Phân tích ứng xử cơ học của phân đoạn dầm hộp bê tông cốt thép trong cầu dây văng một mặt phẳng dây tt tiếng anh

In the design of one plane cable stayed bridge, the cables are located in the middle of the top slab of the cross section; therefore the top slab has to subjected to rather large pull-ou

MINISTRY OF EDUCATION AND TRAINNING

THE UNIVERSITY OF TRANSPORT AND COMMUNICATIONS

BUI NGOC TINH

ANALYSIS OF MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BOX GIRDER IN ONE-PLANE CABLE STAYED BRIDGE

Domain: Transport Construction Engineering

Code: 9580205

SUMMARY OF DOCTORAL THESIS

Hanoi - 2020

INTRODUCTION

1 The necessity of the thesis

Cable stayed bridge was firstly built in Vietnam since 1998 (My Thuan bridge) Sofar, a number of cable stayed bridges were designed and constructed Many of them using two planes of cables as well as the

I and Π type cross section with incline webs to ensure the aerodynamic stability, enhance the lateral rigidity and therefore is able to pass over long span

In comparison to two-plane cable stayed bridge, the one-plane cable stayed bridge help to separate two traffic flows on the bridge by location the plane of cable in the middle of the cross-section; open the better view for transportation and also brings better aesthetic feeling However, since the cable is vertically located in the middle of the cross –section; they subject to only the vertical bending of the girder and do not contribute to the torsional strength of the cross-section That is the reason why the box-type of cross-section (which has high torsional rigidity and aerodynamic stability) is normally used for one-plane cable stayed bridge In Vietnam, there are two one-plane cable stayed bridges, they are Bai Chay bridge and Nga ba Hue bridge In which, Bai Chay bridge ranked the first among the list of longest span one-plane cable stayed bridge in the world at the time of construction (2006)

In the design of one plane cable stayed bridge, the cables are located in the middle of the top slab of the cross section; therefore the top slab has to subjected to rather large pull-out loading in out-of-plane direction This type of loading result in the compression in the slab (due

to the incline of cable), the bending effect in the girder and also the local pull-out loading on the slab; the combination of these effects lead to a complicated stress-strain condition in the slab Because of this reason, othotropic steel decks or composite deck solution is used in many one-plane cable stayed bridges, such as the Rama VIII bridge pass over Chao Phraya river in Bangkor

Reinforced concrete box girder can avoid the fatigue, vibration and large deformation problem as can be happened in steel box girder However, there is no guidelines for calculation of reinforced concrete slab subjected to the local pull-out loading combine with overall compression and bending as explained above

In order to avoid the local damage on the slab, the design solution

in Bai Chay bridge is using the tension pipe connecting the top slab to two bottom edge of the cross-section in order to transfer the pull-out loading in the top slab to the bottom of webs

This is an acceptable solution in term of loading capacity, but leading to many difficulties in construction; and the effect of the solution will be limited at the position where the incline angle of the cable is small and nearly perpendicular to the vertical pipe

Therefore, we decided to carry out the doctoral thesis namely

“Analysis of mechanical behavior of reinforced concrete box girder

in one-plane cable stayed bridge” in order to propose the theoretical

analysis model, validated by experimental study, to analyse the mechanical behavior of reinforced concrete girder in one-plane cable stayed bridge Also, base on the proposed model, analyse the effectiveness of the strengthening method using vertical pipe as used in Bai Chay bridge

The Aims, Objectives and Scope of research as summarized as follows:

- Compare and conclude on the effective solution for

strengthening the concrete box girder subjected to cable force in term of loading capacity

3 Objectives and the Scope of study

Structure: Reinforced concrete box girder subjected to pull out loading in the middle of the top slab;

Material: Reinforced concrete box girder, taking into account the non-linear behavior of steel and concrete

Loading: limited to static loadings

4 Methodology

- Literature review, determine the problem to be studied

- Experimental study;

- Numerical modeling

5 Novel contributions of the study

- Scientific contributions: Non-linear material model is employed for numerical modeling the behavior of concrete box girder of one-plane cable stayed bridge Number of experimental experiments were tested to validate the numerical result

- Application contribution: the thesis results can be applied in modeling the practical concrete box girder one-plane cable stayed bridge; contributes in design and evaluation of cable stayed bridge

6 Structure of thesis

The thesis consists of the Introduction, four main chapters and the Conclusion and Perpectives

Introduction

Chapter 1: Problem statement;

