7d design of steel structures, base bolt joint
TRANSCRIPT
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
1/27
1
7D DESIGN OF STEEL STRUCTURES, BASE BOLT
JOINT
M. HEINISUO1), V. LAINE2)1)Tampere University of Technology, Faculty of Built Environment, Tampere
2)KPM-Engineering Oy, Tampere
ABSTRACT
7D design of steel structures includes 7 components: 3D space, time, cost, fire
simulation and search of good solutions (optimization). The basic idea is to integrate
these 7 components applying modern computer techniques (e.g. product modeling)
enhancing so the entire building process of steel structures. In the paper the general
concept of 7D design is presented. The introduction of fire simulation and search of
good solutions to the integration means, that in the future it may be possible to search
good solutions including cost effectivity with better fire safety of steel buildings. As a
case study the design of base bolt joint is presented as a part of integrated design
process. The component method of Eurocodes is enlarged into 3D in the paper.
KEYWORDS
Steel structure, joint, base bolt, 7D design.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
2/27
2
INTRODUCTION
The next figure illustrates what means 7D for the design of metal structures.
Figure 1. Dimensions in 7D design
Product model including timing are the normal 4D. If cost calculations are involved,
then firstly the naming 4.5D design has been proposed [1]. Now they use name 5D of
that frequently. Note, that here the structural analysis and the resistance checks are
included in the product model.
New dimensions introduced in this research are
simulation of accidents and search of good solutions.
Product model => 3D
Duration => 1D
Cost functions and
cost databases => 1D
Search engines
(optimisation) => 1D
Simulation of accidents
(fire, explosions) => 1D
Solver
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
3/27
3
These two are by no means new items in the structural design, but when they are
integrated applying the product model techniques, the we call the design procedure as a
7D design. The details of the 7D design will be explained in forthcoming reports.
This paper illustrates a small part of the 7D design. The essential item is that all starts
from the product model. There may be different feasible solutions available in theproduct model for e.g. joints of the steel skeleton. The product model (PM)
representation should be such, that all needed information for the tasks shown in the
previous figure are available from PM. E.g. the costs of the joints should be defined
with the required accuracy. To be feasible, the joint should resist all the mechanical
loads both in the normal use and in the accidental situation, e.g. in the fire.
All the tasks to find the good group of feasible candidate joints and to search the best
solution for the case under consideration should be integrated in order to make the
designers life easier. E.g. when considering the base bolt joint, the designer may search
the solutions with thick base plates compared to the solution with thin base plates with
stiffeners. Typically there are a lot, millions of options to look at the good solutions. Itis believed, that the computer may help the designer in making the decision which is the
most suitable solution for the case under consideration.
This paper deals with the joint appearing in almost all the buildings, the base bolt joint.
It is a good starting point to describe the generation of the local joint analysis model
from the geometrical model included in the product model of the steel skeleton.
Moreover, the strength check of this joint is illustrated in the paper. The analysis model
should include the stiffness properties of the joint. In this paper the EN 1993-1-8 [2]
will be applied to check the resistance and the stiffness of the joint. Only the normal
situation is considered in this paper, not fire. The base bolt joint is a good example for
this, because typical base bolt joints appearing in the buildings behave very un-
symmetric when loaded by the different base moments.
Generally, the stiffness properties and the resistance check equations should be
presented in such a form, that they can be applied for the fire case, too. When
considering the real buildings then it is clear, that there are not many joints which
behave in the reality in 2D. Moreover, in practical projects nowadays the steel skeletons
are analysed by the engineers in 3D. The local joint models are presented in 3D in this
paper meaning the extension of the component model of Eurocodes to 3D.
INTRODUCTION TO THE JOINT ANALYSIS
The check of the resistance and stiffness of structural steel joints is one of the major
tasks when designing steel structures. It has been shown by many, that during the design
the essential part of the costs of steel structures will be fixed. The stiffnesses of the
joints may have effect to the behaviour of the entire structure and following the most
novel Eurocodes [2], [3] these effects can be taken into account for the typical joints of
steel structures.
However, the definitions of the stiffnesses of the joints are typically not included into
the design software widely used in the design of steel structures. There exist options togive the joint stiffnesses as numerical values, but the derivations of the final values of
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
4/27
4
the stiffnesses should be done using some other programs which may not have direct
links to the design softwares. The same holds for the checks of the resistances of the
joints and for the cost estimation of the joints. If these are available with ease, then the
real search of good solutions (some call this optimization) would be possible in practical
projects, not only in research projects.
The situation is getting better all the time with the commercial software used in
structural engineering. More analysis options are coming to the modeling software and
more modeling options are coming to the analysis programs. However, the development
is always too slow when discussing with the engineers, and many kinds of efforts are
going on to enhance the design process.
