The specific goals include: - Investigating heat transfer process inside steel members, - Evaluating the effectiveness of gypsum and fireproof mortar layers with two different forms incl
Trang 1MINISTRY OF EDUCATION AND TRAINING
HANOI UNIVERSITY OF CIVIL ENGINEERING
Pham Thi Ngoc Thu
ASSESSMENT OF FIRE RESISTANCE OF PROTECTED STEEL MEMBERS FOR BUILDINGS IN VIETNAM
Major: Civil Engineering Code: 9580201
SUMMARY OF DOCTOR DISSERTATION
Ha Noi – 2021
Trang 2This dissertation has been completed at the Hanoi University of Civil Engineering
Academic advisor: Prof.Dr Pham Van Hoi
Reviewer 1 Prof.Dr Nguyen Tien Chuong
Reviewer 2 Assoc.Prof.Dr Doan Tuyet Ngoc
Reviewer 3 Dr Nguyen Duc Viet
The doctoral dissertation will be defended in front of Doctoral Defense Committee held at the Hanoi University of Civil Engineering
At … … on …………
This dissertation is available for reference at the Libraries as follows:
- National Library of Vietnam,
- Library of Hanoi University of Civil Engineering
Trang 3PREFACE
1 Motivation of the research
Fire safety is always one of the most important concerns when designing buildings and constructions For buildings, countermeasures against fire mainly focus on architectural solutions as well as fireproofing Particularly for steel structures, using traditional materials such as concrete, bricks, gypsum, or mortar for fireproofing is a common solution
The effectiveness of fireproofing solutions is normally evaluated by the duration that the load-bearing members have not reached the critical temperature However, this criterion is usually determined based on the specification provided by manufacturers without an accurate analysis of the behavior of the structure Therefore, it is necessary to develop a procedure to estimate the resistance of structural members in fire conditions, thereby choosing the appropriate solution This is the reason for choosing the topic
“Assessment of fire resistance of protected steel members for buildings in Vietnam” for the dissertation
2 Research objectives
The purpose of the study is to propose a procedure for determining the resistances of protected I-shaped steel members in fire conditions in accordance with construction conditions in Vietnam The specific goals include:
- Investigating heat transfer process inside steel members,
- Evaluating the effectiveness of gypsum and fireproof mortar layers with two different forms including box-shaped cover and contour cover,
- Investigating the behavior of protected steel members in fire conditions
3 Research subjects and scope
- The strength resistance of steel I-shaped beams protected by gypsum or fireproof mortar exposed to the fire from three sides
- The buckling resistance of steel I-shaped columns protected by gypsum
or fireproof mortar exposed to the fire from four sides
In this study, it is assumed that there is no reduction within the lengths of members and the boundary conditions at two ends do not change during the investigations
4 Research methods
- The theoretical method is applied to:
+ analyzing the procedure to design structural members in fire conditions, + analyzing fire models used to determine the temperature on the surfaces and inside structural members,
+ developing a program to calculate the temperature patterns inside unprotected and protected members in fire conditions,
Trang 4+ proposing a simplified method to determine the load-bearing capacity of protected steel members in fire conditions,
+ analyzing obtained results
- The numerical simulation method is employed to:
+ investigating the behavior of protected steel members in fire conditions using the commercial software ANSYS Workbench
5 Scientific basis
- Theoretical basis: systematizing theories related to design protected steel members in fire conditions, collecting insulation materials which are commonly used in Vietnam
- Practical basis: reviewing experimental studies related to the investigation of structural members in fire conditions that are conducted in previous studies, collecting specifications of insulation materials provided by manufacturers in Vietnam
6 Contributions of the dissertation
- Developing an approach based on the finite element method in the MATLAB environment to determine the three-dimensional distributions of the temperature in steel members
- Proposing a simplified method to calculate the load-bearing capacity of protected I-shaped steel members in fire conditions This method can be applied to select suitable fireproofing materials under specific conditions
