Summary of Doctoral thesis in Engineering: Study the deformation stress state of multi-layer reinforced concrete doubly curved shell roof

Thesis studying deformation stress state of two-layer curved reinforced concrete sloped shell roof under the impact of uniformly distributed load in the period before concrete appeared cracks, in case the shell has constant thickness.

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF CONSTRUCTION HANOI ARCHITECTURAL UNIVERSITY LAM THANH QUANG KHAI STUDY THE DEFORMATION STRESS STATE OF MULTI-LAYER REINFORCED CONCRETE DOUBLY CURVED SHELL ROOF FIELD OF STUDY: CIVIL ENGINEERING (CIVIL AND INDUSTRIAL CONSTRUCTIONS) CODE : 62.58.02.08 SUMMARY OF DOCTORAL THESIS IN ENGINEERING HANOI – 2019 The thesis was completed at Hanoi Architectural University Supervisors: Assoc Prof PhD Le Thanh Huan Prof PhD Nguyen Tien Chuong Reviewer 1: Reviewer 2: Reviewer 3: This thesis was presented and defended at Doctorate Examination Council at Hanoi Architectural University At date month year 2019 The thesis is available at the National Library of Vietnam and Library of Hanoi Architectural University LIST OF PUBLISHED SCIENTIFIC ARTICLES OF THE AUTHOR RELATED TO THE THESIS Lam Thanh Quang Khai (2016), Some methods in calculating stresses and deformations of reinforced concrete shell roof structures Vietnam Journal of Construction (ISSN 0866-0762), No 6/2016, pp (165-168) Lam Thanh Quang Khai, Le Thanh Huan (2016), Surveying the stress-deformation of the laminated shell by anisotropic shell theory and equivalent thickness diagram Vietnam Journal of Construction (ISSN 0866-0762), No 8/2016, pp(190-194) Lam Thanh Quang Khai, Le Thanh Huan, Nguyen Tien Chuong (2016), Surveying the stress-deformation of the 5-layer shell roof by reinforced concrete with different boundary conditions Vietnam Journal of Construction (ISSN 0866-0762), No 10/2016, pp(136-140) Lam Thanh Quang Khai (2018), Research the stressdeformation of double-layer reinforced concrete shell by experiment Vietnam Journal of Construction (ISSN 0866-8762), No 3/2018, pp (5861) Lam Thanh Quang Khai, Do Thi My Dung (2018), Stress-strain in multi-layer reinforced concrete doubly curved shell roof 15th World Conference On Applied Science, Engineering And Technology, 12/2018, India (ISBN: 978-81-939929-2-0) INTRODUCTION Reasons for choosing the topic In calculating the reinforced concrete thin shell roof, with thin shell roof types such as: one or two-dimensional curved shell, cylindrical shell, spherical shell according to calculus, numerical methods, experimental With a curved two- dimensional shell roof, the shell is quite special because of the change in curvature on the shell, because different types of boundary structures will greatly affect the deformation stress of the shell and there are few studies for this type of structure Some typical research on two-dimensional curved shells, including analytical studies were introduced by Vlasov [63], Le Thanh Huan [12][13][15][16][65], Ngo The Phong [21] Some research by numerical methods: Ahmad and his colleagues [27], Nguyen Hiep Dong [9][11], Harish and his colleagues [40], Stefano and his colleagues [60] Some experimental studies by Le Thanh Huan [65] and studies of Meleka and his colleagues [51], Sivakumar [59]… However, in fact, using two-dimensional curved shell roofs in Vietnam, there are other layers besides the main bearing concrete shell layer such as waterproof layer, heat-resistant layer or reinforcement layer, reinforcing the shell creating multi-layer shell structure In it, analytic studies were introduced by Ambarsumian [26][66], Le Huan [68], An-dray-ep and Nhi-merop-ski [69] With the assumption that the inner layers of the shell are tightly bound, it is possible to put the multi-layer shell into an equivalent one-layer shell In addition to studying grade composite shells or in addition to shell oscillation or stabilization studies, multilayer shell studies were introduced by authors Rao [56], Mohan [50], Nguyen Dang Quy and his colleagues [52], Ferreira and his colleagues [34], Francesco and his colleagues [35] However, these studies are not really clear and complete in calculating the deformation stress state, the ability to split and slip between layers in the shell and it is still quite complicated in calculation However, in calculating the structure of reinforced concrete thin shell roof with single layer or multiple layers, there are still many issues to be studied and solved such as: It is necessary to solve the system of high-order differential equations, it is not easy to clearly know the stress state of each shell layer, there are not many experimental