The basic idea of this research is to enhance the steel design process by integration of
the stiffness derivation and the resistance check to the design software, in this case to
the product modeling software of steel structures widely used world wide, Tekla
Structures. This program was taken for the reference, because all the industrial partners
of the project use that software daily. The cost estimation and other possibilities toenhance the design process are not considered in this paper.
Different levels of joint models are presented in the literature. An automatic derivation
of the joint analysis models from the product models including geometrical
representations is given in the reference [4]. In that report both local beam and
continuum models were generated for joints and connecting of these to the main
analysis model were considered.
In the reference [4] the idea was to apply neutral product model files to the data transfer
between geometrical modeling and analysis. In this research another method, where the
analysis generation is embedded to the product model, is looked for. The total time for
the data transfer and the computations should be minimized at all stages of the design
process to enhance the design. The use of neutral models means program independence
and the present techniques means the program dependence solution. Both have their
own good features. Anyway it is believed, that the methods developed in this paper, can
be at least partly implemented to both the systems in the long run.
In this paper only beam models are considered and so called EN line for joint design
(explained below) will be followed. The final goal is to cover the typical practical steel
structures, an example is shown in the next figure. It can be seen, that the analysis
model will be rather large without local joint models and then the first step to generatethe local joint models should be kept as small as possible to perform the final
calculations in the reasonable computational time.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
5/27
5
Figure 2. Typical steel structure to be analysed
In the reference [2] is given a component model, which has been originally developed in[5]. This model has been modified in Sheffield University, see [6]. It should be noted,
that the component model can be used for the resistance and the stiffness definitions in
the normal situation and in the fire, too. Comprehensive literature for the model
development of structural steel joints is given in [7]. The modifications done in
Sheffield consider the separation of axial, bending and shear degrees of freedoms and
the extension for the fire cases.
In this project the Sheffield model will be modified further to six and enabling in the
future the enlargement of the model to seven or more degrees of freedom per node. Six
degrees of freedom (Bernoulli-Euler beam) are normal three displacements and three
rotations in the node. The seventh degree of freedom is warping based on the well-known beam theory of Vlasov. The enlargement of Vlasovs beam theory for eight and
more degrees of freedom per node has been presented [8]. That theory includes the
distortional modes of the steel members.
The problem in practise is that there is a lack of programs for practising engineers
where even Vlasovs beam elements are available. It should be noted too, that there
exist a large lack of test results for the stiffnesses and resistances of joints in three
dimensional loading cases, so the method given in this paper should be applied with
care in three dimensions. However, the extension of the component model given in the
Eurocodes, gives the possibility to the logical approach to the three dimensional method
for the structural steel joints.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
6/27
6
In this paper in maximum six degrees of freedoms per node are considered, meaning the
use of Bernoulli-Euler beam elements for the members between the joints. Where the
joint ends and the member starts in the analysis models will be demonstrated in the
following.
The basic components for the resistances and the stiffnesses of the joints are based inthis study on [2] in the normal case. The brief history of the model development in this
EN line is shown in the next figure.
Figure 3. Joint model development in EN line
The Sheffield model modification into the TUT model is explained in details in the
following using the case study for the base bolt joint. One feature when designing the
base bolt joints following [2] is, that the designer should know in advance, which are
the stress resultants of the joint to apply the Tables 6.7 and 6.12 of [2]. This information
is not needed when applying the TUT model, as seen in the following.
The following figure illustrates the original component model and the modified
component model. The figures are from [6].
EN 1993-1-8 Component
model
Tchemmeme at al 1987
Modified component model = Sheffield
model
Modified Sheffield model
= TUT model, This paper
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
7/27
7
Figure 4. Original component model of [2] and the modification (Sheffield model)
The modification of the Sheffield model is given in this report. The base bolt joint is
used to illustrate the model in details. The modification is done by expanding theSheffield model to connect the three dimensional beam element nodes representing the
Component model of EN 1993-1-8
Modified component model (Sheffield model)
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
8/27
8
connected member mechanical behaviour near the joint by applying the basic
component model of [2] in three dimensions. The extension of this model to seven or
more dofs per beam node is obvious, but it is not considered in this paper.
LOCAL ANALYSIS MODEL (TUT MODEL) OF THEBASE BOLT JOINT
Consider the base bolt joints, where the members having the cross-sections shown in the
next figure are connected to the foundations.
Figure 5. Base bolt joints considered
As an introduction the double symmetric mid column joint with only the compressive
axial load is considered. In this case only one vertical spring locating at the member end
point is enough to represent the behaviour of the joint. The top end of the spring is
connected to the member end analysis line node locating just above the base plate and
the lower end of the spring is connected to the foundation. The foundation is supposed
to be absolutely rigid. The spring represents the local displacements of the joint.