- Numerical investigating the behavior of steel members protected by gypsum and fireproof mortar in fire conditions using the commercial software ANSYS Workbench
- Analyzing the obtained results and determining the scope of application for the two above methods
7 Scientific and practical significance
+ Scientific significance: this research summarizes the theoretical basis of the behavior of steel members in fire conditions and outlines the fire design procedure of protected steel members in Vietnam
+ Practical significance: this research provides a background theory and a useful tool for engineers in practical design Based on the results of this research, engineers can develop a library of fire protection solutions and choose an appropriate solution for each specific design case
8 Contents of the dissertation
Chapter 1 Overview of fireproofing solutions and fire-resistance calculation methods for buildings
Chapter 1 presents an overview of fireproofing solutions that are widely used in steel buildings in Vietnam The fire design procedure for steel structures is also introduced Besides, a literature review of fire design methods is carried out in this chapter
Trang 5Chapter 2 Method for solving heat transfer problems in steel members
In this chapter, the heat transfer process and the relationship between the fire models and the structural models when calculating the temperature of structures are presented Next, a novel algorithm called DT3D is proposed in the MATLAB environment to calculate the three-dimensional distribution of temperature in unprotected or protected I-shaped steel members The proposed algorithm can determine the temperature at any position in steel members during the investigation The accuracy of the proposed algorithm is verified by comparing it with results from previous experiments
Chapter 3 Determination of the load-bearing capacity of steel members in fire conditions using the simplified calculation method
Chapter 3 proposes a procedure to determine the load-bearing capacity of insulated steel members in fire conditions using the simplified method called SDM In more detail, the formulas provided in EN 1993-1-2:2005 are utilized
to calculate the load-bearing capacity of steel members at a given time in which the temperature is determined using the proposed DT3D algorithm Several examples of steel I-shaped members protected by gypsum and fireproofing mortar are carried out Based on obtained results, some recommendations for selecting a suitable fire protection solution are drawn
Chapter 4 Investigation of the load-bearing capacity of steel members in fire conditions using the numerical simulation method
In Chapter 4, some numerical models are developed using the commercial software ANSYS Workbench with the aim of investigating the stress-strain relationship and the resistance of protected steel members in fire conditions Three features including Thermal Analysis, Structural Analysis, and Eigenvalue Buckling analysis are used when developing numerical models
A comparison between results obtained from the simplified method SDM and results obtained from the numerical investigation is carried out From that, the range of application of each method is pointed out Additionally, the effectiveness of each fire protection solution is discussed
Conclusions Achievements and recommendations for future work
CHAPTER 1 OVERVIEW OF FIREPROOFING SOLUTIONS AND FIRE- RESISTANCE CALCULATION METHODS FOR BUILDINGS 1.1 Overview of cover forms for protecting steel structures in buildings
1.1.1 Fire prevention solutions for buildings
In Vietnam, fire prevention solutions for buildings are divided into three categories: architectural solutions, technical solutions, structural solutions in
Trang 6which the form of covering load-bearing members with insulation materials
is widely used For steel which rapidly declines load-bearing capacity in fire conditions, fireproofing plays an important role in increasing the fire resistance of steel structures Within the scope of the dissertation, gypsum and fireproof mortar are presented
1.1.2 Gypsum
Fireproof gypsum can exist in the following types: gas gypsum, foam gypsum, fiber reinforced gypsum In heat transfer calculations, the thermal conductivity of gypsum can vary from 0.2 to 0.25 W/moC There are several basic forms of covering: single-sided protection (F1.1a), box-shaped protection (F1.1b), contour protection (F1.1c) Vinh Tuong with Gyproc gypsum board and USG with Boral gypsum board are popular brands in Vietnam
