Tran Tr ansv sver erse se An Anal alys ysis is of a Pr Pres estr tres esse sed d Co Conc ncre rete te Wi Wide de Bo Box x Gird Gi rder er wi with th St Stif iffe fene ned d Ri Ribs bs Man Ma n Zh Zhou ou,, Ph Ph.D .D..1; Jia Jiando ndong ng Zha Zhang ng2; Din Dingyi gyi Yang Yang3; Most Mostafa afa Fahm Fahmii Hass Hassanein anein4; and Lin An5 . d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Abstract: For concrete box girders with wide �anges anges,, a ribbe ribbed d slab can increa increase se the cantilever cantilever length and trans transverse verse stiffness stiffness whil whilee reducing reduci ng the dead weight of the deck. For singl singlee box girder bridges with a large width-to-s width-to-span pan ratio, the traditional traditional cross section of a single-cell box girder (the two-web box section) can lose ef �ciency because of the effect of shear lag, cross-section distortion, and transverse bending moments. A literature search revealed that the prestressed concrete box girder with transverse ribs is already used in certain countries to meet the requirements of wide bridge decks of single-cell concrete box girders. However, little research has been conducted on the mechanical properties of this spine-like box girder, although it has been used in many applications. In this paper, the structural forms and dimensions of a concrete box girder with wide �anges and a ribbed slab are introduced on the basis of design experience. A signi�cant difference in the mechanical performance of ribbed box girders and conventional box girders was observed in the in �uence of the stiffened ribs. Therefore, on the basis of engineering practices, three representative three-dimensional (3D) �nite-element models (i.e., ribbed box girder, equivalent box girder, and ordinary box girder) were established to quantitatively investigat inves tigatee the in�uen uence ce of sti stiffe ffened ned rib ribss on tra transv nsversestressunder ersestressunder theactio theaction n of gra gravit vity y and veh vehicl iclee loa loads. ds. Theresult Theresultss of thi thiss inv invest estiga igatio tion n can be used as a reference for designing and constructing similar projects. DOI: 10.1061/(ASCE)B 10.1061/(ASCE)BE.1943-5592.0001076 E.1943-5592.0001076.. © 2017 American Society of Civil Enginee Engineers. rs.
Authorr keywo Autho keywords: rds: Wid Widee box gird girder; er; Trans Transverse verse ribs ribs;; Tran Transvers sversee anal analysis ysis;; Stre Stress ss conce concentr ntratio ation. n.
Introduction With increasing urban populations and traf �c �ow, prestressed concrete wide-deck box girders have been increasingly used for constructing new and reconstructing old bridges. For prestressed concrete concr ete sing single-ce le-cell ll box gird girders ers wit with h wide �anges anges,, the space between the webs and the cantilever length are large. It is obvious that structural weight will dramatically increase as the concrete deck width increases. Furthermore, increasing the weight will signi�cantly increase transverse stress at the root of the cantilever and in the middle of the slab, where the transverse rigidity of the ordinary box section might be insuf �cient for carrying dead and live loads. Therefore, the traditional box girder form might not be the most economical structural form. Common Common forms of box girders should be optimiz optimized ed to improve their transverse stiffness with due consideration for the mechanica mechanicall performance of the structure and its economics. To reduce the dead weight of the superstructure and to improve the stres stresss condi condition tion,, an improved improved cross cross--
1
Ph.D. Student, Dept. of Civil Earth Resources Engineering, Kyoto Univ., Kyoto 6110011, Japan (corresponding author). E-mail: zhou.man E-mail: zhou.man
[email protected] 2 Professor, Profe ssor, College of Civil Engineering, Engineering, Southe Southeast ast Univ., Nanjing 210096, China. 3 Professor,, College of Architecture Science and Engineering Professor Engineering,, Yangzhou Univ., Yangzhou Yangzhou 225127, China. 4 Associa Ass ociate te Pro Profes fessor sor,, Fac Faculty ulty of Engi Enginee neerin ring, g, Tan Tanta ta Univ Univ., ., Tan Tanta ta 999060, Egypt. 5 Associate Associa te Profe Professor, ssor, Dept. of Civil Earth Resour Resources ces Engineering, Kyoto Univ., Kyoto 6110011, Japan. Note. This manuscript was submitted on July 27, 2016; approved on March 6, 2017; published published online on June 6, 2017. Discussion period open until November 6, 2017; separate discussions must be submitted for indiEngineering, vidual papers. This paper is part of the Journal the Journal of Bridge Engineering, © ASCE, ISSN 1084-0702. © ASCE