When calculating the stiffness of the joint, then in this study the Eurocode [2] is used. In
this compression case the stiffness of the joint is reduced only to the consideration of
the effective compression zone around the parts of the connected member and stiffeners
which are connected to the base plate. The effects of bolts to the compression stiffness
are not taken into account in the final case, i.e. when the grout has been completed. The
effect of the bolt stiffness to the compressive stiffness of the joint has been considered
e.g. in [9].
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
9/27
9
The area of the compression zone, the elastic modulus of concrete at the area and the
depth of the effective compression zone are included in the design equations following
[2]. These together define the compression stiffness of the joint. Different compression
stress distributions have been considered in [9] and the brief background for the
equations appearing in [2] and the comparisons with different analytical and numerical
solutions are given in [10]. In the references [11], [12] are given rather extensivebackground documentations for [2] dealing with the base bolt joints.
In TUT model we do not use only one spring below the column although it would be
enough for the symmetric case in the example above. Instead we use the following rules
for the compressed zones
all compressed flanges are divided into three equal parts and all parts have theown springs,
all webs are divided into one part and these parts have only one spring, for rectangular tubes this rule is applied so that all the sides are considered as
flanges,
for round tubes the rule is applied as shown in the following figures, the divisioninto 8 equal parts in the basic case.
The divisions of the compressed flanges are motivated with the more accuracy when
analysing column bases in the general three dimensional cases. The division of flanges
into two parts would be the minimum for e.g. I-profile weak axis bending, but the third
part may produce more accurate results in the general case. Moreover, the effects of
stiffeners appearing at the base bolt joints, can be taken into account with more ease
when using in minimum three zones for one flange.
The rules given above are illustrated in the following figure for the basic cases. The
widths of the compressed areas are defined using the equations appearing in [2]. The
springs at the compression areas are locating at the centroids of the compressed zones.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
10/27
10
Figure 6. Basic rules for compressed areas
The rigid links shown in the previous figure ensure, that the Bernoulli hypothesis is
valid for the connected column ends. Numerical tests should be done to ensure the
rigidity of these links and to ensure, that the numerical stability will remain when
solving the system matrix equations. In some programs exist possibilities to use the
rigid links, but in this study steel members are used for those, so we can get program
independent solution to this. In the previous studies [13] it has been found that square
steel tubes 800x800x50 are good profiles to this purpose. In that study it was found that
the minimum lengths of the rigid links should be 5 mm to ensure the stability when
solving the system matrix equations. This rule should be checked for the program used
in the structural analysis. The stiffnesses of the rigid links can be defined moresystematically based on the stiffnesses of the springs at the end of the links [10].
It should be noted, that the rigid links should not be too rigid, when combining different
level of finite elements, as shown in [4] for Bernoulli-Euler beam elements and for
planar elements. In that problem Timoshenko beam elements was the proper solution
for the connecting member to avoid numerical difficulties at the interface of two level
elements. In the present case, where Bernoulli-Euler elements are goarsely connected to
spring elements, this problem will not be active.
It should be noted, that if this theory is applied for the Vlasov torsion, then the Bernoulli
hypothesis should be compensated by the use of hypar surface yz at the column enddeformation following the basic assumption of the Vlasov theory, but these cases are
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
11/27
11
not considered in this study. However, if the base plate can be considered as rigid
against bimoments originating from the Vlasov theory, then the rigid links can be used.
Whether the base plate can be considered as rigid in this sense, has been considered in
[14].
One extra basic rule holds for the determination of the compressed area
compressed area should not extent over the base plate or to the area withoutgrout.
Some applications of the rules are given in the next figure. The spring locations are as in
the previous figure. The spring stiffnesses should be reduced or enlarged (see the
stiffener case in the figure) due to the sizes of the compressed areas.
Figure 7. Applications of the compressed areas
It can be seen, that in every case the compression spring does not remain to the mid
plane of the compressed column flange, as is stated in [2]. If there exist no foundation
within the allowed maximum width of the compressed area, then it seems to be
reasonable to move the compression spring away from the mid line of the column
flange, as is the situation in the two right hand cases of the previous figure. At least this
assumption is on the safe side when considering the rules of [2].
The most important conclusion is that the local analysis model can be generated basedon the geometrical entities connected at the joint.
Consider next the tension side of the column base. The tensile resistance of the base bolt
joint is originating from the tensile resistances of the base bolts. The tensile bolts and
the base plate will deform during the tensile loading and the stiffness of the tensile side
of the joint is calculated based on these deformations and the equations appearing in the
Eurocode [2].
Now the following rules can be seen
the springs at the compression side (see figures above) are compression onlysprings,
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
12/27
12
the springs at the tension side are tension only springs.This means that we end up to the geometrical non-linear theory when applying the
component model of [2]. If the program used does not include the possibility to
construct this kind of geometrical non-linearity for all the load combinations, then we
should find some other solution to the problem. There are given proposals to make theproblem under consideration to the linear one in [10]. In this paper also one solution is
shown.