Chapter 2: Study on the mathematical model for analyse the stress-strain condition of reinforced concrete box type girder of one-plane cable stayed bridge;

Chapter 3: Experimental study for validating the “total strain crack” model for reinforced concrete slab subjected to out-of-plane inclined loading

and the Publication list of the Author

CHAPTER 1 PROBLEM STATEMENT

Cable stayed bridge was introduced in the 16th century and was widely applied from 19th century Some initial cable stayed bridges were the combinations of cable stayed bridge and suspension bridge (Brooklyn bridge, for example) In the development of cable stayed bridge, people used the two-plane, three-plane and also four-plane of cables The two-plane cable type were mostly used, however the inconvenience of this type of bridge was the aesthetics and the difficulty

in lanes arrangement One-plane cable type is more beautiful and helps

to reduce the dimension of the substructure However, the most unfavourable problem for one-plane cable stayed bridge is that the cable system can not support the main girder to againts twisting, aerodynamic unstability and vibration In order to enhance the twisting capability and aerodynamic stability, box-type girder was normally employed

For steel box girder, the weight of girder, the thickness of slab is relative small sothat for long span bridge, the girder is usually vibrate with high frequency and leading to the damage on the Asphalt cover layer (happened in Rama VII bridge with the span length equals to 450m) For concrete box girder bridge, one-plane cable leads to a

reinforced concrete slab subjected to out-of-plane pull out loading This problem will be the central question to be solved in this thesis

At the moment (2020), there are two one-plane cable stayed bridges have been built in Vietnam They are Bai Chay and Tran Thi Ly bridge In this type of bridge, a clear design of load transfer path from cable to the girder is necessary At the moment, there is not many researches or studies in this issue, especially the local behavior of the slab on the anchorage zone The literature review showed that it is necessary to continue the research on the connection between cable and the slab of reinforced concrete box girder

The bridge design specifications of Vietnam has not directly mentioned on the analysis of reinforced concrete slab subjected to local pull-out loading The stress-strain condition in the local anchorage zone

of the cable is not similar with the local anchorage zone of tendons in prestress concrete; since it is the combination the overall bending, the overall compression of the slab and the local pull-out at the anchorage region

In this thesis, the author focus on both theoretical aspect and experimental aspect of this problem

CHAPTER 2 THEORETICAL MODEL OF REINFORCED CONCRETE BOX GIRDER SUBJECTED TO CABLE FORCE IN

ONE-PLANE CABLE STAYED BRIDGE

2.1 The current status of the problem

Cable stayed bridge is designed due to the national design specications and standard In Vietnam, bridge design specifications TCVN 11823:2017 is not enough to design the cable stayed bridge, sothat people needs to refer to other specifications/standards which take into account the aerodynamics stability of bridge under wind load The problem of reinforced concrete slab subjected to the tensile force of cable, is the combination of three loading condition: reinforced concrete

slab subjected to compression, to bending and the local pull-out loading Vietnameses design specifications and standards have not mentioned on this combination of loadings

2.2 Propose the “total strain crack” model for analysing the behavior of reinforced concrete slab subjected to cable force in one-plane cable stayed bridge

Reinforced concrete slab subjected to incline out-of-plane loading

is a common type of structure widely used in bridge and other construction For bridges, this type of structure is applied in the slab of one-plane cable stayed bridge or in the hollow tower with the anchorage located inside This type of structure subjects to overall bending, in-plane compresion, local out-of-plane loading and was studied in both modeling and experimental aspects

In numerical modeling aspect, the “multi-layer method” was introduced, in which the slab is divided into many layer, each layer is assumed to have uniforme tension or compression stress perpendicular

to the layer In this type of approach, the reinforcement and concrete is modeled as a “layer”, and can help to estimate the stress-strain condition

in the slab direction However, this method can not take into acount the effect of the stress perpendicular to the slab direction, for example the shear stress Also, this type of method cannot take into account the contribution of local reinforcement, which normally located perpendicular to the loading direction In order to solve this problem, Hrynuk and Vecchio proposed the “multi-layer method” but taking into acount the shear effect The method of Hrynuk and Vecchio helps to solve the reinforced concrete slab subjected to vertical loading However, can not modeling the effect of incline loading and cannot estimate the forming and the development of local cracks

In order to modeling the happen and development of cracks in reinforced concrete structure; there are two approaches They are the

“discrete” model and the “smeared crack” model In “discrete” model, the discontinuity in the displacement field is used to model the crack

