cap 4 2015

4. CONNECTING DEVICES

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Chapter 4

CONNECTING DEVICES

4.1. GENERAL

Connecting devices for steel structures are:

• Welds – are largely used in fabrication of structural members in shops;

• Bolts – are largely used in assembling structural members on the field;

• Rivets – at present they are practically abandoned due to their complicate

technology and high cost.

4.2. WELDING

4.2.1. General

Welding is a technological process that realizes the junction of the members

of a structure into a monolithic elastic network.

To execute a weld, one needs:

• a heat source;

• some adequate additional material.

The weld seam results after local melting in the area of welding (Fig. 4.1). A

number of welding passes, called weld layers , are necessary.

Fig. 4.1. Scheme of a welding process

heat source

parent metal

solidified weld

additional material

weld layer (seam)

molten pool


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The integrity of the welded structure depends on its ability to deform

plastically during fabrication, erection and service. The ability of the welded structure

to deform plastically, avoiding brittle failure primary depends upon:

1. weldability of steel;

2. welding procedure selection;

3. avoidance of notches both in design and fabrication;

4. adequate quality control and inspection.

4.2.2. Weldability

Weldability is defined as “the capacity of a metal to be welded under

fabrication conditions imposed into a specific suitably designed structure and to

perform satisfactorily in the intended service life”.

Weldability is largely depending on the reaction of steel to the drastic heating

and cooling cycle of arc welding. Three of the most important steel properties that

influence weldability are:

• the chemical composition;

• the structural grain size;

• the thickness of the material.

Weldability is expressed by an empirical formula which defines the carbon

equivalent value (CEV):

15

Cu%Ni%

5

V%Mo%Cr%

6

Mn%C%CEV

++++++= ( 4.1 )

A good weldability is obtained when CEV is smaller than 0,42.

Chemical composition. The brittleness that steel may reach after rapid cooling from

high temperature is directly proportional to the carbon content. In order to avoid

brittle failure of the welded structure it is necessary:

• to limit the content in carbon to 0,20 ÷ 0,22%;

• to limit the content in carbon of the additional material to 0,08,..., 0,12%.

Structural grain size. There is a linear relationship between the ferrite grain size and

the Charpy transition temperature between ductile and brittle behaviour; the greater


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the grain size is the greater the transition temperature is. Weldability also varies with

grain size meaning it is favoured by a reduced grain size.

High heat input welds show a larger grain size than the same process at a

lower heat input, because they provide a slower cooling rate. That is why

recommendations usually limit the thickness of a weld layer at about 6mm. A

subsequent pass will refine the grains of a previous pass.

Thickness. Because of their greater mass, thick plates extract heat from the weld

area and cool the weld more rapidly than the same weld on thin plates. As a result,

weldability is affected. There are two possibilities to avoid a tendency to brittle

fracture:

• to limit the thickness of plates;

• to pre-heat the pieces and to hold them at a temperature of a few hundred

degrees before the welding operation.

Conclusions:

Weldability is increased by:

• low carbon content;

• fine grain size;

• restricted low thickness;

and, conversely, is reduced by:

• high carbon content;

• coarse grain;

• big thickness.

4.2.3. Structural welding process and materials

Fusion welding processes vary largely, according to the applied heat source

and to how the molten pool is protected against atmosphere. The most common

welding processes used in commercial structural steel fabrication are:

1. Manual shielded metal arc process (Fig.4.2), (Fig.4.3)

The heat source is the electric arc formed between the electrode and the

parent metal. The developed heat produces a quick melting of the external

coatings of electrodes containing aluminium, silicon and other deoxidizers, which


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protect the area surrounding the arc and the weld pool. This process is widely

applicable to any kind of welds.

Fig. 4.2. Scheme of the manual shielded metal arc process

Fig. 4.3. Schematic image of the manual shielded metal arc process (by courtesy of

www.twi-global.com)

2. Submerged arc process (Fig.4.4), (Fig.4.5), (Fig.4.6)

The heat source is the electric arc formed between the electrode and the

parent metal. The protection of the weld pool, better as in the shielded arc

process, is provided by a granulated deoxidizer flux automatically thrown in

advance and at the same speed of the welding process. This procedure is highly

productive for long weld seams.

additional material

coating

direction of travel

metal arc

weld pool (molten pool)

electrode

protective gas

protecting slag

solidified weld (weld deposit)

parent metal

recovered flux


96

Fig. 4.4. Scheme of the submerged arc process

Fig. 4.5. Scheme of the submerged arc process (by courtesy of www.twi-global.com)

metal arc

molten pool

flux feed line

granular flux

parent metal

direction of travel

solidified weld (weld deposit) slag

bar electrode (continuous wire)


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Fig. 4.6. Image of the submerged arc process (by courtesy of Arc Resources)

3. Gas shielded metal arc process (GMAW - Gas Metal Arc Welding) with

consumable electrode (MIG and MAG). The arc protection is provided by an

inert gas (MIG) (Fig. 4.7), (Fig. 4.8) or by a chemically active gas (MAG). This

procedure is used in welding mild steel and low alloy steel.

Fig. 4.7. Schematic image of MIG welding (by courtesy of www.arcabrasives.com

and www. Luvata.com)


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Fig. 4.8. Image of MIG welding

4. Gas shielded metal arc process with non-consumable electrode . The arc is

produced between a tungsten element and the parent metal. The protection is

provided by argon. This procedure is used especially for welding stainless steel

or aluminium alloys.

5. Electro-slag welding is a special procedure to weld very thick steel parts with

only one pass in a vertical position.