However, the component model mean, that we put the tensile springs at every bolt
centre and the tensile stiffness of that spring is calculated using the equations of [2]. The
major variables to determine the tensile stiffnesses are the effective widths of the base
plates for each base bolts and the elongations of the individual bolts. The following
figure illustrates the local analysis models of the base bolt joints in some cases.
Figure 8. Axial load and bending moment, local analysis models
All the rigid links are connected absolutely rigidly at the shear center (called a mid node
in the following) of the column cross-section to the analysis line of the column at the
level of the base plate top.
All the axial springs can be generated from the geometrical entities connected at the
joint, as shown above.
The four situations can appear, when the shear forces and the torsional moment are
acting at the base bolt joint
shear stresses are transferred by the friction from the column to the foundations,
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
13/27
13
shear stresses are transferred by the base bolts to the foundations, shear stresses are transferred by the distinct shear key embedded with the grout
to the foundations,
shear stresses are transferred by the combination of two or three previoustransfer mechanisms described above.
The last three cases are not considered in this study. Typically the first option to transfer
the shear stresses is to use friction, if possible.
Following the Eurocode [2] the shear stresses can be transferred by the friction from the
column to the foundations using the friction constant 0.2. In this case the compression
zones shown as shaded areas in the previous figures are multiplied by the normal stress
acting at the areas and the sum of these forces multiplied by the friction coefficient
should be larger than the resultant shear force at the column base.
If there exist no torsional moment at the joint, then the resultant shear force is easy to
calculate as the vector sum of the horizontal forces. If there exists the torsional moment,then the plastic theory can be used to calculate the shear stresses appearing at the
compression zones, meaning the uniform distribution of the shear stresses at the
compressed zones. The resultants are locating at the centroids of the compressed zones.
If the shear stresses of the joint are taken by the friction, then at the mid joint the
corresponding degrees of freedoms are fully supported, meaning the displacements in
horizontal directions and the rotation around the column axis.
If the shear stresses are transferred by the base bolts to the foundations then, due to
extra large holes at the base plates, the washers should be welded to the base plates. The
welds and washers should be designed to resist the forces transferred. The forces are
calculated from the shear forces and from the torsional moment e.g. using the elastic
distribution of the shear forces to the bolts. Both compressive and tensile bolts are taken
into consideration and the shear forces at the bolts should be added to tensile forces
acting at the bolts.
In this case there exist supports at the bolts in horizontal directions. These supports can
be considered as absolutely rigid in typical cases.
The situation before grouting should be considered, too. In this case the bolts can resist
the compressive forces and the possibility of buckling of the bolts should be taken intoaccount when checking the resistance of the compressed bolts. The buckling lengths of
the bolts may be taken as the height of the grout. The local analysis model is like given
above for the tensile axial force.
As a conclusion it can be seen, that the local analysis model of the base bolt joint can be
determined based on the geometrical entities connected at the joint. It can be seen, also,
that the geometrical non-linear analysis model is the result where the non-linearity arise
from the compression and tension only springs appearing at the local analysis model.
It should be noted, that if the geometrical non-linear analysis is used to determine all the
stress resultants of the entire frame, then no extra checks as given in [EN 1993-1-1,
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
14/27
14
5.2.2(5)] are needed for the analysis model, because they are involved in the present
model.
How the stiffnesses of the springs are determined in practical cases, is illustrated in the
following for one example case. It should be noted, that the same logic holds for many
other joints appearing in the steel structures. Moreover, the same or similar equations todetermine the stiffnesses and the resistances of the components appear in many joints,
too. The component based methods are generic in this sense and the same equations can
be used for many practical joints.
EXAMPLES OF THE BASE BOLT JOINTS
Consider firstly the base bolt joint illustrated in the next figure. The initial data is the
same as in [15] and in that reference the test result for this joint can be found. The
horizontal load is given in the next figure acting at 1 m from the base plate top surface
and the ultimate moment of the joint was 61.5 kNm in the test.
Figure 9. The base bolt joint [15]
The first thing to consider is the local analysis model for this joint. Then arise the
question, how many compressed zones are at the joint? Typically in this kind of joints
the tensile springs are more flexible than compressive springs allthough they are
locating more far away from the mid node. Suppose, that there exist only three
compressed zones at this joint. Typically at the base bolt joints the major parts of the
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
15/27
15
deformations of the tensile springs occur due to elongation of the bolts, not much due to
deformation of the end plate. This can be seen in this case, too.
The local analysis model of this joint is presented in the next figure. The model is made
applying the rules given above.
