733

DESIGNING BOLTED END-PLATE CONNECTIONS IN COMPLIANCE WITH EUROCODE AND UKRAINIAN CODES: CONSISTENCY AND CONTRADICTIONS

Anatolii Perelmuter1, Eduard Kriksunov1, Igor Gavrilenko1, Vitalina Yurchenko2

1SCAD Soft Ltd., I. Klimenko str. 4/20, 03037, Kyiv, Ukraine. 2Kyiv National University of Civil Engineering and Architecture, Povitroflotskyj av. 31, 03680, Kyiv, Ukraine.

E-mail: vitalinay@rambler.ru

Abstract. The article attempts to reveal consistency and contradictions in design procedures for bolted connections in steel structural joints in compliance with EuroCode on one hand and Ukrainian building codes on the other hand. The need for such a comparison has emerged because European steel components are being imported intensively into the market of Ukraine. A software application for design and analysis of steel structural joints in compliance with differ-ent building codes has been developed and is presented in this paper.

Keywords: steel structural joints, bolted end-plate connections, bolted shear connections, design model, software im-plementation.

Introduction

Bolted end-plate connections are widely used for structural joints in steel frames (Fig 1) in the contempo-rary building practice. The primary advantage of such connections is a simplicity of their on-site assembling. In addition, the end-plate connections make it possible to erect a steel framework in any climatic conditions or to dismount the framework without making any damage to its structural members. Other characteristic features of he bolted end-plate connections include their high reliability under dynamic loadings and facility of the connections supervision ( 2005). On the other hand, struc-tural members to be connected by end-plate connections must be manufactured with high accuracy because such connections do not have a compensatory capability.

The Ukrainian construction market imports a good deal of steel structural components from Europe. Accord-ingly, a lot of European manufacturers are going to the Ukrainian market in order to supply steel components. The basic approach is that the steel structural members are designed and manufactured in Europe and further delivered to Ukraine. Such structural components have to be approved by the local Ukrainian authorities and com-ply with Ukrainian building standards and regulations.

Therefore it seems interesting to consider and com-pare design models and procedures for the bolted end-plate connections used in Ukrainian design codes on one hand and in EuroCode on the other hand, particularly in EN 1993-1-8 which deals with the design and analysis of steel structural joints.

a b c Fig 1. Bolted end-plate connections in steel frames: (a) a joint between an external column and a rafter; (b) a joint be-tween an internal column and a rafter; (c) a field joint on a rafter (photos were provided by ASTRON Buildings S.A.).

734

Design models of bolted end-plate connections

The analysis of a bolted end-plate connection under the simultaneous action of the bending moment and the axial force in the case of an alternating-sign stress distri-bution is a fairly complicated task. The reason is that the strain characteristics of the connection are different in its respective areas of tension and compression. Therefore both the localization of the neutral axis and the accurate stress distribution are not known in advance in the design cross-sections of the connected structural members around the end-plate connection.

An inaccurate and conservative analysis of a bolted end-plate connection can be performed under the assump-tion that the stresses in bolts are proportional to the dis-tance from the point of application of the resultant force in the compressed area (actually, from the center of the compressed flange) to a selected bolt (Fig 2).

In this case, the design force in the most stressed bolt can be found from the following equation:

maxmax

2

1

xm

i ii

yN M

k n y=

=

(1)

cc

a2fl , lw2a

fw, kkffffk , kfw

wf

Nb

Pf

bNdeformed axis of end-plate

Fig 2. A simplified design model of a bolted end-plate connection

QQ

Nb

fP

bN

ft , twfw, kkff

ffk , kfw

a2 w, llf 2a

c c

deformed axis of end-plate

Fig 3. An improved design model of a bolted end-plate connection

where xM is the design bending moment in the joint; m and k are the respective numbers of horizontal and verti-cal rows in the bolted connection; in is the number of bolts in i th horizontal row; iy , maxy are distances from the respective i th and extreme horizontal bolt row to the neutral axis of the member around the end-plate. This approach dictates that the thickness of the end-plate should be found from the bending strength condition for the end-plate in the elastic phase; this value is too conser-vative ( et al. 2009).