Figure 1.1 Forms of covering with gypsum
1.1.3 Fireproof mortar
Fireproof mortar has only one form of protection which is covering around the perimeter of a member The mortar can adhere directly to the surface of the steel member or exist with a reinforcement mesh The minimum thickness of directly bonded mortar is 14mm, of mortar with reinforcement mesh is 50mm In heat transfer calculations, the thermal conductivity of fireproof mortar can vary from 0.15 to 0.25 W/moC Popular fireproof mortar products in Vietnam are Cemgum, Vermiculite, Esscoat, Isolatek,
1.2 Overview of the fire-resistance design procedure for steel structures
1.2.1 Calculation of load-bearing capacity of steel structures in fire
The fire-resistance design process of steel structures includes three steps:
- Analyzing the fire in fire model
- Analyzing the heat transfer from the surface to the positions inside the members in the structural model
- Analyzing the stress-strain behavior, making conclusions about the bearing capacity of steel structures in fire conditions corresponding to the fire resistance levels
Trang 7load-1.2.2 Temperature-time curve in fire models
Three types of fire models including nominal model, parametric model and real model are used to study the effect of temperature variation in fire space The nominal model in ISO is built on the basics of fires of hydrocarbon and cellulose materials (Figure 1.2) The temperature-time curve
is given by:
10
in which T is given in oC and t is in minutes
Figure 1.2 Temperature-time curves in the nominal fire model
1.2.3 Temperature variation inside steel members in the structural model
In three-dimensional space, the temperature can be determined from the numerical solution of the heat flow equation:
in which T=T(x,y,z) represents the temperature within 3-D coordinate system
(x,y,z); r is density; C is specific heat and l is thermal conductivity
In Chapters 2 and 4, the theoretical algorithm using the finite element method to calculate the temperature distribution within steel members in fire conditions and the commercial software ANSYS Workbench are presented ANSYS is a software developed by ANSYS Software (USA), it is based on the finite element method to simulate the behavior of a physical system that is subjected to different impacts
1.2.4 Basic calculation methods
- Simplified calculation models: the formulas for determining the critical temperature, the fire-resistance time and the load-bearing capacity are applicable for the investigation of individual members at elevated temperatures in fire conditions
Trang 8- Tabular method: the simple calculation process is automated, the results are shown through data tables This method is suitable for typical fireproofing solutions and individual members
- Advanced calculation models: this is a complex method in which the change of many thermal-mechanical properties with temperature and time are considered This method is applied to individual components or the whole structural system
1.2.5 Loads and actions in fire conditions
1.2.6 The behavior of steel beams and columns in fire conditions
1.3 Studies on the fire resistance calculation of steel structures
1.3.1 Research results in the world
1.3.2 Research results in Vietnam
1.1.4 Standards and regulations
SUMMARY
- Steel is vulnerable in fire conditions so that protecting load-bearing steel members with insulation materials is a necessary measure to increase the fire resistance of steel structures Currently, gypsum and fireproof mortar are widely used for buildings in Vietnam
- Studies on the behavior of beams, columns in fire conditions focus on unprotected steel or composite members The results obtained from components protected with insulation materials such as gypsum, mortar,… are limited
- The actual design of steel structures in fire in buildings in Vietnam: + Vietnam’s standard system does not have any design procedure for steel structures in fire conditions, researches on this issue are few and not popular + The current design process usually stops at the tabular method which depends heavily on the lookup tables in the catalogs of insulation materials manufacturers
+ Simplified and advanced calculation methods have not been studied for practical application The simplified method is very suitable in the preliminary selection of fireproofing solutions for the steel structures The advanced methods are necessary for the optimal evaluation and analysis of the behavior of the whole structure Thus, establishing a full design procedure applying methods from simple to complex for protected steel members with gypsum or fireproof mortar is needed