Figure 10. Local analysis model of the example joint
It should be noted, that the width of the compressed zone c is different (smaller) when
constructing the local analysis model and when checking the resistance of the
compressed zone following [2]. For the stiffness calculations (the more general equation
is from the reference [11] and the approximative version )25.1( t is from the Eurocode
[2])
mmtmmtE
Ec
c
25.3625.169.372927500
21000066.066.0 33 ==== (1)
MPaEc 27500= is the elastic modulus of the concrete. If 0.2 times the smallersize of the base plate is larger than the grout thickness, then this is the
foundation concrete elastic modulus, if not, then this is the grouting concrete
elastic modulus [11], in this case the smaller size of the base plate is 190 mm
and then 0.2*190 = 38 mm, which is larger than the grout thickness,
MPaE 210000= is the elastic modulus of steel, mmt 29= is the thickness of the base plate.
The stiffnesses of each compressed zones are calculated using the empirical equation
(background, see [10])
mkN
AE
k
effic
ci /275.1
= (2)
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
16/27
16
where
effiA is the compression area i .In our example (the dimensions are rounded to the integer values in mms) the spring
stiffnesses of the compressed springs are
mkNk
mkNkk
mmA
mmAA
c
cc
eff
effeff
/1448000275.1
450727500
/1699000275.1
620827500
4507
6208
2
31
22
231
=
=
=
==
=
==
(3)
The stiffnesses of the tensile springs are
pibi
ti
kk
k11
1
+
= (4)
where
bik is the spring stiffness of the base bolt i , pik is the spring stiffness of the base plate at the base bolt i .
Note, that in [2] is written, that the final tensile stiffness is the sum of the tensilestiffnesses bik and pik . It should be calculated as shown above.
The spring stiffness of the base bolt is
effbi
bibibi
L
AEk
= (5)
where
biE is the elastic modulus of the base bolt i , biA is the area of the base bolt i , effbiL is the elongation length of the base bolt i .
In this case the elongation length was given in the test report [15] mmLeffbi 450= .
Typically it should be calculated using the equations of the Eurocode [8]. It can be
noted from the Eurocode, that the elongation length in the foundations is the traditional
d8 , where d is the diameter of the base bolt and this rule is based on old American
tests on 1950s [16].
In our example
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
17/27
17
( )mkN
L
AEkk
effbi
bibibb /132000
450
283210000
450
2/192100002
21 =
=
=
==
(6)
The spring stiffness of the base plate is calculated applying the modified deflection
equation of the cantilever beam of the length mmm 44761201 == [background to this,
see [10]) and using the effective width mmbeffi 952/190 == of the beam in our case. It
should be noted, that the weld can be taken into account when calculating the length 1m
following the Eurocode, but it was not done in this case. Typically there exist no prying
forces at the base bolt joint due to large deformations of the tensile springs. The
existence of the prying forces should be checked in the general case following the
Eurocode.
In our example
mkN
kk
kk
mkNm
tbE
kk
bp
tt
effipi
pp
/11930011
1
/121400044
2995210000
2125.02125.0
21
21
3
3
31
3
21
=
+
==
=
=
==
(7)
and it can be seen, that the effect of bolt elongation is the major part of the tensile
stiffness. It can be seen, also, that the tensile spring constants are much smaller than
compressive spring constant, so our proposal of three compressed zones was correct.
The total compressive and tensile spring stiffnesses are
mkNk
mkNk
t
c
/2386001193002
/484700016990014480001699000
==
=++=
(8)
Supposing that there exists no axial load the resultant compressive and tensile forces are
m
M
e
MFF tc
190.0=== (9)
The compressive and tensile forces at the springs are
ttt
ccc
cccc
FFF
FFF
FFFF
==
==
===
50.0
30.0847.4
448.1
35.0847.4
699.1
11
2
31
(10)
Consider now the case where the bending moment of the joint is 40 kNm. Then the total
axial forces are in this case
kN
m
kNm
e
MFF tc 210
190.0
40==== (11)
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
18/27
18
The compressive forces at the compressed zones and at the tensile springs are
kNFFF
kNFF
kNFFF
ttt
cc
ccc
10550.0
6321030.030.0
7421035.035.0
11
2
31
===
===
====
(12)
These are used to check the resistance of the joint.
The displacements at the springs are as follows
mm
mm
t
c
880.0119300
1000105
0443.01669000
100074
=
=
=
=
(13)
The rotation at the joint is for the bending moment 40 kNm and using the linear theory
up to that moment
mrad865.40048.0190
880.00443.0==
+= (14)
The stresses of the tensile bolts and of the end plate are
MPa
MPa
pi
bi
2312995
444105000
372282
105000
2=
=
==
(15)
and it can be seen, that the tension resistance of the base bolt and the end plate bending
are critical in this case. It can be seen, also, that the tensile base bolts are yielding with
this load ( MPafMPaf ubyb 500,310 == ), but the ultimate stresses have not yet been
reached. Note also, that the areas of bolts were not clear when taken from the test report
referred.
Note, it is recommended, that the stresses are calculated for every parts allthough
any code does not require it. So you can keep the touch to the results.