studies on the type of reinforced concrete roofs in a layer or many layers… From reference to domestic and foreign sources, there are very few studies on the treatment of multi-layer reinforced concrete shell roofs, the ability to split and slip between layers in a comfortable multi-layer sloped shell roof and the use of metal fiber reinforced concrete layer dispersed in the shells Therefore, the author sees the need to study the topic: "Study the deformation stress state of multi-layer reinforced concrete doubly curved shell roof" to clarify the above problems of multilayer shell is practical in both scientific and practical meaning Objectives of the study Study the deformation stress state of two-layer curved reinforced concrete cshell roof with two positive dimensions Study the effect of parameters on shear stress in the two-layer sloped shell roof and consider the ability to split and slip between layers Object and scope of the research  Object of the research: two-layer curved reinforced concrete sloped shell roof with two positive dimensions  Scope of the research: studying deformation stress state of two-layer curved reinforced concrete sloped shell roof under the impact of uniformly distributed load in the period before concrete appeared cracks, in case the shell has constant thickness Research Methods Study the theory of combining analysis on Sap2000 software and ANSYS numerical simulation Experimental studies were also conducted with shells made of reinforced concrete materials Methods are synthesized, analyzed and compared to evaluate results Scientific and practical significance of the topic  Scientific significance: The thesis contributes to elucidating deformation stress and the ability to split and slip between the shells of the structure of multi-layer curved reinforced concrete sloped shell roof with two positive dimensions  Practical significance: the problem of positive two-dimensional curved sloped shell roof made of multi-layer reinforced concrete material under load, with experimental calculation and numerical simulation, the thesis has drawn some technical comments, so it has practical significance The thesis structure In addition to the introduction, conclusions, recommendations and appendices The thesis is presented in chapters, the content of each chapter is as follows: Chapter 1: Overview of studies of two-dimensional curved reinforced concrete sloped shell roof Chapter 2: Theoretical calculation of multi-layer curved reinforced concrete sloped shell roof with two positive dimensions Chapter 3: Study the deformation stress state of two-layer reinforced concrete sloped shell roof by experiment Chapter 4: Study the state of deformation stress of two-layer sloped shell roof by numerical simulation and parameter survey New contributions of the thesis The contribution of an experimental research result on the behavior of two-layer doubly curved shell roof by concrete and steel fiber reinforcement concrete through the construction of diagrams: deformation, stress, internal force, deflection, load - slip deformation Evaluate the degree of bonding of the shell to the stage before concrete appears cracks Based on experimental research, numerical simulation of ANSYS software, it is concluded that the doubly curved shell roof is made of non-slip concrete materials, capable of working together as a single-layer shell model equivalent to suitable boundary and load conditions Using the built model, studying the effect of shell parameters on the deformation stress state of the comfortable sloped shell roof, including: layer thickness, fiber concrete layer position, fiber content in concrete… CHAPTER 1: OVERVIEW OF STUDIES OF TWO-DIMENSIONAL CURVED REINFORCED CONCRETE SLOPED SHELL ROOF 1.1 Overview of theoretical and experimental studies on a signle-layer two-dimensional curved reinforced concrete sloped shell roof 1.1.1 Theoretical studies 1.1.1.1 Analytical studies To solve the problem of reinforced concrete sloped shell roof, Vlasov [63] has set up a system of two differential equations with two stress and displacement functions to be found as  and w bear the vertical load of qx, y  :     2 4  w    w  w  k1  k 2  D  2    qx, y  x y  x  x  y  y     2w  4  4  4 2w   2   Eh k1  k 2   x x y y y   x (1.1) On that basis, Le Thanh Huan [15][65], Bai cop V.N [67] used the point method (semianalytical) to solve the system of equations Vlasov to find the internal force values, the stress in the positive two-dimensional curved sloped shell roof in different boundary conditions In addition to solve the system of equations Vlasov, Ngo The Phong [21] In addition to solving the system of equations Vlasov, Ngo