Extended finite element method (X-FEM, ED-FEM) is employed for numerical modeling and the “discontinuity” in displacement is taken into account by an additional shape function for the displacement (see Ibrahimbegovic, Armero, ) It is difficult to apply this type of approach for three-dimensional reinforced concrete structure; since it is needed to have the contact relation equation between concrete, reinforcement and bonding in all three dimensions, and will require a huge computational work

The second approach is so-called the smeared crack model In which, the displacement field is still assumed to be continuous field after crack In term of finite element method, the crack is modeled as a displacement inside the finite element, but not in the nodes The

“smeared crack” model was studied by many authors, but initialy proposed by Vecchio and then developed by Selby for three-dimensional element, namely “total strain crack” model The “total strain crack” model theoretically can model the forming and development of crack in three-dimensional refion, therefore can be applied in such type of structure like deep beam, or the anchorage zone

of prestressed concrete construction The application of “total strain crack” model in modeling the reinforced concrete slab subjected to perperdicular compression was performed by Ngekpe and Barisua and give reasonable results However, this model have not been applied in modeling the reinforced concrete slab subjected to out-of-plane incline compression or tension In the experimental aspect, there is only few reports on the reinforced concrete subjected to vertical loading, but not many research on the reinforced concrete slab subjected to incline loading In this thesis, the author will also carry out experimental research on this issue

In the “total strain crack” model, the direction of principal stress

is assumed to be same with the direction of principal strain

Figure 1 Stress-strain condition

Since this model apply for reinforced concrete material then the technical properties of concrete and reinforcement is necessary, including: young modulus, Poission ratio, tensile strength, compressive strength and the fracture energy For fracture energy (Gf), one can refers

to the value from CEB-FIP 1990 as shown in equation 1 and table 1

In which, fcm is the average compressive strength of concrete, fcm0

is the reference compressive strength, equals to 10 MPa The value of reference fracture energy (Gf0) is selected due to the maximum aggregation dimension (Dmax) as shown in Table 1:

Figure 2 Relation between stress-strain of reinforced concrete

in principal direction in compression and tension

There are a number of mathematical models were proposed for the stress-strain relation of concrete under compression and tension Equation 2 introduces the equation of Thorenfeldt for compression and

Equation 3 introdues the equation of Vecchio and Collins for tension

cr c

E f

'

1 1

1

200 1

0

(3)

The shear stress – shear strain behavior of concrete is assumed to

be linear, with a reduction factor β

r

In which β is the reduction factor of shear modulus G due to cracks β equals to from 0 to 1

For reinforcement, the elasto-plastic model can be employed:

y si si

s si

f

E f

“total strain crack” model

CHAPTER 3 EXPERIMENTAL STUDY ON REINFORCED CONCRETE SLAB SUBJECTED TO INCLINE LOADING

In ordre to prove the capability of “total strain crack” model in modeling the behavior of reinforced concrete slab subjected to incline loading, experiments were carried out and the results are compared to the numerical analysis

3.1 Experimental model

Reinforced concrete slabs with three incline angles of loading (α) (25, 45 and 70°) are considered

Figure 3 Experimental samples

In each incline angle, three experimental samples are made The reinforced concrete slab is 10cm in depth, 500cm in width and 600cm in length The compressive strength of concrete is 40MPa, the maximum aggregate dimension of concrete is 20mm Two layers of reinforcement are arranged, with the spacing is 15×15cm A steel plate is put under the compression force, on the top face of the slab and welded into

reinforcement layer of the slab An incline compression (P) was put on the middle-top of the slab The compression P increases with time until the slab is failure; strain in concrete and reinforcement, deflection in the slab are measured during compression

3.2 Modeling results

The experimental slabs are numerical modeled using “total strain crack” model; the input parameter of material are showed in the table 2

Table 2 Material parameters

Reinforcement CB400V

Concrete C40

3 Compressive strength f'c 40 MPa

From the above parameters, the stress-strain relation curve of reinforced concrete is made The reinforced concrete slab is modeled by finite element method (3d brick element for concrete, 1d element for steel bar) (see figure 4)

Figure 4 Reinforced concrete slab model

The compression force P increases in 11 levels (with Pu is the ultimate load of compression), which the specific value in the Table 3

Table 3 Values of compression force (P)

The calculated deflection of the slab, stress in the reinforcement

of the slab with different incline angle is shown in the Table 4 and Figure 5 In the figure 5, the dashed lines show the result at 20cm from the central point of the slab while the normal lines show the result at the central point of the slab

Table 4 Calculation results