The design of bolted end-plate connections is regu-lated in Ukraine by the effectual Guidelines ( 1988, 1981) which were prepared as a supplemental standard to corresponding chapters of SNiP -23-81* and SP 53-102-2004. Accord-ing to these Guidelines, the end-plate connection design should be based on the following criteria:

the load-bearing ability of a bolt in tension and shear;

the load-bearing ability of an end-plate in bend-ing, and in possible surface tearing (peeling) in a heat-affected zone;

the load-bearing ability of fillet welds between an end-plate and an adjacent section of a struc-tural member.

End-plate bolted connections of open-profile struc-tural members are considered to be a set of T-shaped elementary connections. The strength of a bolted end-plate connection as a whole is treated as the sum of those of its elementary connections. The design procedure for the connections is based on an elastic behavior of the T-shaped elements that consist of bolts and adjacent pieces of the end-plates (Fig 3).

To check the load-bearing ability, an additional stress (a contact force) caused by a prying lever effect should be taken into consideration. This contact force is a resultant of whatever stresses appear when two contigu-ous end-plates are pressed together. The location of the resultant depends on the thickness of the end-plates. There is an additional factor in the bending analysis of the end-plates: the design bending moment can be re-duced by taking into account the end-plate being elasti-cally clamped under the bolt. Thereby we can reduce the thickness of the end-plate. This approach is based on experimental computations carried out by various re-searches ( 1985, De Lima et. al. 2002, Vrtes and Ivnyi 2005).

According to ( 1988, 1981), the load-bearing ability of a bolted end-plate con-nection is considered to be sufficient when the following condition is met:

, , ,

1

extn

b b int b ext ii

N n N N=

+

(2)

where ,b intN is the load-bearing ability of a bolt in an

internal zone which is assumed equal to the bolts prestressing force,

, 0b int b bt bnN R A= ; 0b is a factor to take into account an individual bolt behavior, stress re-

735

laxation, and a non-uniformity in the stress distribution; btR is a design strength of the bolt for tension; bnA is a

net cross-section area of the bolt; bn is the number of bolts in the internal zone;

, ,b ext iN is a design force per one bolt of the external zone of i th -shaped elementary connection; the force is defined by the following formula:

, ,

1min ; 1,3 ib ext i i bt bn bt bn

i iN R A R A

+

=

(3)

where i is a factor assumed to depend on the bolts dimensionless stiffness parameter, i :

0,5088 0,23561lgi i = (4)

( )

32

0,5i

ifi f

bdtt d

=

+

(5)

260,9i bt bn i

i f yR A b

t R

= (6)

where ib is the distance from the bolts axis to the edge of the fillet weld of i th T-shaped elementary connection;

i is the end-plates width per one bolt of the external zone of i th -shaped elementary connection, ft

is the end-plates thickness; i is a parameter that expresses a relation between the distances from the bolt center to the application points of contact forces caused by the prying lever effect and from the bolt center to the edge of the connected structural members profile; parameter i

is defined by the following equation:

( ) ( )

3 21,4 1,0 1,0 0i i i i i i + = (7) One of striking differences between EuroCode and

the Ukrainian building codes related to the design of bolted end-plate connections is that EuroCode requires the propagation of plastic deformations to be taken into account. A lot of researches ( 1989,

2005) have addressed the design analysis of bolted end-plate connections in steel frameworks where plastic deformations are taken into account. This ap-proach provides an opportunity to use reserves of the load-bearing ability of bolted end-plate connections by allowing a plastic deformation to develop in those and in adjacent sections of the connected structural members. This will make the required thickness of the end-plate as small as possible.

The analysis of bolted end-plate connections where plastic deformations are taken into account is performed using a limit equilibrium method (Sumner and Murray 2003, Undermann and Schmidt 2005). Tree potential failure mechanisms are considered: (i) failure of bolts, (ii) failure of bolts with a simultaneous partial propagation of plastic deformations in the end-plate, and (iii) a plastic collapse of the end-plate (Sokol et al. 2002, Urbonas and Daniunas 2004, Pisarek and Kozlowski 2006) (Fig 4).