The compression area width when checking the compression resistance of the concreteshould be calculated using the equation
j
yp
f
ftc
=
3(16)
where
t is the thickness of the base plate,
ypf is the yield strenght of the base plate,
jf is the cylindrical strength of the concrete and this is chosen (either the grout or thefoundation) as the elastic modulus above applying the rule by Weynand.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
19/27
19
In this case
mmf
ftc
j
yp43
383
25029
3=
=
= (17)
The compressive stresses at the compression parts are
MPa
MPa
c
cc
5.125044
63000
3.116576
74000
2
31
==
===
(18)
and it can be seen, that the compression resistance of the concrete is not critical in this
case.
The tensile resistance of the bolt is according to the Eurocode using the material factor
0.12 =M (note, that in the design case the value 1.25 should be used)
257.1105
1321322835009.09.0
9.0
2
====
= kNAfAf
R bubM
bubb
(19)
The end plate bending stresses are more critical because 250/231=1.08. So the bending
moment resistance according to the Eurocode [2] of the joint is 1.08*40 = 43 kNm.
The linear phase of the moment-rotatio curve can be drawn up to the moment 2/3*43 =
29 kNm and after that the curve is non-linear. The following figure illustrates themoment-rotation curve based on Eurocodes [2], tests [15] and ANSYS simulations [10].
Figure 11. Moment-rotation curve of the example joint
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
20/27
20
The initial rotational stiffness in the linear phase for this joint is according to the
Eurocodes
mrad
kNm
rad
kNmSini 2.88221
0048.0
40=== (20)
and this holds up to the moment 29 kNm and after that the non-linear moment-rotation
relationship according to [2] should be used. The end plate bending is the most critical
for the bending and using the material factor 1.25 for the ultimate tension resistance of
the bolts, then the bolt tension resistance is the most critical.
As a summary of the example the following results are got
Moment resistance of the joint in the test: 61.5 kNm. Moment resistance using the Eurocodes: 43 kNm. Initial rotational stiffnes of the joint using the Eurocodes: 8.2 kNm/(mrad). The utility ratios (using material factors 1.0) at the ultimate moment 43 kNm
following the Eurocodes:
Base plate: 1.00, Base bolts: 43*105/(40*132) = 0.86, Concrete compression: 43*12.5/(40*38) = 0.35.
Other comparisons between the proposed method and test results are given in [10].
The following example illustrates the analysis of the entire frame including the local
joint models described above. Consider the portal frame including two HEB240 (S355)
columns and one IPE500 (S355) beam. The mid planes of the profiles webs are at the
plane of the frame without eccentricities.
The joints between the beam ends and the column tops are absolutely hinged. The mid
distance of the columns is 10 m and the height from the base plate top to the mid line of
the beam is 4 m.
The base bolt joints at the column bases are as described in the following figure. The
steel material is S355, the bolt are type Peikko and the grouting and the foundationconcrete is C40/50 and the elastic modulus used in the calculations is 35000 MPa.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
21/27
21
Figure 12. Base bolt joints of the frame example
Only one load case is considered here to demonstrate the effect of the joint stiffness to
the behaviour of the frame. Other load cases including the 3D behaviour of the samecase are given in [10]. The loads of the frame are acting at the plane of the frame and
they are
dead load of two columns and one beam, total: columns 2*4*83.2 + beam1*10*90.7 = 666 + 907 =1573 kg,
no dead load is supposed to the joint entities. This load may be derived from theproduct model and put to the mid node,
the uniform load acting downwards at the mid line of the beam at the entirebeam 30 kN/m,
the horizontal point load 20 kN acting at the left corner of the frame.The frame and its loads are given in the following figure.
Figure 13. The portal frame and the loads
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
22/27
22
The local candidates for the joint models are given in the following figure. The
locations and stiffnesses of the compression and tension only springs have been
determined using the rules given above.
Figure 14. Local joint model candidates for the frame example, left and right and the
coding of left joint
Next thing to do is to solve the system equations of the static problem. This was done in
this study applying the program Robot Millenium 20. The calculations in the non-linear
case were performed using the Newton-Raphson procedure available in the program.
The details of the calculations are given in [10].
After solving the statics the strength check of the entire frame can be done using the
results of the non-linear case. In principle we do not need any classification of the joints
in this case, because the effects of joint stiffnesses are taken into account by the
analysis.
If we want to know the classifications of the base bolt joints based on [2] then we
calculate the initial stiffnesses of the left and the right joints as follows
mradkNmS
mrad
kNmS
iniright
inileft
5.5800084.0
18.49
3.2100165.0
18.35
==
==
(21)
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
23/27
23
where the moments and rotations are taken from the analysis results. It can be seen, that
the stiffness of the used base bolt joint differs depending on the bending moment
direction applied to the joint.