The Phong used Navier's double trigonometric series, the single trigonometric series of Levi, the method of general torque theory to be distributed to determine internal forces and bending moments for curved shells 1.1.1.2 Studies according to numerical methods a) Method of successive approximations The essence of this method is to solve the generalized second-order differential equation of the form:  wi  wi wi  wi  2w w 2w w  w n   wi    p                    i i i i i         i 1     This method of successive approximations is also used by author Nguyen Hiep Dong [9][10][11] in his doctoral dissertation and articles published in the country b) Finite Element Method Method using flat plate type elements: Using flat triangular elements, flat quadrangular elements have been presented quite well in the documents: Richard [55], Lee and his colleagues Method using curved shell elements: In order to better approach the geometry of the shell structure, in analysis using curved shell elements, there are also many documents that are quite well presented.: [31][36][66] Thanks to the application of Finite Element Method, with the support of computer facilities, many forms of thin shell structure have been studied and developed by many domestic and foreign authors, such as: Bandyopadhyay and his colleagues [29] analyzed the curvature of a two-dimensional curved shell structure The displacement fields are made of polynomial approximations Do Duc Duy [8], Dang Van Hoi [18], Tram Anh Tu [17] have further clarified the deformation stress of a two-dimensional curved sloped shell roof, solving complex problems that have almost never been solved before, such as the impact of air temperature, the influence of boundary structures… Hyuk Chun Noh [39] I have studied the limited capacity of large-scale reinforced concrete thin shell structure, taking into account both geometric nonlinearity and nonlinear shell material Harish and his colleagues [40] I have studied the stress deformation of two-dimensional curved concrete shell with Sap2000 software under load evenly distributed to the shell In addition to studying deformation stresses of shells, Stefano [60] have also studied new design methods to minimize the use of shell materials such as shell shape, boundary conditions, and loads… 1.1.2 Experimental studies Le Thanh Huan [65] studied the deformation stress in a positive two-dimensional curved sloped shell with a square model of organic glass material Recently, Meleka and his colleagues [51] carried out to evaluate the repair and reinforcement of reinforced concrete shell with openings with polymer reinforced fiberglass materials (GFRP) Sivakumar and his colleagues [59] studied the stress and curvature of the curved shell with the rectangular surface, the curvature at the top of the shell is 80mm, the edge beam is 40 × 50mm, with the shell thickness of 20mm and 25mm Jeyashree and his colleagues [45] I studied the stress and displacement of the comfortable sloped shell with two-dimensional curved squares with the size of 68 × 68cm under the concentrated load at the top General comments on theoretical and experimental studies of single-layer shells: The study of theory or experimentation of two-dimensional curved sloped shell roofs only stops at the comfortable one-layer sloped shell roof type, not to mention the multi-layer shell structure Therefore, the thesis continues to focus on the study of multi-layer two-dimensional curved sloped shell roofs 1.2 Overview of theoretical and experimental studies on multi-layer two-dimensional curved reinforced concrete sloped shell roof From the equation system of Vlasov, Ambarsumian [26] From the equation system of Vlasov, Ambarsumian has developed an anisotropic multi-layer shell theory for thin shell problems and is considered a theoretical basis for multi-layer shell studies Ambarsumian has concluded that the layers work in the elastic phase, not sliding on each other to allow us to no longer consider the strain stress of each individual layer Rao [56] has developed stiffness matrices for multi-layer anisotropic sloped shells in rectangle, the deformation stress state of the shell is calculated based on the intermediate surface of the shell After that, Le Thanh Huan [14][68] in his study was based on Ambarsumian's anisotropic multi-layer shell theory, which continued to be developed for the multi-layer positive twodimensional reinforced concrete sloped shell roof problems with the assumption that the layers stick together In 2001, An-dray-ep and Nhi-me-rop-ski [69] has published its work on plates and anisotropic multi-layer shells, bending, stability and vibration with a