“7.3 Welding processes ( EN 1090–2 [20] ) Welding may be performed by the following welding processes defined in EN ISO 4063: 111: Manual metal-arc welding (metal-arc welding with covered electrode); 114: Self-shielded tubular cored arc welding; 121: Submerged arc welding with one wire electrode; 122: Submerged arc welding with strip electrode; 123: Submerged arc welding with multiple wire electrodes; 124: Submerged arc welding with metallic powder addition; 125: Submerged arc welding with tubular electrodes; 131: Metal inert gas welding; MIG-welding; 135: Metal active gas welding; MAG-welding; 136: Tubular-cored arc welding with active gas shield; 137 Tubular-cored arc welding with inert gas shield; 141: Tungsten inert gas welding TIG welding; 21: Spot welding; 22: Seam welding; 23: Projection welding; 24: Flash welding; 42: Friction welding; 52: Laser welding; 783: Drawn arc stud welding with ceramic ferrule or shielding gas; 784: Short-cycle drawn arc stud welding.


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Resistance welding processes 21, 22 and 23 shall only be used to execute welding of thin gauge steel components. Additional information is given:

• in EN ISO 14373 for process 21(spot welding); • in EN ISO 16433 for process 22 (seam welding; • in EN ISO 16432 for process 23 (projection welding).

The diameter of spot and projection welds shall be checked during production by means of peel or chisel testing according to EN ISO 10447. Other welding processes shall only be used if explicitly specified”.

4.2.4. Metallurgic phenomena in the welding process

Essentially, there are three metallurgic phenomena:

1. A hard zone appears in the parent metal near the weld seam, which can lead to

so-called cold cracking (Fig. 4.9). The origin of this phenomenon is assigned to

the hydrogen absorbed by the weld material in the molten state. The tendency to

brittle cracks may be moderated by pre-heating the part to be welded and by

using electrodes with basic coating.

Fig. 4.9. Scheme of the material structure near a weld seam

2. Lamellar tearing is a separation or a crack in the base metal, caused by

through-thickness weld shrinkage stairs (Fig. 4.10). It is a result of the reducing of

ductility in the through-thickness direction, which can be lower than in the

conventional longitudinal tests.

hardness

cracks

2 … 6mm


100

Fig. 4.10. Lamellar tearing

3. Hot cracking can occur in the molten area. These cracks form during the

solidification process and they are explained by the presence of some impurities

solidifying at a lower temperature than steel (Fig. 4.11).

Fig. 4.11. Hot cracks

4.2.5. Thermal phenomena in welding process

The heating-cooling cycles during welding produce (Fig. 4.12):

• internal stresses (residual stresses);

• deformations (Fig. 4.13).

The greater deformations are the lower stresses are.

lamellar tearing

steel plate σres = (0,5 … 1,0) × fy


101

Fig. 4.12. Residual stresses and residual deformations

Fig. 4.13. Example of residual deformations after welding (angular distortion)

4.2.6. Welding positions

The most common welding positions are as follows:

1. Flat position

butt welds fillet welds

Fig. 4.14. Flat position

2. Horizontal position

longitudinal shrinkage weld seam


102

Fig. 4.15. Horizontal position

3. Vertical position

Fig. 4.16. Vertical position

4. Overhead position

Fig. 4.17. Overhead position

Flat position requires the simplest technology. The overhead position is the

most complicated one and, consequently, prone to poorer quality.

4.2.7. Weld details

In order to avoid unfavourable weld details, the following are recommended:


103

1. Avoid overwelding (Fig. 4.18). This requires the use of an appropriate weld

size, not larger than the one given by calculation.

Fig. 4.18. Example of oversized weld seam

2. Avoid asymmetry (Fig. 4.19).

Fig. 4.19. Example of asymmetric weld seams

3. Avoid lamellar tearing (Fig. 4.20). Lamellar tearing means failure of a hot rolled

plate or of a hot rolled shape because of cracks formed along the rolling direction.

These cracks create separation plans among longitudinal fibres.

Fig. 4.20. Example of details that may favour lamellar tearing

4. Avoid susceptible details (Fig. 4.21). Some details might favour lamellar tearing

or brittle fractures.

OK NO oversized weld (too much heating)

desirable

desirable

notch effect

lamellar tearing


104

Fig. 4.21. Examples of susceptible details and improved ones

5. Avoid weld fatigue (Fig. 4.22). Any change in section should be “stream-lined”.

Fig. 4.22. Example of “stream-lined” details to avoid fatigue and brittle fractures

4.2.8. Welding defects

Welding defects are:

• cracks – the worse defect;

• blow holes – metallurgic defect;

• lack of penetration;

• porosity;

• slag inclusions.

susceptible details improved details

NO YES

“stream line”

“stream line”


105

4.2.9. Weld inspection methods

1. Visual Test (VT)

It is the most economical test. The magnifying glass detects surface

imperfections, porosity, slag, cracks, irregularities, etc.

2. Dye (Liquid) Penetrant Test (DPT) (Fig. 4.23)

This test uses a red dye penetrant applied to the work from a pressure spray can.

Fig. 4.23. Dye penetrant test

3. Magnetic Particle Test (MPT) (Fig. 4.24)

A magnetizing current is introduced over a dry red magnetic powder. This

induces a magnetic field in the work that will be distorted by any cracks or

inclusions, located on or near the surface.

Fig. 4.24. Magnetic particle test

This method will indicate surface defects, like fine cracks not to be observed by

liquid penetration (cracks filled with slag, difficult for liquid to penetrate).

4. Radiographic Test (RT.)

Radiographic testing is basically an X-ray film process. Internal defects may be

put in evidence (porosity, blow holes, slag inclusions, cracks appear as darker

stains (spots) on the film).

subvisible crack

red penetrant applied in excess

excess removed

visible indication

white developer applied

current

red dry powder


106

5. Ultrasonic Test (UT)

The ultrasonic inspection process is analogous to radar. The method is based on

the variations in reflections due to differences in acoustic properties (pulse echo)

caused by defects (at the boundary).