If an end-plate has a considerable bending stiffness, then the failure of the end-plate connection occurs as a consequence of that of bolts loaded by external forces in the absence of prying-lever contact forces. The load-bearing ability of such a connection will be defined com-pletely by that of bolts in tension (Urbonas and Daniunas 2004):

, ,T I t ii

F B=

(8)

If the bending stiffness of end-plates is lower (they are designed with a smaller thickness), the failure of the end-plate connection occurs as a result of that of bolts together with a partial propagation of plastic deforma-tions in the end-plate. The load-bearing ability of this connection can be found from the equation of a balance between the external and internal works (Urbonas and Daniunas 2004, Kozlowski and Pisarek 2005):

( )

,1, 2

pl tT II

M eBF

e m

+

=

+

(9)

Q

Q

M

pl,2

pl,2

M

M

pl,2

pl,2

M

Q

B

t

F

T

t

B

Q

1

M

pl,1

pl,1

MM

pl,1

pl,1

M

1

2

Q

B

t

T

F

t

B

Q

e

m

m

e

Q

B

t

F

T

t

B

Q

Fig 4. Design models of bolted end-plate connections according to EN 1993-1-8

736

If a thin end-plate is used, the failure of a bolted connection occurs by propagation of plastic deformations in the body of its end-plate. The load-bearing ability of the bolted connection in this case will be defined purely by that of the end-plate:

,1 ,2,

2 2pl plT III

M MF

m

+

= (10)

It should be noted that the propagation of plastic de-formations in end-plates and adjacent sections of con-nected structural members increases the overall deform-ability of a structure, and this fact should be taken into account appropriately in a subsequent nonlinear structural analysis (Cerfontaine and Jaspart 2002, Jaspart 2000).

Consistency and contradiction

The primary and most significant difference between the European design regulations and those of Ukraine is that the former require that the influence of the actual stiffness of a steel structural joint on the real behavior of a loaded steel framework should be analyzed. This is an implementation of one of prospective contemporary trends in the structural design and analysis. The service-ability of structural joints can be assessed not only by their strength, as in the Ukrainian building regulations, but also by their deformability or compliance (Da Silva et. al. 2002).

EuroCode defines a procedure for calculating the ro-tation stiffness, jS , of a structural joint. It depends on stiffness factors ik of particular structural members in-cluded in the joint (see Table 6.11 in EN 1993-1-8). For end-plate bolted connections in frame structures, the ini-tial rotation stiffness

,j iniS

can be calculated by the fol-lowing formula:

2

, 1j ini

i i

z ES

k

=

(11)

where E is an elasticity modulus; z is a lever arm (see Fig 6.15 in EN 1993-1-8).

jM

semi-rigid

rigid

nominally pinned

Mj

j,iniS

Fig 5. A rotation stiffness-based classification of joints

The value of rotational stiffness ,j iniS is a criterion

suggested by EuroCode to classify joints into nominally pinned, rigid, and semi-rigid ones (Fig 5). It is important that structural properties of joints remain in compliance with design assumptions made in the global analysis of the entire structure and in the design procedures of par-ticular structural members. In particular, the calculated joint compliance must be sufficient to permit the same rotation angle as that obtained by the static analysis (Faella et. al. 2000, Urbonas and Daniunas 2003).

It should be noted that the effect of an actual joint stiffness in steel frameworks becomes especially signifi-cant for structural joints with bolted connections of bear-ing type that possess a higher deformability comparing to both welded connections and other types of bolted con-nections. The reason is primarily a bearing deformation that emerges in bolt holes of connected members (Krumm 1991, Kuhlmann et. al. 1998).

There is a European categorization of bolted connec-tions which needs to be made consistent with the national design codes for EuroCode to be implemented in Ukraine.

According to Ukrainian building standards and regu-lations (SNiP -23-81*, a draft DBN V.2.6-: 200), all bolted connections of steel structures are divided into (i) shear connections and (ii) frictional (or slip-resistance) connections depending on their external force transfer mechanism. Flange connections (or bolted end-plate con-nections) make up a separate class of bolted connections, and specific standard documents ( 1988, 1981) are used to regulate the design and analysis of such connections.