different approach to the shell theory of Ambarsumian Equal and continuous equations are written in tense form In the study, Carrera [30] studied multilayered shells, but only general theory studies, not to mention the possibility of sliding separation of shells Francesco and his colleagues [35] studied the positive two-dimensional curved sloped shell on the Winkler-Pasternak elastic foundation by general differential method Currently, from many domestic and foreign sources, no empirical studies have been found on the behavior of the sloped shell roof and considering the possibility of splitting and sliding of multi-layer positive two-dimensional curved shell roofs with reinforced concrete materials in large sizes To elucidate the deformed stress of the multi-layer positive two-dimensional curved reinforced concrete sloped shell roof and consider the possibility of sliding separation of layers, the thesis presents the following research contents 1.3 The contents need to be studied by the thesis  Study the deformation stress state of multi-layer shell roof according to analytical solution and solution of the solution method through Sap2000 software  Study the state of deformation stress of two-layer sloped shell roofs by experiment  Study the state of deformation stress of two-layer sloped shell roof by numerical simulation  Study the effect of each layer thickness, fiber concrete layer position to the deformation stress state of the sloped shell roof and consider the ability to split and slip between shells by numerical simulation CHAPTER 2: THEORETICAL CALCULATION OF MULTI-LAYER POSITIVE TWODIMENSIONAL CURVED REINFORCED CONCRETE SLOPED SHELL ROOFS 2.1 Concepts and applications of thin shell roofs 2.1.1 The concept of thin shell roof Two-dimensional curved shell roof: The two-dimensional curved reinforced concrete shell roofs is called slope when the slope of any point on the surface of the shell compared to the bottom plane does not exceed 180 or the curvature ratio f is the largest (The height from the center of the plane contains corners to the top of the shell roof) on the short side f  [15] a 2.1.2 Application scope and advantages of thin shell roof Thin reinforced concrete roof: Widely used in construction works Thin reinforced concrete roof is a form of space structure with advantages [15]: Suitable for large aperture works, large space without intermediate columns Compared with plans for using flat structures with the same aperture, the thin shell roof has a self weight reduction of 20-30%, creating architectural works with rich and impressive shapes thanks to the curved surface and large scale of the roof 2.1.3 Two-dimensional curved sloped shell roof has been built in and out of the country Table 2.1: Construction of two-dimensional curved sloped shell roofs has been built Construction Thickness Year of of shell completion 3030m 9cm 1931 UK 18.925.9m 9cm 1951 UK 38.168.5m 7.6cm 1963 Viet Nam 1818m 7cm 1996 No Name of works The works of Wiesbaden Germany Brynmawr rubber factory Smithfield Poultry market location Hall of Hanoi National University Surface size 2.2 Basic calculation theory of a 1-layer positive two-dimensional curved sloped shell roof 2.2.1 Vlasov's equation system [63]     2 4  w    w  w  k1  k 2  D  2    qx, y  x y  x  x  y  y     2w  4  4  4 2w   0    Eh k  k  x x x y y y   There are many methods to solve the system of differential equations of level (2.5), but it is not very simple The complexity is that for a sloped reinforced concrete roof, two functions  and w must be found so that they both satisfy the system of equations (2.5) and satisfy different boundary conditions 2.2.2 The calculation of the shell according to the non-torque state 2.2.2.1 Use Navier's double trigonometric series [21] The non-torque internal force of the shell is determined by the formula (2.7): N1  N2  16q2  mk 2 16q 2 m n  nk m n n mx ny sin sin 2 a b m  k  n y x  m mx ny sin sin 2 a b m  k  n y x  (2.7) 2.2.2 Application of Lévi single trigonometric series [21] Non-moment internal force of the shell is determined by the formula (2.9): N1   N2  4qR  4qR  Ch y  nChn b sin  n x n 1 Ch y   n 1  Chn b  sin  n x n  n  (2.9) 2.2.2.3 Application of point method (semi-analytical method) Depending on the requirement of works use, marginal structures have different forms, such as structure of flat trusses, beam, wall or rows of column or pillars at corners…Bai cop [67] and L T Huan [15][65] have presented circumstances upon applying the non-torque theory 10 N   N   16qR12   m m1.3 n1,   n 2 m m n sin sin  mn a b m  n  n    mn 16qR12       m1.3 n1, 2 sin m n sin a b (2.39) Vertical displacement (deflection): w 