EN 1090-2:2008 [20] “Inspection before and during welding shall be included in the inspection plan according to the requirements given in the relevant part of EN ISO 3834. Non destructive testing (NDT) methods shall be selected in accordance with EN 12062 by personnel qualified according to Level 3 as defined in EN 473. Generally ultrasonic testing or radiographic testing applies to butt welds and penetrant testing or magnetic particle inspection applies to fillet welds. NDT, with the exception of visual inspection, shall be performed by personnel qualified according to Level 2 as defined in EN 473. 12.4.2.4 Additional NDT methods The following NDT methods shall be carried out in accordance with the general principles given in EN 12062 and with the requirements of the standard particular to each method: a) penetrant testing (PT) according to EN 571-1; b) magnetic particle inspection (MT) according to EN 1290; c) ultrasonic testing (UT) according to EN 1714, EN 1713; d) radiographic testing (RT) according to EN 1435. The field of application of NDT methods is specified in their relevant standards”.

4.2.10. Strength of welded joints

In the Romanian code STAS 10108/0–78 [7] there are two important types of

weld seams, with respect to their behaviour and to their design models:

• butt welds;

• fillet welds.

The main difference is that in this model butt welds behave like parent material, while

fillet welds resist always by shear stresses τ.

All important steel design codes distinguish between two types of weld seams:

• butt welds;

• fillet welds.

In the case of butt welds , the weld seam is placed in the thickness of a connected

part, whilst fillet welds are always placed in the angle between the connected parts.


107

Fig. 4.25. Classification of weld seams

Checking a welded connection generally consists of the following steps:

1. Establishing the design cross-section and its geometrical characteristics;

2. Reducing loads in the centre of gravity of the cross-section;

3. Establishing the stress distribution on the cross-section;

4. Checking the seam in the most loaded points.

The beginning and the end of a weld seam are generally weak zones; many

defects are found there. That is why these weak parts are neglected when

establishing the strength of the joint. In order to avoid “losing” a part of the seam, it is

possible to use some additional pieces from where to start and to end welding.

These pieces are made of copper (Fig. 4.26). In the end they are cut down and the

entire seam is reliable. The use of additional pieces (“run on ” and “run off ” plates )

is strongly recommended for butt welds.

Fig. 4.26. Example of using “run on” and “run off” plates

Weld seams are noted on drawings according to SR EN 22553 (ISO 2553).

end lap weld seams T – joints overlapping weld seams

butt weld seams fillet weld seams

“run on” plate cutting line


108

4.2.10.1. Butt welds

The European standard EN 1993-1-8 [14] accepts two types of butt weld

seams :

• full penetration butt welds ;

• partial penetration butt welds.

The full penetration butt welds can be checked similarly to the parent material, whilst

the partial penetration butt welds are checked like fillet weld seams.

The design cross-section of the weld seam must be established before any

design procedure.

Fig. 4.27. Dimensions of a butt weld seam

ds LaA ⋅= ( 4.2 )

)a2(LLd ⋅−= ( 4.3 )

a – the throat (effective thickness); it is equal to the thickness of the thinner

joined member (Fig. 4.19);

Ld – the design length of the seam; it is obtained by deducing the bad parts of the

seam from the actual length L (4.3); if “run on” and “run off” plates are used, it

is equal to the actual length of the seam (Fig. 4.27).

1. Butt weld subjected to axial force (NEd) (Fig. 4.28)

a

a

a

a

L

NEd NEd Ld

a

σ

y y

z

z


109

Fig. 4.28. Butt weld seam subjected to axial force

The stress distribution is constant on the cross-section:

w

Ed

A

N=σ ( 4.4 )

2. Butt weld subjected to shear force (VEd) (Fig. 4.29)

Fig. 4.29. Butt weld seam subjected to shear force

Generally, the stress distribution is a parabola described by Juravski’s relation:

y

yEd

Iw

SV

⋅⋅

=τ ( 4.5 )

where:

Sy – static moment of the area of the part of the cross-section that tends to

slide in the point where τ is calculated;

w – width of the cross-section in the point where τ is calculated;

Iy – second moment of the area (moment of inertia) of the cross-section about

y-axis (axis normal to the shear force).

The maximum shear stress is obtained in the neutral axis (Fig. 4.29a), where the

static moment Sy has the maximum value:

y

max,yEdmax Iw

SV

⋅⋅

=τ ( 4.6 )

In cases where there is an important variation in the value of the width w of the

cross-section, Juravski’s relation describes a leap in the diagram and the

parabola is flattened. In these cases, a simplified distribution is accepted (Fig.

4.29b), considering that the entire shear force is resisted only by the web.

( a ) ( b )

Ld

a

t

t

hw tw

b

τ

VEd

VEd

VEd

VEd

τ

y y y y

z

z

z

z


110

vw

Ed

A

V=τ ( 4.7 )

wwvw haA ⋅= shear area of the weld seam ( 4.8 )

3. Butt weld subjected to bending moment (MEd) (Fig. 4.30)

Fig. 4.30. Butt weld seam subjected to bending moment

Generally, the linear stress distribution is described by Navier’s relation:

zI

M

y

Ed ⋅=σ ( 4.9 )

where:

Iy – second moment of the area (moment of inertia) of the cross-section about

y-axis (axis normal to the plane of the bending moment).

z – the distance from the considered point to the neutral axis (in the plane of

the bending moment).

The maximum stress is obtained when z takes the greatest value:

y

Edmax

y

Edmax W

Mz

I

M =⋅=σ ( 4.10 )

where:

Wy – cross-section modulus about y-axis (axis normal to the plane of the

bending moment).