sectional form, namely a box girder with a ribbed slab, has been used in Europe since the 1970s. In general, the length of the side cantilever of a conventional box girder is less than 4 m, and it is used for pedestrians and cyclists. Once side cantilevers exceed approximately 4 m, they should be prestressed or include ribbed or propp propped ed slabs. Thus, the leng length th of a ribb ribbed ed cantilever cantilever can be greatly extended. For instance, the cantilever of the Vejie Fjord Bridge in Denmark is 8.8 m. Ribbed slabs can be adapted to make a bridge deck thinner and can effectively reduce transverse normal stress at the root of the haunch caused by dead load or vehicle loads. The transverse bending moment capacity is the controlling factor for the dimensions of a wide bridge deck. Although this type of ribbed box section has been used in engineering practice in many countries, most existing bridges were designed on the basis of practical experience. Few scholars have conducted quantitative studies of the basic mechanical behaviors of this type of structure. The concept of using ribbed box sections and their dimensions were brie�y introduced by Benaim (2007 ( 2007), ), but the effects of longitudinally distributed transverse ribs on the mechanical behavior of the stiffened deck have not been studied. Rodriguez (2004 (2004)) noted that the use of a ribbed top slab is an effective approach to increasing the transverse stiffness of wide single-cell box girders. Zheng and Liu (2009 (2009)) brie�y introduced the structural forms and mechanical characteristics of wide box girder gir derss as wel welll as the their ir eco econom nomic ic fac facto tors. rs. Ram Ramakk akko o (1984 1984)) described the design and construction of the Twelve Mile Creek bridges and noted that a 10% reduction in weight was achieved by using transverse ribs instead of a haunched slab with variable thickness. Both the solid top slabs of all segments and the transverse ribs should be transversely posttensioned with straight tendons. The St. Andre de Cubzac Bridge, which has a 17-m-wide single-cell box girder and ribbed top slab, was designed by worldrenowned bridge designer Jean Muller with segmental prefabrication (Tassin (Tassin 2006). 2006). These studies only brie�y introduced this type
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of structure and its mechanical properties; thus, the structural analysis and quantitative evaluation of these special box girders in previous studies are insuf �cient. However, there are signi�cant differences between wide box girders with ribbed slabs and conventional box girders, because the transverse ribs change the path of the load transmission. Therefore, certain additional design factors in this spine-like box section should receive greater attention from engineers. The in�uence of stiffening ribs on transverse mechanical behavior and the differences between ribbed box girders and conventional box girders were determined in this study for the �rst time. In addition, in this report, the authors summarize rational structural forms and their dimensions as well as some notable proceedings in their design and application. The results of this work can serve as a reference for those designing similar engineering projects.
Structural Forms and Applications The prestressed concrete wide �ange box girder with transverse ribs was widely used in highway bridges and urban viaducts in Europe and the United States in the 1960. This structure has also seen recent widespread use in Japan. Some bridges constructed using it are shown in Table 1 (Grattesat et al. 1982; Bassi et al. 1984; Prade 1990; Leonhardt 1994; Podolny and Muller 1994; Jaeger et al. 2000; Tanis et al. 2002; Murugesh 2008). The sectional forms and structural features of this type of bridge are discussed later in this paper.
Ribbed Cantilever Slabs For a wide-body box girder with a side cantilever longer than approximately 4 m, a ribbed slab can be used to increase the reinforced concrete lever arm while reducing the dead weight of the deck, as shown in Fig. 1. The dimensions and spans of transverse stiffeners are determined by the live design load. The deck slab for a ribbed side cantilever will generally be 200 mm thick with ribs at the centers of approximately 3 –5 m. The rib height at the root of the cantilever is generally 1/7 to – 1/9 of the length of the cantilever slab. Transverse ribs are usually set in the middle (or at both ends) of the segments. The most common arrangement is to
provide ribs across the full width of the deck, as shown in Fig. 1(a). However, this arrangement is not necessary; as long as the webs and slabs are designed correctly, the ribs under the top slab between two webs can be removed [Fig. 1(b)]. The rib might also be deepened to directly apply bottom �ber compression to the bottom �ange of the box, as shown in Fig. 1(c). Note that the stress concentration is distinct in the ribbed slab, because the section stiffness varies periodically along the longitudinal direction. A reasonable design should ensure that the concentrated moment in the ribs can be accepted by the webs of the deck or by the overall structure. In practical engineering, a transverse prestressing tendon is usually set in the ribs.