16qR12 EhC     m1.3 n1, m  n 2 mn  sin m n sin a b (2.40) Bending moment:  2  m n  16qR1h M     C m1.3 n1,3    m  2  m n  16qR1h M     C m1.3 n1,3    m       2 2  2   2    P1 R1 n F2  m  n 2 2 a h mn P1 R1 m F2  m  n 2 2 a h mn     m n  sin sin a b     m n  sin sin a b   Example 2.1: Positive two-way curved shell roof with the square surface dimension a=b=36m, curve radius R1=R2=1.25a Layer I: the concrete layer with thickness of h I=10cm, B25, modulus of elasticity EI=315000kG/cm2 Layer II: the concrete layer with steel mesh B20, thickness of hII=4cm, EII=265000kG/cm2 Similar poisson ratio v=0.2 Load, including dead load and live load on the roof is 500kG/m2 Calculating internal force, stress and deflection of shell roof with margine is pin-connected frame system Solution: Figure 2.14 Internal force, stress, deflection diagram of double-layer shell [68] 11 2.4.1.2 Solution of finite element method by Sap2000 software a) Construction of shell roof structure model Figure 2.18 Internal force and deflection diagram of double-layer shell Note: Red line: based on analytical solution [68]; Blue line: based on Sap2000 Remarks: Variance of internal force is from 11.8% - 31%, variance of deflection is from 12% - 21% For reinforced concrete structure, various marginal structures have different hardness, significantly influencing on deformation and stress of shell structures In order to clarify stress and deformation at marginal region as well as influence of shell layers, the author carries out calculating of 5-layer shell roof with both marginal conditions: clamp and pin, as follows: 2.4.2 5-layer shell roof 2.4.2.1 Stress and deformation of 5-layer shell roof with pinned marginal condition a) Analytical solution Example 2.2: Positive two-way curved shell roof with the square surface a=b=36m, R1=R2=45m, including layers: layer (bottom) by concrete B25 with thickness h1=3cm, E1  315000kG / cm2 ; layer with thickness h2=19cm, E2  141750kG / cm2 ; layer by concrete B25 with thickness h3=3cm, E3  315000kG / cm2 ; layer by concrete B20 with thickness h4=5cm, E4  264915kG / cm2 ; layer (top) by concrete B5 with thickness h5=2cm, E5  10710kG / cm2 12 Similar Poisson ratio v=0.2 Load, including dead load and live load on the roof if 500kG/m Calculating internal force, stress and deflection of shell roof with margine is pin-connected frame system Figure 2.20 Internal force and stress diagram of pinned marginal 5-layer shell b) Solution of finite element method by Sap2000 Hình 2.22 Internal force diagram of pinned marginal 5-layer shell Remark: “Stress distribution of multi-layer shell depends on the number of layer and modulus of elasticity of each layer”, these are problems on reinforced concrete multi-layer shell roof which are not clearly assessed 2.4.2.2 Stress and deformation of 5-layer shell roof with clamped marginal condition a) Analytical solution Thus, in the analytical method, application of double trigonometric series sin  , sin  is not still appropriate b) Solution of finite element method by Sap2000 software 13 Figure 2.25 Internal force, stress and deflection diagram of clamped marginal 5-layer shell Remark: Internal force N at a location approaching the clamped marginal condition is less than the pinned marginal condition, and internal force N is more than the pinned marginal condition The result shows influence of marginal conditions is very important 2.5 Remark Through the value of internal force and stress in shell, it is shown that “Stress distribution of multi-layer shell depends on the number of layer and modulus of elasticity of each layer” The results of internal force, stress and deflection based on analytical solution and Sap2000 are similar, thus, the theory of single-layer shell may be applied to determine stress and deformation in shell with suitable load CHAPTER 3: RESEARCH ON STRESS AND DEFORMATION IF REINFORCED CONCRETE DOUBLE-LAYER SHELL ROOF BASED ON EXPERIMENT 3.1 Objective and content of experimental research 3.1.1 Objective of experimental research a) To studye working capacity of concrete layers with different strength b) To build diagrams : deformation, stress, internal force, deflection, relation between load creep deformation of shell 3.1.2 Content of experimental research Including: Making design of experiments, carrying out experiments and handling experimental results 14 3.2 Basis for design of experimental models 3.2.1 Basis for design of experimental models In theoretical researches [26][66][68], it is assumed that layers of shell roof are adhered, but it is not specified which marginal structure is applied and how load is limited 3.2.2 Establishment of experimantal models