4. Butt weld connection subjected to axial force, shear force and bending moment

(NEd, VEd, MEd) (Fig. 4.31)

MEd MEd

Ld

a

y y

z

z

σ

t *

Mσ *

Nσ


111

Fig. 4.31. Butt weld seam subjected to axial force, shear force and bending moment

Solving the general problem given in figure 4.31 means using linear superposition

of relations (4.4) – (4.10) and checking the stress state in the most loaded points by

means of relations (4.11) – (4.13).

0M

y

y

Ed

W

EdMNmax

fz

I

M

A

N

γ≤⋅±=σ±σ=σ ( 4.11 )

0M

yV

3

f

γ⋅≤τ ( 4.12 )

( )0M

y2V

2*M

*Neq

f3

γ≤⋅+σ±σ=σ τ ; N

*N σ=σ ; *

y

Ed*M z

I

M ⋅=σ ( 4.13 )

When using relation (4.13), σ and τ must be calculated in the same point (z*) and in

the same loading situation.

The values of the normal design strength sR and of the shear design strength sfR

according to the Romanian code STAS 10108/0–78 [7] may be found in table 4.1.

The values of the yielding limit fy are given in tables 3.6 and 3.7, while the value of

the safety factor γM0 may be found in table 3.8.

4.2.10.2. Fillet welds

The profile of a fillet weld can have different shapes:

flat convex concave concave with

VEd

MEd

NEd hw

t

tw

b

y y

z

z σN σM τV

z*


112

Fig. 4.32. Possible profiles of a fillet weld unequal legs

In the model used in the Romanian code STAS 10108/0–78 [7] the design thickness

of the cross-section of the seam is defined by the height of the greatest isosceles

triangle that can be inscribed in the cross-section of the weld seam (Fig. 4.25).

In the model used in EN 1993-1-8 [14] the effective throat thickness of the seam is

defined by the “height of the largest triangle (with equal or unequal legs) that can be

inscribed within the fusion faces and the weld surface, measured perpendicular to

the outer side of this triangle” (Fig. 4.33 (EN 1993-1-8 [14] Fig. 4.3)):

Fig. 4.25. Design cross-section of a fillet weld seam

Fig. 4.33. Throat thickness of a fillet weld (EN 1993-1-8 [14] Fig. 4.3)

Once the thickness of the design cross-section (throat) established, the design

section of the weld seam is obtained by bringing the rectangles defined by relations

(4.14) and (4.15) in the plane of the connection.

dw LaA ⋅= ( 4.14 )

)a2(LLd ⋅−= ( 4.15 )

a – the effective throat thickness (Fig. 4.33) (design thickness of the cross-

section of the seam);

Ld – the design length of the seam; it is obtained by deducing the bad parts of the

seam from the actual length L (4.15); these parts are situated at each end.

The effective throat thickness a can be 25, 3, 35, 4, 5, 6, 7 ... mm and it generally

shall satisfy the following requirements (Fig. 4.33), (Fig.4.34a):

a a a a


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minmax t7,0at3,0 ⋅≤≤⋅ ( 4.16 )

( a ) ( b ) ( c )

Fig. 4.34. Geometric requirements for the effective throat thickness of fillet welds

For shapes like angles (Fig.4.34b) or channels (Fig.4.34c):

min2max t7,0at3,0 ⋅≤≤⋅ ( 4.17 )

( )pg1max t85,0 ;t7,0minat3,0 ⋅⋅≤≤⋅ ( 4.18 )

where:

tg – thickness of the gusset;

tp – thickness of the shape (profile);

tmin – the minimum thickness of the connected elements (min ti).

There are also limitations for the length Ld of the weld seam (Fig. 4.35):

( )a60L

mm40

b

U , L shapes rolledhot fora15

plates fora6

d ⋅≤≤

−⋅⋅

(STAS 10108/0–78) ( 4.18 )

a150Lmm30

platesfor a6d ⋅≤≤

⋅

(EN 1993-1-8 [14]) ( 4.19 )

In lap joints longer than 150a, a reduction factor βLw.1 multiplies the length Lj:

βLw.1 = 1,2 − 0,2Lj /(150a) but βLw.1 ≤ 1,0

Lj is the overall length of the lap in the direction of the force transfer.

a t1

t2

a1

tg

tp tp

tg

a2

a1

a2


114

Fig. 4.35. Geometric requirements for the length of fillet weld seams

Depending on their position with respect to the main force, fillet weld seams

can be classified as:

• side (longitudinal) weld (Fig.4.36a);

• end (transverse) weld (Fig.4.36b);

• combined weld (Fig.4.36c).

( a ) ( b ) ( c )

Fig. 4.36. Types of fillet weld seams

Combined welds are not recommended because of the different stiffness of side and

end welds, which generates a non-uniform behaviour of the connection. Tests

showed that fillet welds generally fail due to tangential stresses that are developed in

inclined planes at 45°.

EN 1993-1-8 [14] accepts two checking models for fillet welds:

• the directional method (Fig. 4.37);

• the simplified method where the loading state is reduced to shear stresses τ.

N N b

L a L

model stress distribution

real stress distribution


115

Fig. 4.37. Stresses on the throat section of a fillet weld, according to the directional

method (EN 1993-1-8 [14] Fig. 4.5)

Following this, the design relations are as follows.