Coffered Cantilever Slabs For long-span cantilever slabs subjected to gravity and concentrated live loads, solid slabs can become uneconomically heavy. In this case, it is worth exploring the use of a coffered slab, as shown in Fig. 2. The longitudinal and transverse cross stiffeners are considered to be reasonable when they are 40–60 cm tall and 20–50 cm thick. The stiffening ribs can be located at centers of approximately 1.5–4 m in the longitudinal direction and 1.5 m in the transverse direction. The thickness of the top slab can be reduced to between 170 and 180 mm in this case. The transverse ribs need to locally increase in depth at the junction with the deck to control shear stresses and to reduce maximum reinforcement density over the top of the web. This type of ribbed slab reduces the disparity in the stiffness in the transverse and longitudinal directions, improving the spread of the concentrated load.
Case Study: Project Background The approach of the Second Yangtze River Bridge in Wuhu, located in the southern region of Anhui Province in China, was chosen as a case study. This bridge is the �rst precast segmental prestressed concrete box girder bridge with transverse ribs under construction in China. The superstructure is a prestressed concrete continuous box girder with a 16.25-m-wide and 0.24-m-thick top slab and a 0.2-m-thick bottom slab, a depth of 2.6 m, a cantilever length of 4.5 m, a 6.08-m-wide bottom slab and a 0.4-m-thick web. Each span is
Table 1. Examples of Box Girder Bridges with Ribbed Cantilever Slabs Name
Location
Vejie Fjord Bridge Sallingsund Bridge Twelve Mile Creek bridges Viaduc du Lac de Gruyère Saint-Andre-de-Cubzac Bridge New Beni ci a-Mart inez Bridge
Denmark Denmark Canada Switzerland France America
Depth (m)
Width (m)
2.5–6 2.5–5.9 2.82 4 2.5–5.5 4.5–11.4
27.6 16.1 13.5 23.7 17 24
Web distance (m) 10.0–11.96 6.0–8.1 7.6 6
—
16.7
Cantilever (m) 7.82–8.8 4–5.05 2.95 8.85
—
3.65
Fig. 1. Cross-sectional forms of a box girder with a ribbedcantilever slab: (a)Section 1; (b) Section 2; (c) Section 3
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Fig. 2. Cross-sectional form of a box girder with a coffered cantilever slab: (a) elevation; (b) plane . d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Fig. 3. Elevation and cross-sectional dimensions: (a) overall size of the structure; (b) dimensions of the cross-section (Note: Units are millimeters)
40 m long, and each precast segment is 3 m long. The transverse ribs are located at the middle of the segment and are 0.3 m wide and 0.2 m deep near the cantilever end and 0.9 m deep near the web. The cross-sectional dimensions of the bridge are shown in Fig. 3. A wide box girder with a long cantilever and transverse ribs has many bene�ts, such as its lighter weight, fewer materials, and lower cost. In addition to broadening the bridge deck, both sides of the long cantilever can provide enough headroom for ground transportation. A double-column pier and bored pile foundation are used for the substructure. The dimensions of the bridge with an elevation and for a cross section are shown in Fig.3.
