b)

Figure 16.

The mode shapes of modal after strengthening: (a) mode No.1, (b) mode No.2 (cont)

345



(c)

(d)

Figure 17.

(continued) The mode shapes of modal after strengthening: (c) mode No.3, (d) mode No.4

346



3. The results of theoretical analysis of static and dynamic structural responses after strengthening show that the tensile stresses are decreased and become less than the allowable limit values in the codes. The compressive stresses are increased and meet the allowable limit values in the codes. The values of vertical deflection are decreased after strengthening The values of natural frequencies after strengthening are increased and the natural frequency is equal to 5.60 Hz which is more than the natural frequency before strengthening which is equal to 4.963 Hz, indicating that the strengthening method is effective to reduce the vibration of the bridge structure. Therefore, the strengthening methods are effective to improve the bearing capacity and elastic working state of the bridge structure and to increase the service life of the bridge structure.

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