1. Fillet weld subjected to axial force

• when the force acts in the centroid line of the connection (Fig. 4.38)

Fig. 4.38. Axial force acting in the centroid line of a fillet weld connection

)a2(LLd ⋅−= ( 4.20 )

dw La2A ⋅⋅= ( 4.21 )

d,vww

EdN f

A

N ≤=τ ( 4.22 )

2Mw

ud.vw

3ff

γ⋅β= ( 4.23 )

Strictly according to EN 1993-1-8 [14], the weld seam is considered to be

concentrated in the root of the weld . The check is done on unit of length:

Rd,wEd,w FF ≤ ( 4.24 )

afF d,vwRd,w ⋅= ( 4.25 )

NEd NEd

L a L

a

a

Ld


116

• when the force acts with an eccentricity from the centroid line of the

connection (e.g. angles, channels, etc.) (Fig. 4.39)

Fig. 4.39. Axial force acting with an eccentricity by the centroid line of a fillet weld

)a2(LL 11d ⋅−= ( 4.26 )

)a2(LL 22d ⋅−= ( 4.27 )

1d11w LaA ⋅= ( 4.28 )

2d22w LaA ⋅= ( 4.29 )

b

ebNN Ed1

−⋅= ( 4.30 )

b

eNN Ed2 ⋅= ( 4.31 )

d,vw1w

11N f

A

N ≤=τ ( 4.32 )

d,vw2w

22N f

A

N ≤=τ ( 4.33 )

2. Fillet weld subjected to shear force

• when the shear force acts together with a bending moment, Juravski’s relation

is used

d,vwy

yEdV f

Iw

SV≤

⋅⋅

=τ ( 4.34 )

or in cases where there is an important change in the width w of the cross-

section, the simplified relation (4.35) may be used, where Avw is the shear

area of the cross-section (area of the web for I and H shapes)

d,vwvw

EdV f

A

V ≤=τ ( 4.35 )

NEd NEd

N1

N2

L

a1 L

a2 L

a1

a2

e

b

Ld1

Ld2


117

• when the shear force does not act together with a bending moment (a

“scissors-like” force or a force acting in the plane of the connection, in the

centre of gravity of the connection, on any direction), relation (4.36) is used,

where Aw is the total area of connection

d,vww

EdV f

A

V ≤=τ ( 4.36 )

3. Fillet weld subjected to axial force, shear force and bending moment acting

normally to the plane of the connection (Fig. 4.40)

Fig. 4.40. Fillet weld connection subjected to moment acting normally on the plane

Solving the general problem given in figure 4.40 means using linear superposition

of the previously presented relations and checking the stress state in the most

loaded points, always keeping in mind that all stresses that are developed in a

fillet weld connection are shear ones.

w

EdN A

N=τ ( 4.37 )

vw

EdV A

V=τ ( 4.38 )

or, by using the general relation (not a common situation)

y

yEdV Iw

SV

⋅⋅

=τ ( 4.39 )

zI

M

y

EdM ⋅=τ ( 4.40 )

maxy

EdMmax, z

I

M ⋅=τ ( 4.41 )

The checks to be done are:

T

M

N

element cross-section

connection design cross-section

y y

z τN τT τM 1

2


118

• in the farthest points away from the centre of gravity welded connection (point

1 in figure 4.40)

d.vwMN f≤τ±τ ( 4.42 )

• theoretically, in any point on the cross-section and especially at the edge of

the web for I cross-section, the geometric sum of stresses (point 2 in figure

4.40)

( ) ( ) d.vw2

T2

MN f≤τ+τ±τ ( 4.43 )

2Mw

ud.vw

3ff

γ⋅β= ( 4.44 )

where:

βw – correlation factor, given in table 4.1.

Table 4.1. Correlation factor βw (EN 1993-1-8 [14] Tab. 4.1)

Standard and steel grade Correlation factor

βw EN 10025 EN 10210 EN 10219

S235 S235 H S235 H 0,8 S235 W

S275 S275 H S275 H S275 N/NL S275 NH/NLH S275 NH/NLH 0,85 S275 M/ML S275 MH/MLH

S355 S355 H S355 N/NL S355 H S355 NH/NLH 0,9 S355 M/ML S355 NH/NLH S355 MH/MLH

S355 W

S420 N/NL S420 MH/MLH 1,0 S420 M/ML

S460 N/NL S460 M/ML S460 NH/NLH S460 NH/NLH 1,0

S460 Q/QL/QL1 S460 MH/MLH

The values of the ultimate strength fu are given in tables 3.6 and 3.7, while the

value of the safety factor γM2 may be found in table 3.8.

The values of the shear design strength sfR for fillet weld seams according to the

Romanian code STAS 10108/0–78 [7] may be found in table 4.1.


119

4. Fillet weld subjected to axial force, shear force and bending moment acting in the

plane of the connection (Fig. 4.41)

According to the previously presented relations,

w

EdN A

N=τ ( 4.45 )

w

V A

V=τ ( 4.46 )

zII

M

zx

EdxM ⋅

+=τ ( 4.47 )

xII

M

zx

EdzM ⋅

+=τ ( 4.48 )

Fig. 4.41. Fillet weld connection subjected to in-plane moment

Considering fvw.d given in relation (4.44) for fillet welds, the check to be made in

the farthest point away from the centre of gravity (point 3 in figure 4.41) is:

( ) ( ) d.vw2

zMT2

xMN f≤τ±τ+τ±τ ( 4.49 )

In all the previously presented fillet weld connections whenever the seams are

doubled (they are situated on both sides of a plate), the areas and the moments of

inertia (second moments of the area) are doubled on the same geometric

configuration.

Table 4.1. Strength of weld seams according to STAS 10108/0–78 [7] Weld type Compression Tension Shear

T

M N

a design cross-section

x

z

x x

z

z

τN τxM

τT

τzM

3


120

Butt weld RRsc = RRs

i = for automatic welding, followed by non-destructive tests

R8,0Rsi ⋅= for manual welding

R6,0Rsf ⋅=

Fillet weld – – R7,0Rsf ⋅=

R = design strength of the parent material Whenever a connection contains in the same cross-s ection butt welds

and fillet welds, it is treated as a whole and only the checks differ, depending

on whether the checked point is situated on butt we ld or on fillet weld.

4.3. BOLTS

4.3.1. General

The more general term “fasteners” includes bolts and rivets. The behaviour of

rivets is very much alike the behaviour of bolts and they are very rarely used today.

