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.

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

Supervisors:

1 Assoc Prof PhD Le Thanh Huan

2 Prof PhD Nguyen Tien Chuong

At date month year 2019

The thesis is available at the National Library of Vietnam and Library of Hanoi Architectural University

OF THE AUTHOR RELATED TO THE THESIS

1 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)

2 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)

3 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)

4 Lam Thanh Quang Khai (2018), Research the

stress-deformation of double-layer reinforced concrete shell by experiment

Vietnam Journal of Construction (ISSN 0866-8762), No 3/2018, pp 61)

(58-5 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

1 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 thanh Huan [68], An-dray-ep and Nhi-me-rop-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

layer reinforced concrete doubly curved shell roof" to clarify the above problems of

multi-layer shell is practical in both scientific and practical meaning

2 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

3 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

4 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

5 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

6 The thesis structure

In addition to the introduction, conclusions, recommendations and appendices The thesis is presented in 4 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

7 New contributions of the thesis

1 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

2 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

3 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

and w bear the vertical load of q , x y :

w y x

w x

w D y

k x k

y

w k x

w k Eh y y x x

, 2

0 2

4 4 2 2 4 4

4 2

2 2 2 2 1

2 2 2 2 2 1 4

4 2 2 4 4

On that basis, Le Thanh Huan [15][65], Bai cop V.N [67] used the point method

(semi-analytical) 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:

p w w

w w

w w

w w

w

i

i i i i i i i i i

2 2 2

2 2

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 dimensional reinforced concrete sloped shell roof problems with the assumption that the layers stick together

two-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 DIMENSIONAL CURVED REINFORCED CONCRETE SLOPED SHELL ROOFS

TWO-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 4 corners to the top of the shell roof) on the short side

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

No Name of works Construction

location Surface size

Thickness

of shell

Year of completion

2.2 Basic calculation theory of a 1-layer positive two-dimensional curved sloped shell roof 2.2.1 Vlasov's equation system [63]

w y x

w x

w D y

k x k

y

w k x

w k Eh y y x x

, 2

0 2

4 4 2 2 4 4

4 2

2 2 2 2 1

2 2 2 2 2 1 4

4 2 2 4 4

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):

y n a

x m n k m k m

n q

2 2 2 2

2

y n a

x m n k m k n

m q

.2.2.2 Application of Lévi single trigonometric series [21]

Non-moment internal force of the shell is determined by the formula (2.9):





b nCh

y Ch qR

n

x b

Ch

y Ch n

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 4 corners…Bai cop [67] and

L T Huan [15][65] have presented 3 circumstances upon applying the non-torque theory

2.2.3 Shell calculation based on moment states

2.2.3.1 Shell calculation based on marginal effect theory[15][21]

a) In case of shell having pinned connection with marginal strucrure:

Figure 2.9: Bending moment diagram in case of shell having pinned connection with margine

b) In case of shell having clamped connection with marginal structure:

Hình 2.10: Bending moment diagram in case of shell having clamped connection with margine

2.2.3.2 Shell calculation based on general theory of moment [21]

Expressions of internal force and moment as follows:

n k m k m

nK q

N

mn

2 1 2 2 2 2

mK q

N

mn

2 1 2 2 2 2

K m q

a

2 1 2 2 2 2 4

K n q

a

2 1 2 2 2 2 4

2 2

2.3 Calculating theory of doubly curved shell roof with multiple layers

2.3.1 System of equation for solution of reinforced-concrete doubly curved shell roof with multiple layers by rectangle [26][68]

Figure 2.12 Quantity of roof layers

See the following equation:

2.3.2 Stress and deformation of doubly curved shell roof with multiple layers

Internal force of shell roof is determined as follows:

b

n a

m m

n qa

3 6

2 6 2

m n

m qa

3 6

2 6 2

m mn

m A n A m a A n a A qa

m n

i i

i i

2 2 4 7 2 2 2 2 6 2 3 4 5 2 3 2 4 4 6

m mn

n A m A n a A m a A qa

i i

i i

2 2 2 2 11 2 2 2 10 2 2 3 4 9 2 3 4 8 6

m mn

a n A m A n

A m A qa

M

i i i

2 3 4 2 2 17 2 16 2 2 2 15 2 14 4

m mn

a m A n A m

A n A qa

M

i i

i i

2 3 4 2 20 2 2 19 2 2 15 2 2 18 4

Figure 2.13 Orthotropic double-layer shell roof [68]

Internal force is:

 

b

n a

m mn

m n m qR

2 2 2 2 2

m mn

n n m qR

2 2 2 2 2

m mn

n m EhC

qR w

2 2 2 2 2

m mn

F n n m h a R P vn m n m C

h qR M

2 2 2 2 2 2

1 2 1 2 2 2 2 2 2 2 2

m mn

F m n m h a

R P vn m n m C

h qR M

2 2 2 2 2 2

1 2 1 2 2 2 2 2 2 2 2

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]