for thesis - Because the model of reinforced concrete shell roof is relatively large and the way to form and make experiments on multi-layer shell roof is complicated with a lot of time, through the ANSYS simulation, it is showned that if surfance dimension 33m, it is qualified to sensitively response to the load - In application of shell roof in Vietnam, the underlying layer of shell roof is a main bearing layer, waterproof concrete layers, heat-resistant concrete layers with low strength lies on shells In case of shell repairment, it will be researched by simulation with BTS layer lying on plain concrete 3.3 Design and manufacture of experimental models 3.3.1 Materials - Concrete B20 (M250) for plain concrete and B30 (M400) for fiber reinforced concrete - steel fiber (0.5-L30mm): stell fiber meets ASTM A820-01 [23], fiber direction ratio is from 50 to 100 meeting ACI 544.1R-1996 [22] 3.3.2 Experimental models Figure 3.2 Design of shell roof 33m based on experiments 3.3 Purpose, type and position of pasting strain gage - Purpose of pasting strain gage (tenzomet resistor): measure deformation  on concrete surfaces and on reinforcement in each layer, thereby determining stresses and internal forces at the pasting positions 15 - Type of strain gage and strain gauge equipment: using strain gage type BX120-30AA, Leaf form with 30mm long, 3mm wide, resistor Rgage=120, gage coefficient =2.081% Using the strain gage device of Data loger TDS-530 (30 channels), Data loger TDS-601 (10 channels) by Vietnam Institute for Building Science and Technology IBST and Strain Indicator P-3500, set of channel switch SB10 (10 channels) - Position of pasting strain gage: from preliminary calculation results and simulation results on ANSYS software - Paste method: [48] 3.3.4 Manufacture laboratory samples The steps are as follows: - Step 1: processing the formwork in accordance with the shape of the positive two-direction curved shell roof - Step 2: pouring concrete for layer 1, which is steel fiber concrete with 2% content of steel fiber in concrete, - Step 3: continue to process reinforcement, strengthen edges, paste strain gage to the middle steel, the strain gage is welded with anti-interference electric wires 3.3.5 Sample maintenance: according to TCVN 8828-2011 [5] 3.4 Test for physical and mechanical properties of materials 3.4.1 Test for determining compressive strength of concrete: TCVN 3118-1993 [1] 3.4.2 Test for determining elastic modulus of concrete: TCVN 5726-1993 [2] 3.4.3 Steel tensile test In the shell, there is no bearing steel bar in the shell, so it is not experimented for steel tensile 3.5 Test of 2-layer reinforced concrete shell roof 3.5.1 Layout diagram of test equipment e) Position pasting strain gage on the underside f) Position pasting strain gage on the topside 16 g) Paste strain gage on steel at layer h) Paste strain gage on steel at layer Figure 3.11 Position pasting strain gage on the shell 3.5.2 Conduct the test: Implemented as follows: Step 1: Preparation work, Step 2: Install and check measuring devices, Step 3: Start the test 3.5.3 Test result of 2-layer shell roof SHEAR DEFORMATION Figure 3.15 Relationship between the load and the shear deformation of the shell Comment: Shear deformation (Figure 3.15) at load level 611kG/m2 4.310-5, vis still small compared to the extreme relative deformation of concrete which is cu=3.510-3 See as at the shell edge of shear deformation, the layers are very small and can be ignored, meaning that the steel pins linked between the two shells are not effective Figure 3.16 Deformation in the layers of the shell 17 Figure 3.17 Stress in layers of the shell Figure 3.18 Internal force Nx, Ny of the shell Figure 3.19 Compare stress and deflection results by EXP and SAP Comment: We see that the position inside the shell has negligible stress difference between the experiment and Sap2000 3.6 Comment The layers of shell roof not slip on each other, working together as a multi-layer structure, can use the equivalent single-layer shell model when the load is appropriate CHAPTER 4: STUDY ON THE DEFORMATION STRESS STATE OF TWO-LAYER SHELL ROOF BY NUMERICAL SIMULATION AND PARAMETER SURVEY 18 4.1 Introduction about ANSYS software and study contents 4.1.1 Brief introduction about ANSYS software The sequence of solving structural problems in works with ANSYS software includes the following basic steps and is divided into groups: data processing, calculation and processing of calculation results 4.1.2 Contents of numerical simulation study - Build the FEM for the two-layer roof shell of the two layers to experiment - Completing the FE model by adjusting the input parameters