Bolts are connecting elements largely used on field at the erection stage when

structural members are to be assembled in order to realise a steel structure. Figure

4.42 shows a steel frame built on field using bolted connections.

Fig. 4.42. Example of steel frame built on field using bolted connections

Bolts used for structures generally consist of the following components:

• a metal cylindrical shank, partially threaded and having a head, usually

hexagonal (Fig. 4.43a);

• a nut, usually hexagonal (Fig. 4.43b);

• one or two washers, usually round (Fig. 4.43c).


121

( a ) ( b ) ( c )

Fig. 4.43. Components of a bolt

A bolted connection results by twisting the nut until a firm contact is obtained

between the plates to be assembled (Fig. 4.44a). In bolted connections subjected to

vibration, spring washers (Grower) (Fig. 4.44b) or lock nuts (Fig. 4.44c) should be

used in order to avoid any loosening of the nuts.

( a ) ( b ) ( c )

Fig. 4.44. Possible components of a bolted connection

4.3.2. Classification of bolts

Bolts can be classified as:

• normal bolts;

• high strength bolts.

Table 4.2 shows the mechanical properties of the most common bolts used in steel

structures depending on the bolt grade. Bolts are defined by two numbers: the first

one is the ultimate strength, fub, in hundreds of N/mm2. The second one is ten times

the ratio between the yielding limit, fyb, and the ultimate strength, fub.

Table 4.2. Main mechanical properties of the most common bolts [2] Type Grade fub (N/mm 2) fyb (N/mm 2) εεεεu (%) fkb (N/mm 2)

4.6 400 240 22 240 Normal bolts 5.6 500 300 20 300 6.8 600 480 8 420


122

High strength 8.8 800 640 12 560 bolts 10.9 1000 900 9 700 fub is the minimum tensile strength determined on the entire bolt fyb is the minimum yield stress determined on the entire bolt εu is the ultimate strain fkb is the characteristic strength value, equal to the lower between fyb and 0,7fub

Table 4.2. Main mechanical properties of the most common bolts (EN 1993-1-8 [14]

Tab. 3.1)

Bolt grade 4.6 4.8 5.6 5.8 6.8 8.8 10.9

fyb (N/mm2) 240 320 300 400 480 640 900

fub (N/mm2) 400 400 500 500 600 800 1000

The diameters in mm of the bolts usually used in steel structures are: 10, 12, 14, 16,

18, 20, 22, 24, 27, 30, 33, 36.

4.3.3. Behaviour and design resistance of bolts

4.3.3.1. Loading and tightening

The behaviour and the design resistance of bolts substantially depend on:

• loading type;

• tightening type.

Loading type. From the loading type point of view, bolts can be classified as:

• bolts loaded perpendicular to their axis (shear connections) (Fig.4.45a);

• bolts axially loaded (tension connections) (Fig.4.45b).

( a ) ( b ) Fig. 4.45. Loading types of bolts

Tightening type. Tightening can be:

• normal tight;

F/2

F/2

F/2 F/2

F/2 F/2

F


123

• controlled tight.

In both types of tightening, the bolt is introduced in a 2...3mm larger diameter hole. If

the difference between the diameter of the hole and the diameter of the bolt

(clearance) is less than 0,3mm the connection is called fitted connection . The

nominal clearance in standard holes is:

• 1mm for M12 and M14 bolts;

• 2mm for M16 to M24 bolts;

• 3mm for M27 and larger bolts.

Normal tight is defined as the tightness that exists when members to be connected

are in firm contact. This may usually be realised by the full effort of a man using an

ordinary wrench. The tightening produces a self-stress loading consisting of:

• tension in the bolt, balanced by compression in the plates (a certain friction also

results between plates in contact);

• a twisting moment in the bolt balanced by friction between the plate and the

washer and between this one and the nut.

Controlled tight is defined as the tightness corresponding to a fully pre-tensioned

bolt. The control of tightening refers to the preload force Nt to be induced in the

shank of the bolt by a twisting moment Mt applied to the nut (by using a calibrated

impact wrench or by using “turn-off the nut” method).

4.3.3.2. Spacing of holes

Fig. 4.46. Spacing of holes

p1 p1

p1

p2

t1

t2

e2

e2

e1 e1


124

Table 4.3. Minimum and maximum spacing, end and edge distances (EN 1993-1-8

[14] Tab. 3.3)

Distances and spacings

Minimum Maximum1) 2) 3)

Structures made from steels conforming to EN 10025 except steels conforming to

EN 10025-5

Structures made from steels conforming to

EN 10025-5

Steel exposed to the weather or other corrosive influences

Steel not exposed to the weather or other corrosive influences

Steel used unprotected

End distance e1 1,2d0 4t + 40 mm The larger of 8t or 125 mm

Edge distance e2 1,2d0 4t + 40 mm The larger of 8t or 125 mm

Distance e3 in slotted holes

1,5d0 4)

Distance e4 in slotted holes

1,5d0 4)

Spacing p1 2,2d0 The smaller of 14t or 200 mm

The smaller of 14t or 200 mm

The smaller of 14tmin or 175 mm

Spacing p1,0 The smaller of 14t or 200 mm

Spacing p1,i The smaller of 28t or 400 mm

Spacing p2 5) 2,4d0 The smaller of 14t or 200 mm

The smaller of 14t or 200 mm

The smaller of 14tmin or 175 mm

1) Maximum values for spacings, edge and end distances are unlimited, except in the following cases:

– for compression members in order to avoid local buckling and to prevent corrosion in exposed members and;

– for exposed tension members to prevent corrosion. 2) The local buckling resistance of the plate in compression between the fasteners should be

calculated according to EN 1993-1-1 using 0,6 p1 as buckling length. Local buckling between the fasteners need not to be checked if p1/t is smaller than 9 ε . The edge distance should not exceed the local buckling requirements for an outstand element in the compression members, see EN 1993-1-1. The end distance is not affected by this requirement.