In its turn, EuroCode identifies five categories of bolted connections: three categories , and of shear connections, and two categories D and E of tension con-nections (see Table 1). Bolted connection of the A cate-gory (bearing type) is a prototype for our usual shear connection where external forces are resisted by shearing in bolts and bearing of connected members in holes.

In bolted connections of the and categories, high-strength preloaded bolts of grades 8.8 and 10.9 are used. An external shear force that acts on the joint is re-sisted by friction forces between the contact surfaces of the connected members due to the preloading of the bolts. Bolted connections of the and categories are, as we can see from EuroCode, essentially the same as bolted frictional connections identified in the Ukrainian design code. Meanwhile, one of the most significant differences of EuroCode from the Ukrainian design code is that the former requires the check of the load-bearing ability of bolted connections to be based on design load combina-tions in both the ultimate limit state and the serviceability limit state.

The following categories of bolted connections, where the bolts are in tension, are usually employed in bolted end-plate connections between steel structural joints. If preloaded high-strength bolts of grades 8.8 and 10.9 are used, then those bolted connections belong to category E, otherwise to category D.

737

Table 1. Categories of bolted connections Category of bolted connections

according to EuroCode Criteria of load-bearing

ability Notes Analog from Ukrainian

design code

(bearing type) , ,v Ed v RdF F

, ,v Ed b RdF F

Bolt grades from 4.6 through 10.9 or non-preloaded high-strength bolts

Shear connection

(slip resistance in ser-viceability limit state) , , , ,v Ed ser s Rd ser

F F

, ,v Ed v RdF F

, ,v Ed b RdF F

Preloaded high-strength bolts of grades 8.8 and 10.9

Shea

r con

nect

ions

(slip resistance in ulti-mate limit state) , ,v Ed s Rd

F F

, ,v Ed b RdF F

, ,v Ed net RdF N

Preloaded high-strength bolts of grades 8.8 and 10.9. For

,net RdN , see EN 1993-1-1

Frictional connection

D (non-preloaded) , ,t Ed t RdF F

, ,t Ed p RdF B

Bolt grades from 4.6 through 10.9 or non-preloaded high-strength bolts

Flange connections in tension

Tens

ion

co

nnec

tions

E (preloaded) , ,t Ed t RdF F

, ,t Ed p RdF B

Preloaded high-strength bolts of grades 8.8 and 10.9

Flange connections in tension

Table 2. Minimum permissible spacing, end, and edge distances Limit value

Minimum permissible distance SNiP II-23-81 DBN .2.6 (draft) EN 1993-1-8

1. between centers of the holes in the following direction: ) along external force, 1,minp :

when 375ynR < N/mm2 02,5d 02d 02,2d

when 375ynR > N/mm2 02,5d 03d 02,2d

b) across external force, 2,minp :

when 375ynR < N/mm2 02,5d 02d 02,4d

when 375ynR > N/mm2 02,5d 03d 02,4d

2. from the center of hole to the element edge: ) along external force, 1,mine :

when 375ynR < N/mm2 02d 01,5d 01,2d

when 375ynR > N/mm2 02d 02,5d 01,2d

b) across external force, 2,mine : with sheared edges 01,5d 01,5d 01,2d with rolled edges 01,2d 01,2d 01,2d c) for slip-resistance bolted connection on any edge and with any external force direction, 1,mine , 2,mine

01,3d 01,3d 01,2d

Legend: 0d is the diameter of a hole; yn yR f=

is a nominal yield strength.

738

It seems also interesting to compare different build-ing code requirements to bolt spacing, end, and edge distances. EuroCode and the Ukrainian building code regulate minimum and maximum permissible spacing, end, and edge distances between holes in bolted connec-tions (see Tables 2 and 3). For connected members in tension, the maximum permissible distances are set mainly in order to ensure an appropriate closeness of a bolted connection and thereby to avoid corrosion. For connected members in compression, the maximum per-missible distances are to prevent local buckling.