from the test results of normal concrete materials, fiber concrete and steel fibers 4.2 Select modeling of fiber reinforcement smeared in concrete To modeling fiber reinforcement in concrete, three models are used: smeared model, embeded model and discrete model [24] [32] Thus, in this study, fiber reinforcement smeared in concrete should use the smeared model to be reasonable 4.3 Select modeling cracks in concrete Currently, cracks in concrete are modeled in two basic forms: discrete model and smeared model [38] In this study, we select the smeared model for cracks in concrete 4.4 Select the interface model between layers of concrete In calculation, it is possible to use the interface element or thin layer element to simulate the shear interface surface between two different concrete layers [19] 4.5 Building finite element model for the shell roof 4.5.1 Elements in the model Concrete simulation element: SOLID65 element Interface element: simulated by the type of TARGE170 element for 3D interface The object surface is modeled by the type of CONTA173 element 4.5.2 Divide mesh for the model The principle when dividing the mesh must ensure that elements shall share nodes together, so we divide by shell thickness equal to layer (ESIZE, ALL, H1) and divide the mesh freely (MSHKEY, 0) with mesh shape divided into 3D tetrahedral blocks (MSHAPE, 1,3D) 4.5.3 Edge conditions and effective load The shell is rigidly linked with edge curved beams The effective load distributes on the top side of the shell at the nodes of tetrahedral block mesh (NSLA, R, 1), by P compressive force evenly distributed on the shell surface (SF, ALL, PRES, P) 4.6 Material model 4.6.1 Concrete material model 19 Figure 4.10 Strain stress curve of concrete when pulling and compressing an axis [28] 4.6.1.1 Strain stress model of concrete under compression Through serveying strain stress models of concrete under compression is presented above and the results of strain stress of tested concrete (Figure 3.9), we see that the test results are consistent with Kachlakev's model 4.6.1.2 Strain stress model of concrete when under the tensile This model is already defined in ANSYS (Figure 4.15) [24] 4.6.2 Destruction standards of concrete Willam and Warnke's destruction standards are used in this study and defined in ANSYS Concrete will be cracked or crushed if it satisfies the equation (4.10) [64] 4.7 Input parameters for the model In ANSYS, to enter the input parameters for concrete element SOLID65, we must enter the following basic parameters: Cutting force transmission coefficient when crack is opened   , Cutting force transmission coefficient when crack is closed  C  , Cracking stress when tensiling an axis  f r  , Crushing stress of an axis  f C' , Coefficient is reduced and weak due to cracking when tensiling (default select as 0.6), Elastic modulus EC  ,7 Poisson's coefficient, Curve of stress strain relationship of concrete 4.8 Research results between the test and numerical simulation 4.8.1 Deflection in the shell Figure 4.17 Deflection of methods 20 4.8.2 Stress in the shell Figure 4.18 Stress of methods 4.8.3 Deflection and stress of the shell roof at the load level starts appearing concrete cracks Period starts appearing concrete cracks: Load level P=14kN/m2=1400 kG/m2, stress 13.38kG/cm2 then, the first crack appears in the shell, running along the lower edge of the BTS layer, the maximum deflection at the top of the shell is 0.17mm 4.8.4 Comment The analytical results show that this FE model is suitable with the test and other software (Sap2000) It is possible to use the ANSYS model to servey the effects of layer thickness, fiber concrete layer position to strain stress in the shell and the ability to split and seperate among layers 4.9 Survey the parameters affecting the strain stress of the shell roof by numerical simulation 4.9.1 Thickness parameters of each layer a) The deflection of the shell of the survey cases b) Stress x c) Stress y Figure 4.22 Deflection and stress of survey cases 21 4.9.2 Position parameters of fiber concrete layers a) Shell feflection of case and case b) Stress x c) Stress y Figure 4.23 Deflection and stress of case and case 4.9.3 Servey shear layers in the shell roof Table 4.7: The result of the largest tangential stress calculation BTS 2cm under the BTS 3cm above the BTT 3cm layer BTT 2cm layer Tangential Stress max 0.094MPa 0.069MPa Corresponding normal stress 0.346MPa 0.276MPa Stress component Comment: When the affected shell of the load is evenly distributed on the top of the shell perpendicular to the shell surface, there is a phenomenon of shearing among layers in the roof After being affected by