3) t is the thickness of the thinner outer connected part. 4) The dimensional limits for slotted holes are given in […] 5) For staggered rows of fasteners a minimum line spacing of p2 = 1,2d0 may be used, provided

that the minimum distance, L, between any two fasteners is greater than 2,4d0, see […] d0 – diameter of the hole; see Fig. 4.46


125

4.3.3.3. Behaviour of bolts in tension

Tension is applied on the bolt (Fig. 4.47) at the contact between one plate and

the head of the bolt (or the washer which is under the head) at one end and at the

contact between the other plate and the washer which is under the nut at the other

end. A bolt in tension fails in the most reduced cross-section, in the threaded zone of

the shank. The area of the cross-section of the bolt, As, in this zone can be taken

from tables or it may be calculated using relations (4.50) and (4.51).

Fig. 4.47. Bolt in tension

4

dA

2s

s

⋅π= ( 4.50 )

d89,0ds ⋅≅ ( 4.51 )

In the case of rivets, the shank fills the hole and the area is:

4

dA

20

0

⋅π= ( 4.52 )

The design resistance of a bolt in tension is:

2M

sub2Rd,t

AfkF

γ= (EN 1993-1-8 [14], Tab. 3.4) ( 4.53 )

where:

k2 = 0,63 for countersunk bolts or 0,9 otherwise;

fub – ultimate strength of the material of the bolt;

The design resistance of a rivet in tension is:

2M

0urRd,t

Af6,0F

γ= (EN 1993-1-8 [14], Tab. 3.4) ( 4.54 )

where:


126

fur – ultimate strength of the material of the rivet;

In the case of bolts, a second failure mode is possible, by punching. The punching

shear resistance for a bolt is:

2M

upmRd,p

ftd6,0B

γ⋅⋅⋅π⋅= ( 4.55 )

where:

dm – the mean of the across points and across flats dimensions of the bolt head or

the nut, whichever is smaller;

tp – thickness of the plate.

4.3.3.4. Behaviour of normal bolts in shear connections

Figure 4.48 shows the behaviour of a normal bolt in a shear connection.

Fig. 4.48. Stress distribution in a “bearing type” connection

The following states can be noticed when loading a bolted connection normally on

the axis of the bolt (Fig. 4.49):

• Phase 1 The bolt is generally introduced in a 2...3 mm larger hole and it is

normally tightened. A friction force Ff results between plates in contact. In this

phase, when loading, no relative displacement is noticed until the load F reaches

the friction limit Ff (Fig. 4.49).

F

F/2

F/2

bearing pressure

model used for the stress distribution

real stress distribution

shear force


127

Fig. 4.49. Typical load – deformation curve for a usual “bearing type” connection

• Phase 2 When F = Ff, slipping of the joint begins under a force F practically

constant. Slipping stops when the contact shank – plates is realised.

• Phase 3 is characterized by an elastic behaviour, meaning that the

displacement ∆∆∆∆L is proportional to force F.

• Phase 4 is characterized by a plastic behaviour, i.e. large deformations occur for

a slight load increase and the joint fails at an ultimate value Fu.

Failure at the ultimate load can be one of the following:

1. collapse due to hole failure in bearing (Fig.4.50a);

2. collapse due to bolt failure in shear (Fig.4.50b);

3. collapse by shear failure of the connected plates (Fig.4.50c);

4. collapse by failure of plates in tension (Fig.4.50d).

( a ) ( b ) ( c ) ( d )

Fig. 4.50. Typical failure modes for a usual “bearing type” connection

Phase 1

Phase 2

Phase 3

Phase 4

F

Fu

Ff

ΔL = L – L0

F F F F

d e1

b F/2 F/2 F/2 F/2

Bearing failure of plate

Shear failure of bolt

Longitudinal shear

failure of plate

Plate failure in tension


128

1. Bearing failure of the plate (Fig.4. 50a). Plate failure is a result of the bearing

force produced at the contact between the bolt and the plates in connection. The

bearing resistance of the contact between the bolt and one plate is:

2M

ub1Rd,b

tdfkF

γα= ( 4.56 )

The bearing resistance of a connection with one bolt is:

2M

minub1

Rd,b

tdfkF

γ

α=

∑ ( 4.57 )

bg,p

ming,p

bg,pg,p

RtdN

RtdN

⋅⋅=

⋅⋅=

∑ ( 4.42 )

where:

d is the nominal diameter of the bolt;

t is the smallest thickness of plates in contact;

∑min

t is the minimum value of the sum of the thickness of the plates which tend

to go in the same direction;

αb is the smallest of αd ; u

ub

f

f or 1,0;

in the direction of load transfer:

- for end bolts: αd = 0

1

d3

e ; for inner bolts: αd =

4

1

d3

p

0

1 −

perpendicular to the direction of load transfer:

- for edge bolts: k1 is the smallest of 7,1d

e8,2

0

2 − or 2,5

- for inner bolts: k1 is the smallest of 7,1d

p4,1

0

2 − or 2,5

m

kbg,p

RR

γ⋅β= is the design strength calculated with:

• Rk – the characteristic strength of plates (= fy); • γm = 1,25 – partial safety factor of the material; • β = 2,0 usually.