Finite-Element Model: Calculation Models The 40-m-long simply supported beam of the approach was built in Abaqus, as shown in Fig. 4. A 3D 8-noded hexahedral element (C3D8R) was used to simulate a box girder with transverse ribs, and a truss element (T3D2) was used to simulate the prestressing tendons. The prestressing force effect was applied by using the equivalent lowering temperature method, and the prestressing elements were embedded into the solid elements by coupling nodal © ASCE
degrees. End displacement was constrained to form a simply supported beam. To evaluate the effects of the transverse ribs on the mechanical performance of the wide box girder, three types of box girder models with different cross sections were established. Model 1: ribbed box girder based on the design scheme of the actual bridge, as shown in Fig. 5(a). Model 2: equivalent box girder for which the volume of the transverse ribs is redistributed to the top slab, as shown in Fig. 5(b). Model 3: ordinary box girder for which the transverse ribs in Model 1 are removed, as shown in Fig. 5(c). The thickness of the cantilever root section and the middle slab of Model 2 are 10 cm and 2 cm thicker than those of Model 3, respectively. •
•
•
Model Parameters Prestressed concrete beams typically use C50 concrete with a compressive strength of 50 MPa. In this study, concrete box girders were assumed to be homogeneous elastic bodies with a density of
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Fig. 4. Finite-element model of a box girder with transverse ribs
Fig. 5. Three types of box girder models with different cross sections: (a) Model 1 (ribbed box girder); (b) Model 2 (equivalent box girder); (c) Model 3 (ordinary box girder)
2,500 kg/m3. A linear stress-strain relationship was used in the �nite-element model to represent the concrete material with a modulus of elasticity of 32.5 GPa and a Poisson’s ratio of 0.2. Because it is a high-grade structural material, 1,860-MPa, low-relaxation prestressing steel strands are used in bridge design. In the elastic stage, the constitutive relation for prestressing tendons has linear elasticity. The elastic modulus of the prestressing tendons is 206 GPa, and their Poisson’s ratio is 0.3. The density and linear expansion coef �cients of the prestressing tendons are 7,800 kg/m3 and 1.0 10–5 /°C, respec tively.
Calculation Loads A dead load and worst-case live load were used in the �nite-element models. The dead load includes the structural weight of the beam and the prestressed reinforcement effect. In general, vehicle loads are a dominating load that controls the design of the top slab. To comprehensively evaluate the in�uences of the transverse ribs on the transverse stress of the ribbed cantilever and the ribbed top �ange slab, a �ve-axle heavy vehicle with a weight of 55 t (Ministry of Communications of the People ’s Republic of China 2004) was selected for use as the live load, and four load cases were established with various vehicle load positions, as shown in Fig. 6(a). © ASCE
The worst loading arrangement along the longitudinal direction was determined by the bending moment in �uence lines when the midspan moment reached its maximum, as shown in Fig. 6(b).
Results of Calculation and Comparisons Under dead and live loads, the transverse stresses of points A and B were selected to represent the mechanical characteristics of the hogging moment region near webs. The stress and de�ection of point C were selected to represent the sagging moment region at the middle of the upper �ange, as shown in Fig. 7. The transverse stress and de�ection of a longitudinal calculation path located along points A, B, and C were extracted from the results of the �nite-element calculation, and the numerical results are shown in Figs.8–14.
Under the Action of Gravity The numerical results of the transverse stress and the de�ection along Paths A, B, and C for each �nite-element model under gravity areshown in Figs. 8 and 9. Finite-element analysis indicated that the transverse ribs can effectively reduce the transverse stress of the wide box girder with a
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. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Fig. 6. Arrangement of vehicle load: (a) transverse arrangement of vehicle loads; (b) longitudinal arrangement of vehicle loads (Note: Units are meters)
Fig. 7. Positionsof calculated points (Note: Units are meters)
stiffened slab under gravity in the sagging moment region or the hogging moment region. This study also found that the phenomenon of stress concentration and mutation is most serious around the stiffened ribs, which obviously differs from that of conventional box girders. Considering the numerical computation results of Model 3 (ordinary box girder) as a reference, the average transverse stress of Path A in Model 1 under gravity was 33.3% less than the stress in Model 3; however, the transverse stress of Path A in Model 2 increased by 19.0% as a result of increasing self-weight, as shown in Fig. 8(a). In this study, it was observed that part of the bending momentis concentrated in thediscrete stiffened ribs; thus, themaximum transverse tensile stress near the root of the cantilever can be © ASCE
effectively reduced and the cantilever can be widened. Moreover, the same phenomenon occurs inside the box girder. The longitudinal distribution of transverse tensile stress under the slab is not uniform. The average transverse stress of Path C in Model 1 under gravity was 59.7% less than the stress in model-3. The transverse stress of Path C was similar in Model 2 and Model 3, as shown in Fig. 8(b). It should be noted that the stress concentration is more obvious in the internal ribs, as shown in Fig. 8(b) (the peak tensile stress under theinternalribs is approximately four times the average stress under the top �ange). As shown in Fig. 8(c), under selfweight, the maximum de�ection of the midspan of Model 1 approaches the de�ection value of Model 2, and the midspan
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de�ection of Model 3 without stiffening ribs is slightly smaller than the midspan de�ection of Model 1 and Model 2. In addition, because of the discontinuity of section stiffness, there are obvious �uctuations in the top stress Path A, as shown in Fig. 9(a). In addition, stress is distinctly concentrated around the internal stiffened ribs; thus, the same phenomenon of stress mutation occurs in stress Path C [Fig. 9(b)].