the load, at the interface position between the two shell layers, there is a relative strain between the two layers equal to 110-3 and still much smaller than the relatively limited strain of concrete cu = 3.510-3 4.10 Stress strain state of the roof shell 3636m a) Stress and deflection of the shell in case of considering nonlinear of materials 22 a) When concrete starts to crack b) When concrete starts to sabotage Figure 4.26 Stress of the shell when the content of steel fiber core changes a) When concrete starts to crack b) When concrete starts to sabotage Figure 4.27 Deflection of the shell when the content of steel fiber core changes b) Comparing the stress and deflection of the shell when analyzing linear and nonlinear of materials a) When concrete starts to crack b) When concrete starts to sabotage Figure 4.28 Stress of the shell when analyzing linear and nonlinear 23 a) When concrete starts to crack b) When concrete starts to sabotage Figure 4.29 Deflection of the shell when analyzing linear and nonlinear c) Shearing among shell layers Table 4.12: Results of shearing calculation when steel fiber content changes Value Content of 0% fiber Content of 8% fiber Tangential Stress max 0.408MPa 0.389MPa Corresponding Normal Stress 1.705MPa 1.774MPa Load causes shearing 900 kG/m2 950 kG/m2 Comment: When this load causing shearing has not been passed, the layers inside the shell not have a shearing phenomenon, so in calculating, the roof shell can use the equivalent singlelayer shell theory 4.11 Comment A survey among layers shows that shear strain is very small, can be ignored and able to return to the equivalent single-layer shell theory when the load is appropriate In addition to the numerical simulation of the tested roof shell, the thesis also extends the studied problem with layer span shell roof and nonlinear materials CONCLUSIONS AND RECOMMENDATIONS I Conclusion The thesis has designed, fabricated and tested a shell model with quite large size of × 3m made of concrete and smeared steel fiber reinforced concrete, which are usually done on small models and convertible materials Can evaluate the linking level among the shell layers Has implemented the calcultation of numerical simulation of experimental shell roofs using ANSYS software Comparing numerical simulation results with results calculated with Sap2000 software and experimental results to evaluate simulation parameters, from which there is a basis for surveying the layer parameters and evaluating the the shearing level among layers Through the experimentation and calculation of numerical simulation, it has determined that the load causing shearing When this load has not passed, the inner layers of the shell not have a shearing phenomenon, so in calculating the roof shell can use the equivalent single-layer shell theory II Recommendations - Recommendations: ▪ When the load applied to the shell is equal to the load itself and the live load on the roof, it is possible to completely replace the reinforcement of the bar in the double-sided curved shell roof 24 with many layers using steel fiber reinforced concrete When the load is overtaken, the shell roof will be cracked, so it is necessary to arrange steel bars with the outer structure of the fiber reinforcement ▪ When calculating the shell design, in addition to the position near the edge with complex strain stress, it is also necessary to consider at the position of the shell top and the shell angles ▪ It is possible to use an equivalent single-layer shell theory with appropriate edge and load conditions - Development direction of the topic: ▪ Subsequent studies can be developed for shell roof with openings and in different types of thin shell roofs such as: Spherical shell roof, cylindrical roof, negative double-sided curved shell roof, etc for problems of heat and wind , different types of edge conditions ▪ Studying to build general equations containing shell thickness parameters affecting the strain stress state in the shell, or studying to build equations containing shell span parameters ... choosing the topic In calculating the reinforced concrete thin shell roof, with thin shell roof types such as: one or two-dimensional curved shell, cylindrical shell, spherical shell according... Objectives of the study Study the deformation stress state of two-layer curved reinforced concrete cshell roof with two positive dimensions Study the effect of parameters on shear stress in the two-layer... Chapter 3: Study the deformation stress state of two-layer reinforced concrete sloped shell roof by experiment Chapter 4: Study the state of deformation stress of two-layer sloped shell roof by numerical