As it can be seen from Tables 2 and 3, in all cases EuroCode defines lower values for both minimum and maximum permissible distances between holes in bolted connections. Additionally, it defines special cases where a local buckling analysis should be performed for plates in compressed connected members in the area between bolts, in the external forces direction.

As for the distribution of external forces in bolted connections, EuroCode takes into consideration a certain non-uniformity of the distribution between bolts in a long lap joint (a shear multi-bolted connection). For such cases EuroCode suggests using factor L when calculating shear resistance

,v RdF

of bolts as shown below:

2,v Rd L v ub s MF f n A = (12) where A is the gross cross-section area of a bolt;

2M

is a partial safety factor for bolted connections; ubf is a given ultimate tensile strength of the bolts; sn is the number of shear surfaces; v is a factor calculated ac-cording to Table 3.4 of EN 1993-1-8 depending on a bolts strength grade.

The value of factor L

varies from 1,0 to 0,75 and depends on the distance between the centers of end holes in a bolted connection, jL

(Fig 6), and on the bolt diame-ter d according to the following formula:

( )

1 0,005 15 , 0,75L j LL d = (13)

In similar design cases, SNiP II-23-81* uses only the service factor 0,9b = for shear multiple-bolted connec-tions when calculating both the shear and the bearing bolt resistance. In this way, SNiP II-23-81* actually allows for the case where bolts in a joint might not start resisting the load at the same time.

Table 3. Maximum permissible spacing, end and edge distances

Limit value Maximum permissible distance

SNiP II-23-81* Draft DBN V.2.6 EuroCode 3 EN 1993-1-8

1. between centers of bolt holes, 1,maxp , 2,maxp :

) in end rows in the absence of curb angles, either in tension or compression

08d or min12t 08d or min12t min14t or 200mm

b) in inner rows and in the end row in the presence of curb angles:

in tension 016d or min24t 016d or min24t min14t or 200mm

in compression 012d or min18t 012d or min18t min14t or 200mm

2. from the center of a hole to the elements edge:

1,maxe , 2,maxe 04d or min8t 04d or min8t min4t + 40mm

FF

e 2

2p

1ep1

1l =0,6pef

Legend: 0d is the diameter of a hole; mint is the thickness of a thinner outer element of the bolted connection. Note: The maximum permitted distances between the centers of holes and that from the center of a hole to the elements edge are presented here for steel structures made of steel as defined in EN10025, except for steel defined in EN10025-5.

739

FFjLL

LL j

F F

jLL

LL

bL

16d 65d 66d15d

0,75

1,00,9 II-23-81*

EN 1993-1-8 .2.6

0 0 j

Fig 6. Reduction of load-bearing ability of bolts in a long lap joint

The draft of a new Ukrainian building code for steel structures (DBN .2.6-: 200) defines the usage of a service factor with the value of 0,9 for bolted connections that resist shear and bearing. In addition, the DBN draft includes a correction introduced to allow for a non-uniform distribution of external forces between fasteners in a connection, for design cases where the distance be-tween the end bolt holes in the direction of the force ex-ceeds 16 diameters of the holes (Fig 6).

If a bending moment acts in a connection, the distri-bution of the internal forces between the fasteners should be assumed dependent on the bolted connection type. According to the Ukrainian building code, the distribu-tion of the internal forces between the fasteners can be assumed uniform (i. e. as in a rectangular stress diagram) for frictional bolted connections, and non-uniform (as in a triangular stress diagram) for shear bolted connection.

As for EN 1993-1-8, it has a strict requirement that the distribution of the external forces between the fasten-ers in a connection should be elastic for C category bolted connections, i.e. for frictional high-strength grade 8.8 and 10.9 preloaded bolt connections designed for ultimate limit states. In addition, an elastic distribution of the ex-ternal forces is required also for other categories of bolted connections in cases where the design bearing resistance of bolts exceeds the shear resistance. In other cases EN 1993-1-8 assumes a plastic distribution of the exter-nal forces between the fasteners in steel structural joints. Software implementation

A software implementation of the design and analy-sis procedures for bolted end-plate connections between steel joints in framework structures is the COMET appli-cation included in the SCAD Office software suite ( et al. 2008). The COMET software ap-plication is used to perform a structural assessment of design decisions and to develop designs of typical joints of steel structural systems widely used in civil and indus-

trial engineering. The application helps perform a struc-tural appraisal of a steel joint according to the require-ments of SNiP -23-81*, SP 53-102-2004 and EN 1993-1-8 and design a steel structural joint based on a particu-lar prototype.