The classification parameters following [2] are
9.911259210000
10455800
6.311259210000
104213000
5
5
=
=
=
=
=
=
rightright
rightiniright
right
leftleft
leftinileft
left
IE
HSR
IE
HSR
(22)
Both these are in the range [0.5; 25] meaning that the base bolt joints are classified as
semi-rigid. The maximum utility ratios for the second load case are for the left joint
0.27 and for the right joint 0.53 [10] meaning that the right joint is the critical. The
maximum utility ratio also means, that the load may be enlargedproportionally about47%.
The effects of the base bolt stiffnesses to the buckling lengths of the columns can be
calculated from the lowest eigenvalue for the proper buckling case. It is known, that for
the absolutely rigid base bolts in this case the buckling lengths for both columns are
twice the lengths H of the column, i.e. 8 meters. The lowest plane frame buckling
eigenvalue is 68.17=cr and the buckling lengths of the columns are then
HmP
EIL
cr
cr ==
== 35.238.9
15000068.17
10112592100004
(23)
To linearize the problem we may assume, that the rotational stiffnesses are defined
without axial forces, as was done above for the example of the tubular column joint,
knowing, that the solution will be approximative. Moreover, it is known, that the
rotational stiffness is dependent on the direction of the bending moment. Next we
assume, that it is not so, but we use themean of the rotational stiffnesses to calculate
the linear rotational stiffness for the joint.
Now we have linearized the problem and we can use the linear theory. The
computational time will not increase compared to the traditional case without anystiffnesses at the joints. When we have solved the bending moments and the axial forces
at the base bolt joints, then we can define the resistances of the joints according to [2].
The results for the frame example are collected to the following tables. The case TUT
linear means the approximative theory described above. There are given the means of
the rotational stiffnesses, which are used in the calculations in the case TUT linear for
both column bases. The detailed calculations are given in [10].
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
24/27
24
Table 1. Results for the frame caseCase Stiffness/left
kNm/rad
Stiffness/right
kNm/rad
Moment/left
kNm
Moment/right
kNm
Horizontal
disp.
column top
mm
Rigid 40.09 39.91 9.1
TUT non-linear 21321 58548 35.18 49.18 14.6
TUT linear 13016/26978 40929/26978 40.06 39.94 15.0
Casecr of
Eurocodes
HLcr / crL
m
Max utility
left
Max utility
right
Rigid 24.31 2.00 8.00 - -
TUT non-linear 17.68 2.35 9.38 0.27 0.53
TUT linear 16.51 2.42 9.71 0.32 0.42
It can be seen, that the maximum utility ratios may be about 20% either on the safe or
on the unsafe side, when considering the components of the base bolt joint in this
example and using the linearized theory, and compared to the non-linear theory.
Moreover, the buckling lengths of the columns and the horizontal displacements are a
little bit larger in the linearized case as they are when using the non-linear theory.
However, when designing steel structures these kinds of errors may be accepted e.g. in
the preliminary design stage. This means that we propose the following user interface
for the base bolt macro including the choice of the applied theory when analysing the
structures. Before this screen there are the necessary user interfaces to choose all the
geometrical entities of the joint.
There are two extra choices appearing in the following figure. These are meant for
estimating only. When using the two first theories, then no geometrical entities are
needed. The second method (rigid) is as a default, meaning this can be used without any
work of the designer, the designer need not even open the whole interface of the macro,
simply only put this macro active to the joint. When using TUT linear or TUT non-
linear models for the base bolt joint, then all the geometrical entities must have some
values, because the stiffnesses and the resistance checks are calculated based on the
information of the geometrical entities of the joint.
The given displacements or stiffnesses for the entire foundation should be given in this
interface or somewhere else.
The column should be vertical and the orthogonal layout of the column profile with
respect to the base bolt group is required. Moreover, the base bolts should locate
between the lines connecting the flange edges of I-profile columns. This requirement for
the tubular rectangular columns may be removed in the near future. The equations have
been derived for this case [10], other theory see [17]. The tests to verify these theories
will be reported in the near future in TUT.
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
25/27
25
Analysis model of the joint
Take one of the following. If you dont take any, then the absolutely rigid model is used.
Figure 23. Proposal for the user interface of the base bolt macro, structural analysis
CONCLUSIONS
The following conclusions can be done based on the results of the paper.
Local analysis models (TUT models) can be generated from the geometricalentities of the joints. This means automatic generation from the product model.
The TUT model enlarges the component method of Eurocodes to threedimensions.
The use of non-linear TUT model leads to the very good agreement in the casesconsidered when comparing the results to the test results available dealing with
o the resistances of the joints ando the stiffnesses of the joints in the normal situation.
In the fire situation the similar research will be done in the near future. The use of non-linear TUT model leads to the application of the geometrical
non-linear theory for the entire frame.
