7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT

7/28/2019 7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT

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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.


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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


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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


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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.


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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.


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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


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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)


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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].


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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.


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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


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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,


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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,


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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,


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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


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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)


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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


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( )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)


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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.


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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


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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.


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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


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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)


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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].


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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.


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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


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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


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[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

Documents

7D DESIGN OF STEEL STRUCTURES, BASE BOLT JOINT