Under the Actions of Vehicle Loads The numerical results of the transverse tensile stress and the de�ection along Paths A, B, and C for each � nite-element model under different vehicle load conditions are shown in Figs.10–13.
. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Case 1: Eccentric Load Acting on the Cantilever Slab One vehicle was applied to the cantilever slab according to the in�uence line for the bending moment at midspan, as shown in Fig. 10. The extrema of the transverse tensile stress appear at the 12- and 14-t wheel positions along Path A. Under this condition, the phenomenon of stress disturbance near the stiffener ribs is no longer obvious. However, the peak stresses obtained from each calculation model were different. Similarly, considering the numerical computation results of Model 3 (conventional box girder) as a reference, the peak tensile stress of Path A in Model 1 under Case 1 was 2% less than the stress in Model 3; however, the peak tensile stress in Model 2 was only 8.7% lower than that of Model 3.
Case 2: Symmetrical Load Acting on the Top Slab between the Webs For a wheel load symmetrically applied to the top slab between the webs, the tensile stress �elds of Path B (hogging moment region) and Path C (sagging moment region) are shown in Fig. 11. For the hogging moment region, the peak tensile stress of Path B in Model 1 under Case 2 was 34.5% less than the stress in Model 3, and the peak tensile stress in Model 2 was only 13.8% less than the maximum stress in Model 3, as shown in Fig. 11(a). For the sagging moment region, the peak tensile stress of Path C (on the underside of the top �ange) was 36.8% less than the result in Model 3, and the peak tensile stress of Model 2 was 21% lower than that of Model 3, as shown in Fig. 11(b). The stress is distinctly concentrated in the stiffened ribs near the wheel loads. The maximum transverse tensile stress under the stiffened rib (Path C 0 ) is approximately � ve times greater than the stress under the top slab (Path C). In addition, the structural stiffness of the box girder with discrete stiffened ribs also increased to some extent. From Fig. 11(c), the maximum vertical deformations of Model 1 and Model 2 are approximately 88.4% and 92.3% that of Model 3, respectively.
Case-3: Eccentric Load Acting on the Top Slab between the Webs
Fig. 8. Transverse stress gravity
© ASCE
� eld
of the ribbed box girder under
Fig. 12 shows a case where wheel loading was eccentrically applied to the top slab between the webs. The values and the law of stress and deformation were the same as those for Case 2. Speci�cally, in Case 3, the peak tensile stress of Path B in Model 1 was 40.8% less than the stress in Model 3, and the peak tensile stress in Model 2 was only 11.3% less than the maximum stress in Model 3, as shown in Fig. 12(a). For the sagging moment region, the peak tensile stress of Path C (on the underside of the top � ange) was 43.2% less than the result in Model 3, and the peak tensile stress of model-2 was 27.6% lower than that of Model 3, as shown in Fig. 12(b). From
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. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Fig. 9. Transverse stress �elds: (a) Path A (root of thecantilever slab); (b) Path C and C 0 (middle of the upper �ange)
as shown in Fig. 13(a). In Case 4, the peak tensile stress of Path B in Model 1 was 40.5% less than the stress in Model 3, and the peak tensile stress in Model 2 was approximately 16.5% less than the maximum stress in Model 3, as shown in Fig. 13(b). For the sagging moment region in Case 4, the peak tensile stress of Path C in Model 1 was reduced by 51.7% compared with the stress in Model 3, and the peak tensile stress in Model 2 was approximately 21.8% less than the maximum stress in Model 3, as shown in Fig. 13(c). Similarly, very obvious concentrations of stress and strain � elds were observed in the stiffened ribs between the webs. In load Case 4, the maximum vertical deformations of Model 1 and Model 2 are approximately 92.7% and 95.4% that of Model 3, respectively [Fig. 13(d)].
Vehicle Load and Transverse Prestressing under the Action of Gravity
Fig. 10. Transverse tensile stressof Path A in Load Case 1
Fig. 12(c), the maximum vertical deformations of Model 1 and Model 2 are approximately 89.4% and 95.4% of the maximum vertical deformation of Model 3, respectively.