The stiffnesses of joints are automatically taken into account in the structuralanalysis.
No extra checks due to the second order theory is needed after the analysis,because they are involved into the non-linear analysis.
The proposal is given to reduce the non-linear case as series of linear cases andthe algorithm seems to work in the case considered [10]. The algorithm was not
implemented in this research.
The proposal is given (TUT linear) to linearize the non-linear case using themean of rotational stiffnesses without axial forces. This may be used in the
Hinge for two momentsRigid for torsional moment
Rigid for three forces
Absolutely rigid forThree moments
Three forces
TUT linear
Stiffnesses for two moments
Rigid for torsional moment
Rigid for three forces
(Calculates the spring
stiffnesses as means withoutaxial force according to
report/TUT)
TUT non-linear
(Component method of EC in
three D according to
report/TUT)
This choice leads to the
geometrical non-linear theory
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
26/27
26
preliminary design stage. The errors of 20% in the utility ratios of the joints
(safe and unsafe) are shown using this approach in one extremely simple case.
It is recommended, that the final design will be done using the non-linear theoryif the computational times are reasonable. The computational times are highly
dependent on the sizes of the problems.
Applications to other structural steel joints are given in the near future. Next task is to implement the results to the design software in the near future
including the fabrication cost information and the development of the cost
estimation module for the practical use for the engineers.
The user interface to the joint macro dealing with the choice of the analysismodel of the base bolt joint was proposed. Estimating variations are given, too.
After the implementation the search of good solutions can be done fluently alsoin the preliminary design stage.
Modern computers, computational tools and programs have made it possible todevelop this kind of method and the results can be used by the practising
engineers, because they have these modern systems in every day use nowdays.
This project has been completed in the close interaction between practising
engineers and the research staff.
Term near future means that the tasks are included in the on-going national 7Dproject.
REFERENCES
[1] Salonen M., Rautakorpi J., Heinisuo M., Proposal for 4.5 Dimensional Design via
Product Models and Expert System, Lecture Notes in Artificial Intelligence 1454, Sub-
series on Lecture Notes in Computer Science, Ian Smith (Ed.), Artificial Intelligence inStructural Engineering, Information Technology for Design, Colloboration,
Maintenance, and Monitoring, Springer-Verlag, Berlin, 1998, pp. 464-468
[2] EN 1993-1-8, Eurocode 3: Design of steel structures, Part 1-8: Design of joints,
CEN, Bryssels, 2005
[3] EN 1993-1-1, Eurocode 3: Design of steel structures, Part 1-1: General rules and
rules for buildings, CEN, Bryssels, 2005
[4] Heinisuo M., Rautakorpi J., Tersrungon rakenneanalyysin tuotemallin generointi
geometrian tuotemallista, Report 25, Tampere University of Technology, Department of
Civil Engineering, Structural Mechanics, Tampere, 1998 (in Finnish)
[5] Tchemmemegg F., Tautschnig A., Klein H., Braun Ch., Humer Ch., Zur
Nachgiebigkeit von Rahmenknoten Teil 1 (Semi-rigid joint of frame structures, Vol 1
in German), Stahlbau 56, Heft 10, 1987, pp. 299-306
[6] Burgess I., Connection modelling in fire, Proceedings of Workshop Urban Habitat
Constructions under Catastrophic Events, COST C26, Prague 30-31.3.2007, pp. 25-34
-
7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT
27/27
27
[7] Block F. M., Development of a Component-Based Finite Element for Steel Beam-
to-Column Connections at elevated Temperatures, PhD Thesis, University of Sheffield,
2006
[8] Heinisuo M., Liukkonen V.-P., Tuomala M., New beam element including
distortion, Nordic Steel Construction Conference 95, Malm, Sweden, June 19-21,Swedish Institute of Steel Construction, Publication 150, Vol I, 1995, pp. 65-72
[9] Raiskila M., Diplomity, Tampereen teknillinen korkeakoulu, Tampere, 1985 (in
Finnish)
[10] Laine V., Diplomity, Tampereen teknillinen yliopisto, Tampere, 2008 (in Finnish)
[11] Weynand K., Semi-Rigid Behaviour of Civil Engineering Structural Connections,
COST C1, Column Bases in Steel Building Frames, European Comission, Brussels,
1999
[12] Wald F., Column Bases, CVUT, Praha, 1995
[13] Nevalainen P., Diplomity, Tampereen teknillinen korkeakoulu, Tampere, 1990 (in
Fnnish)
[14]
[15] Picard A., Beaulieu D., Behaviour of a simple column base connection, Canadian
Journal of Civil Engineering, 1984
[16] Salmon C. G., Shenker, Moment-Rotational Characteristics of Column
Anchorages, Transactions of the ASCE, 1956
[17] Wald F., et al, Effective Length of T-stub of RHS Column Base Plates, Czech
Technical University, 2000