Unlike invention, a prototype-based engineering consists of choosing and utilizing an available solution. This is the approach implemented in the COMET soft-ware; it is based on choosing from a set of parametrized standard structural designs of joints (prototypes) ( et al. 2008). The set of parameters for a prototype depends on what design conditions are prede-fined (material, internal forces etc.); they cannot be de-termined independently because a certain interrelation-ship might exist between them.

The COMET application uses the above approach and thereby enables an engineer to improve his efficiency by providing him with a wide range of prototypes. In this way, a highly qualified personnel does not have to do a routine technical work of checking and correcting a mul-titude of parameters to comply with building codes and design specifications.

After a structural scheme is selected for a joint, the system helps determine all parameters of it (they must comply with building codes, a number of structural or design constraints, and catalogues of steel members). Both the building requirements and structural constraints are mandatory, and any violation of those is not an op-tion. However, there are also design constraints violating which would only cause a warning, and the application can generate a decision with the violations thus made.

The input data for computer-aided design of steel structural joints include a joints type or configuration, types and sizes of cross-sections of connected structural members, and internal forces acting in adjacent sections of the connected members.

The user has the options of either accepting the sug-gested decision or modifying it to his preferences, in order to take into account a technology used to manufac-ture the involved steelwork members, requirements of unification of the structural scheme within the framework of a project or anything else (design team, manufacturing plant etc.), the usage of standard decisions commonly used in the project or team as well as the quality assur-ance system, marking system etc.

Having done this, the software performs an appraisal of the joints design and generates a drawing: a sketch of the design where all involved parameters and properties are laid out. In order to be able to make additions or changes to the design thus generated, or to alter the repre-sentation format (such as dimensioning, legends etc.), the system can export the graphical results of the design pro-cedure as a DXF (AutoCAD) file.

A set of incoming parameters and a set of outgoing parameters are defined for each of joint prototypes (de-sign parameters for structural decisions); methods have been determined to identify those groups of parameters. The representation of the structural joint becomes a basis on which a mathematical model of the design problem is formulated. The mathematical model includes a set of

740

design variables (unknown parameters of the design deci-sion for the joint) and a set of constraints.

The set of constraints comprises: constraints by the load-bearing ability of con-

nected structural members and auxiliary struc-tural elements (strictly speaking, the load-bearing ability of connected members should be ensured before starting the design or structural assessment of the joint; the checks performed here are just additional majority-decision checks which ensure the members are strong enough in the elastic phase of their behavior); these constraints are defined by building re-quirements;

assortment-based constraints for shaped and sheet steel;

structural constraints which reflect the way parts are manufactured; geometrical constraints posed by mutual arrangement of the structural members due to localization of welding and bolted connections; possibility of welding to-gether elements of different thickness etc.);

criterial constraints such as a minimum weight of auxiliary elements in a designed joint (gusset plates, ribs, support tables etc.) or a minimum labor content of manufacturing.

The COMET software provides the following groups of prototypes for steel structural joints: nominally rigid and nominally pinned column bases, beam and raf-ter splices, hinged and rigid joints between columns and rafters, truss joints. A considerable part of structural steel joints use bolted end-plate connections (such as beam and rafter splices as well as rigid joints between rafters and columns). In order to analyze and design such joints, the COMET software implements actual Guidelines ( 1988, 1981), as well as EN1993-1-8, and uses the design models of bolted end-plate connections presented above.

The nomenclature of prototypes of beam-to-rafter splices using bolted end-plate connections implemented in the Beam-To-Beam Joints mode of the COMET application is presented in Fig 7.