Case 4: Eccentric Load Acting on the Top Slab (Three Vehicles) The stress and deformation of each �nite-element model were studied under multiple vehicle loads, as shown in Fig. 13. The transverse stress in the hogging and sagging regions of the top �ange was the focus of this study. For the hogging moment region in Case 4, the peak tensile stress of Path A in Model 1 was 46.9% less than the stress in Model 3, and the peak tensile stress in Model 2 was only 6.6% less than the maximum stress in Model 3, © ASCE
According to the studies discussed earlier, the stress concentrations in the stiffened ribs should receive suf �cient attention in engineering design. Therefore, the transverse prestressed steel wire should be set not only in the top slab but also in the stiffened ribs. Threeply high-strength low-relaxation prestressing steel strands with a diameter of 15.2 mm were evenly applied to the top slab, and the space between two adjacent prestressing steel strands was 750 mm. Tension control stress was determined to be 1,395 MPa, and the same prestressing tendons were also arranged in the discrete stiffened ribs. The numerical results of the transverse tensile stress along Pats A and C of Model 1 under the actions of gravity, vehicle load (Case 2) and transverse prestressing are shown in Fig.14. Fig. 14 shows that the transverse prestressing tendon reduced the stress concentration in the stiffened ribs. In addition, the maximum transverse tensile stresses in the hogging moment region (Path A) and the sagging moment (Path C) were very close. These results indicate that the arrangement of double-layer prestressed reinforcements can improve stress states and make stress conditions more reasonable.
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. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Fig. 11. Transverse tensile stress and vertical displacement of each calculation path in Load Case 2
© ASCE
Fig. 12. Transverse tensile stress and vertical displacement of each calculation path in Load Case 3
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. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 7 1 / 7 1 / 6 0 n o o g e i D n a S , a i n r o f i l a C f o y t i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D
Fig. 13. Transverse tensile stress and vertical displacement of each calculation path in Load Case 4
Conclusions A new type of wide prestressed concrete box girder with transverse ribs was studied in this paper. First, the structural characteristics and the general demand for this ribbed box girder in construction are introduced. Then three types of 3D �nite-element models were established in Abaqus according to a practical engineering case study to investigate the in �uences of transverse stiffened ribs on the transverse mechanical behavior of this irregular box girder. On the basis of this study, the following conclusions can be drawn: 1. Stiffened ribs can effectively improve the stress state at the root of the cantilever as well as at the middle of the top slab. To quantitatively analyze the effects of stiffened ribs on the mechanical performance of the structure, three representative �nite-element models were established in Abaqus: the ribbed box girder (Model 1), the equivalent box girder (Model\ 2) and © ASCE
the ordinary box girder (Model 3). The results of numerical calculation showed that the average transverse tensile stress at the root of the cantilever in Model 1 under gravity was 33.3% less than the stress in Model 3. However, the transverse stress at the root of the cantilever was actually greater by 19.0% in Model 2 than in Model 3. Similarly, the average transverse stress of the lower edge path of the top slab in Model 1 under gravity was 59.7% less than the stress in Model 3, and the transverse stress of the middle section of the top slab in Model 2 was similar to the results of Model 3. The investigated structure presented the same mechanical behavior under vehicular loads. 2. The overall structural stiffness of the box girder with transverse ribs was also improved. The maximum de�ection of Model 1 was 10% less than that of Model 2 when subjected to symmetrical vehicle loads. Therefore, this spine-like box girder can obtain a larger cross-sectional moment of inertia than Model 2, in which the volume of these stiffened ribs was redistributed to the top slab.
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the National Nature Science Foundation of People ’s Republic of China (Grant 51578479). This �nancial support is gratefully acknowledged.
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Fig. 14. Transverse tensile stress and vertical displacement of Paths A and C
3. Although the average transverse tensile stress was reduced in Model 1, the stress concentration and mutation were the most serious around the stiffened ribs. This result obviously differs from the results obtained for conventional box girders. The peak tensile stress in the stiffened ribs is approximately four to �ve times larger than the average tensile stress. This phenomenon means that a considerable portion of the bending moment is concentrated in these thin stiffening ribs and can also explain why the stiffening ribs improve the stress state.
Acknowledgments
The authors express their gratitude for funding from the Priority Academic Program Development of Jiangsu High Education Institution (Grant CE02-1-12). This study was also supported by
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J. Bridge Eng.