CHAPTER 2 METHOD FOR SOLVING HEAT TRANSFER PROBLEMS IN STEEL
MEMBERS
Trang 92.1 Heat transfer
Heat can flow due to the temperature difference in three distinct mechanisms: heat transfer, conduction and radiation
2.2 Thermal properties of steel
Thermal properties of steel such as thermal conductivity coefficient, specific heat capacity, thermal conductivity coefficient vary markedly depending on the temperature
2.3 Heat transfer in three-dimensional space
2.3.1 Heat transfer equation in three-dimensional space
Let us consider a three-dimensional element of unit volume dV=dxdydz
with temperature-dependent heat transfer A basic equation of heat transfer
has the following form:
where: C is specific heat capacity, r is the material density, Q is the inner
heat generation rate per unit volume, l is the thermal conductivity coefficient
of the material Equation (2.1) is considered with boundary conditions:
- Specified temperature T= T o on boundary S T ; T o is simply a constant in a lot of practical applications
- Specified heat flow q = q o on boundary S q;
- Specified heat flow from convection q c = h(T c - T) on boundary S c,
where h is the convection coefficient, T c is the convective exchange temperature
2.3.2 Algorithm DT3D applying 3D finite element method (FEM) in heat transfer
(a) In global coordinate system X (b) In local coordinate system W
Figure 2.1 Survey 6-surface element
Let us consider the heat distribution of a 6-surface element with 8 nodes
(1,2,3,4,5,6,7,8) in X(x,y,z) coordinate system (Figure 2.1a) After
transforming to the reference element defined in local coordinate system
W(x,h,z) (Figure 2.1b), temperature function T(x,y,z) will convert to
Trang 10T[x(x,h,z), y(x,h,z), z(x,h,z)] Vector of temperatures at nodes T e = [T 1 T 2 T 3
T 4 T 5 T 6 T 7 T 8 ]’
Shape functions N i are defined that N i (x,h,z) = 1 at node i and = 0 at other
nodes (Lagrange function):
N 1 = (1-x)(1-h)(1-z)/8 N 5 = (1-x)(1+h)(1-z)/8
N 2 = (1+x)(1-h)(1-z)/8 N 6 = (1+x)(1+h)(1-z)/8
N 3 = (1+x)(1-h)(1+z)/8 N 7 = (1+x)(1+h)(1+z)/8
N 4 = (1-x)(1-h)(1+z)/8 N 8 = (1-x)(1+h)(1+z)/8 (2.2)
The temperature T and the coordinates of a point M(x,y,z) are denoted
with the coordinates of nodes:
x h z
ù
¶ é¶ ù
ú ê ú
¶ ú ê¶ ú ú
¶ ê¶ ú
ú ê ú
¶ ú ê ¶ ú ú
x h z
x h z
z z z
x h z
ù
¶ ú
¶ ú ú
¶ ú
¶ ú ú
¶ ú
¶ û
=
11 21 31
J J J
éêêêë
12 22 32
J J J
13 23 33
J J J
ùúúúû
x
J y
T T
z
x h z
* 21
* 31
J 1 J
d etJ J
éêêêêë
* 12
* 22
* 32
J J J
* 13
* 23
* 33
J J J
ùúúúúû
T T T
x h z
method Assuming that the element is a domain V, V is divided into 8
Trang 11sub-elements and the answer of (2.1) is * 8
Substitution of T* into (2.1), we have surplus:
Galerkin’s finite element method establishes an integral formula to
minimum surplus (2.7) and the value of T i are calculated from the following equation:
Trang 12¶ ü + =
í ý
¶
The temperature T varies in the time domain between the n and n+1 time
levels Using a Taylor series and neglecting the second-and higher-order terms, we can write the relationship between the temperature at the nth and n+1th level: T ( n ) T ( n 1 ) T n
Assuming the variation T is linear from nth to n+1th level, the temperature
at t (n+k) time can be written: T ( n k )+ =kT ( n 1 )+ + -(1 k T) n (2.16) Replace (2.15) and (2.16) into (2.14):
( ) ( n 1 ) ( [ ] [ ] ) n ( { }( n 1 ) { }( n ))
C +k t K T D + = C -( 1 k ) t K T- D +D t k f + +( 1 k ) f
-(2.17) Because the thermal conductivity of steel l a varies significantly with temperatures, it is necessary to choose a small enough interval Dt so that the
error of l a between two-time levels is acceptable, that is:
Relative error value ( ( n 1 ) )2
a( i ) i
a( i ) ( n 1 ) 2
a( i ) i
d( l + )=l + -l là is an absolute error of thermal conductivity
at node i at time level n+1 We can take k=0,5 and use the formula (2.17) to
determine the temperature in time level The calculation steps of the DT3D algorithm are presented according to the diagram in Figure 2.2
2.4 Calculation and verification examples
2.4.1 Calculation example
Trang 13Figure 2.2 The diagram of the DT3D algorithm
Figure 2.3 The temperature at point W1-4 according to the experiment and DT3D
2.4.2 Verification example (Steel column inserted in two sides of the web
with brick - Experiment No 45 of BSC and Swinden Laboratories)