HpKfwhw

C tf

Bp

tf

bf

TpTp

Kff

C

Dp

Dp S

D

n n

D

S

C1D

p

C

Kff

Tp Tp

bf

tf

Bp

tfC

hw Kfw Hp

C2

C2C1

n

D

S

C

Kff

Tp Tp

bf

tfBp

tfC

hw Kfw Hp

Dp

a b c

HpKfwhw

C tf

Bp

tf

bf

TpTp

Kff

C

Dp

S

D

n

Lo LoTo C2

C1

Kfw

LoLo

C

HpKfwhwtf

Bp

tf

bf

TpTp

C

S

D

n

KffKfw

Dp

To

d e

C2

HpKfwhw

C tf

Bp

tf

bf

TpTp

C

C1

S

D

n

C1C2

Kfw

C1C2To

LoLo

n

D

S

C

Tp Tp

bf

tf

Bp

tfhw Kfw H

p

C

Lo LoKff Kff

f j Fig 7. Prototypes of structural designs of splices between beams and rafters using bolted end-plate connections

741

These joints are most often designed to match the outer dimensions of an end-plate to the height of a beam (Fig 7, ). If the bending moment acting in the joint can-not be taken on completely by the bolts located between the beam flanges, then there appears a necessity to de-velop design decisions with extended end-plates and out-side bolt rows which increase the end-plate height down-wards (Fig 7, b, d) or upwards (Fig 7, c, e) depending on the bending moments sign. If there are considerable alternating-sign bending moments, designs of bolted end-plate joints with extended end-plates and outside bolt rows on either beam flange (Fig 7, f, j) are used.

The nomenclature of prototypes of rigid joints be-tween rafters and columns using bolted end-plate connec-tions, which are implemented in the Beam-To-Column Joints mode of the COMET application, is presented in Fig 8. If a considerable bending moment acts in the joint, and the value of this moment exceeds the load-bearing

ability of the rafter, then the COMET software provides several prototypes of joint design decisions with haunches (see Fig 8, e, f). For several prototypes of joints between rafter and columns, a feature for specifying a rafter slope (Fig 8, d, f) also has been implemented.

The design and analysis of bolted end-plate connec-tions in beam and rafter splices as well as rigid joints between columns and rafters can be performed for several design load combinations when the joint experiences a simultaneous action of a bending moment, axial and shear forces. In addition, internal forces in the abutting column sections can be specified for joints between rafters and columns: an axial force, two bending moments about the main axes of the columns cross-section, and correspond-ing shear forces.

Interfaces of the Beam-To-Beam Joints and Beam-To-Column Joints modes of the COMET soft-ware are presented in Fig 9 and Fig 10, respectively.

C2

C1

S

bf

tf

Bp

tfhw

Dp

TrTpV

L

n

CH

pC

K1

DD

K1

CH

pC

Tp

Dp

hwtf

Bp

tf

bf

S

C1

C2

C1

Ts

HsBs

b

D

S

Tp bf

tf

Bp

tf

C

hw

K1

Hpn

C

Dp

Dp

Dp

Dp

C

n

HpK1

C

Bp

bfTp

S

D

ab

hwtf

tf

c d

DpD

p

CHp

K1

hw

C

tf

Bp

tf

bfTp

S

D

n1

Hv

C

Lvn2 n2 Lv

C

Hv

n1

D

S

Tpbf

tf

Bp

tf

C

hw

K1

HpC

Dp

Dp

ba

e f Fig 8. Prototypes of structural designs of rigid joints between a rafter and

a column using bolted end-plate connections

742

Fig 9. Interface of the Beam-To-Beam Joint mode of the COMET software

Fig 10. Interface of the Beam-To-Column Joint mode of the COMET software (rigid joints)

Conclusion

This paper presents principles for the design of bolted end-plate connections in structural joints of steel frames according to EuroCode and the Ukrainian building codes. Consistency and contradictions in the design pro-cedures for bolted connections based on different design codes have been identified.

A software implementation for the design and analy-sis of bolted end-plate connections in steel joints of frame structures has been presented. The application helps per-form a structural assessment of design decisions and de-velop designs of typical joints for steel structural systems widely used in civil and industrial engineering.

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