2. Shear failure of the bolt (rivet) (Fig. 4.50b). The bolt fails in shear under a force

per shear plane equal to:


129

2M

ubvRd,v

AfF

γ⋅⋅α= ( 4.58 )

where the shear plane passes through the threaded portion of the bolt (A is the

tensile stress area of the bolt As):

- for strength grades 4.6, 5.6 and 8.8: αv = 0,6

- for strength grades 4.8, 5.8, 6.8 and 10.9: αv = 0,5

- where the shear plane passes through the unthreaded portion of the bolt (A is

the gross cross section of the bolt): αv = 0,6

In the case of rivets, the shear resistance per shear plane is:

2M

0urRd,v

Af6,0F

γ⋅⋅= ( 4.59 )

bf

2bfbp,f R

4d

RAN ⋅⋅π=⋅= ( 4.43 )

where: b

fR is the shear design resistance of the bolt

m

kbf

R6,0R

γ⋅=

• Rk – the characteristic resistance of the bolt; • γm = 1,25 – partial safety factor of the material;

Ab is the cross-section area of the bolt equal to:

• 4d

A2

b

⋅π= when the shear plane passes through the unthreaded part of

the bolt (d is the nominal diameter of the bolt);

• 4d

A20

b

⋅= π when the shear plane passes through the threaded part of the

bolt.

d89,02

dddd mn

0res ⋅≅+== (Fig. 4.40)

dn = diameter of the core of the shank; dm = average diameter; d = nominal diameter; dres = resistant diameter.

Fig. 4.40. Cross-section of the bolt and the resistant area [12] The design resistance in shear of a bolt or a rivet is:

Rd,vfRd,nv FnF ⋅= ( 4.60 )

where:

d dn dm dres


130

nf is the number of shear planes .

3. Longitudinal shear failure of plate (Fig. 4.50c) . The resistance against

longitudinal shear failure of the plate is:

2M

u01

3

ft

2

de

γ⋅⋅⋅

− ( 4.61 )

In order to avoid shear failure of plates, the following requirement should be satisfied:

ff1 NRt2d

e ≥⋅⋅

− ( 4.45 )

The minimum required edge distance e1 (Fig.4.39c) results from relation (4.61),

where Rf is the shear design strength of the material of the plate. The minimum

required edge distance e1 is generally given in codes (if eactual > e1 there is no

need to check the condition (4. 61)). Usually, it is greater than two times the

diameter of the hole.

4. Plate failure in tension (Fig. 4.50d). Generally, the elastic stress distribution

around a hole is the one given in figure 4.51a.

Fig. 4.51. Stress distribution around a hole

If the hole is assumed to be an ellipse it can be proved that the maximum stress

is given by the following relation:

+⋅σ=σca2

1avmax ( 4.62 )

where:

F F F

F/2 F/2 ( a ) ( b )

2c

2a

t

d

b

1 1

real distribution model distribution


131

σav – average stress in the plate;

a – half of the axis normal to the stress (Fig. 4.51a);

c – half of the axis along the stress (Fig. 4.51a).

In the special case of a circular hole, it results:

avmax 3 σ⋅=σ ( 4.63 )

yavmax fσ3σ ≤⋅= (for structural steel) ( 4.47 )

Based on the good plastic properties of structural steel, which is a fundamental

requirement in this case, the simplified distribution given in figure 4.51b is

accepted. The resistance against plate failure in tension is: This leads to the

following condition, according to the Romanian code STAS 10108/0–78 [7]:

( )2M

u0Rd,u

ftdb9,0N

γ⋅⋅−⋅= (EN 1993-1-1, rel. (6.7)) ( 4.64 )

( )0M

y0Rd,net

ftdbN

γ⋅⋅−= (EN 1993-1-1, rel. (6.8)) ( 4.65 )

( ) FRtdb ≥⋅⋅− ( 4.48 ) where:

b – width of the plate that is being checked (Fig. 4.51b);

d0 – diameter of the hole (Fig. 4.41b);

t – thickness of the plate that is being checked (Fig. 4.51b);

d – diameter of the hole (Fig. 4.41b); R – design strength of the material of the plate; F – axial force in the checked cross-section (1-1). Remark The uniform stresses distribution which is assumed in calculus when

checking an element is unfavourably affected by the presence of the hole.

4.3.3.5. Behaviour of bolts in tension and shear

When a bolt or a rivet is subjected to tension and shear, an interaction relation

must be used:

0,14,1 ,

,

,

, ≤+Rdt

Edt

Rdv

Edv

F

F

F

F ( 4.66 )

All the values of the resistance are summarized in the following table from EN 1993-

1-8 [14]:


132

Table 4.4. Design resistance for individual fasteners subjected to shear and/or

tension (EN 1993-1-8 [14] Tab. 3.4)

Failure mode Bolts Rivets

Shear resistance per shear plane

Fv,Rd = 2M

ubv Af

γα

- where the shear plane passes through the threaded portion of the bolt (A is the tensile stress area of the bolt As):

- for strength grades 4.6, 5.6 and 8.8: αv = 0,6

- for strength grades 4.8, 5.8, 6.8 and 10.9: αv = 0,5

- where the shear plane passes through the unthreaded portion of the bolt (A is the gross cross section of the bolt): αv = 0,6

Fv,Rd = 2

06,0

M

ur Af

γ

Bearing resistance 1), 2), 3) Fb,Rd = 2M

ub1 tdfk

γα

where αb is the smallest of αd ; u

ub

f

f or 1,0;

in the direction of load transfer:

- for end bolts: αd = 0

1

3d

e ; for inner bolts: αd =

4

1

3 0

1 −d

p

perpendicular to the direction of load transfer:

- for edge bolts: k1 is the smallest of 7,18,20

2 −d

e or 2,5

- for inner bolts: k1 is the smallest of 7,14,10

2 −d

p or 2,5

Tension resistance 2) Ft,Rd = 2

2

M

sub Afk

γ

where k2 = 0,63 for countersunk bolt, otherwise k2 = 0,9.

Ft,Rd = 2

06,0

M

ur Af

γ

Punching shear resistance

Bp,Rd = 0,6 π dm tp fu / γM2 No check needed

Combined shear and tension

0,14,1 ,

,

,

, ≤+Rdt

Edt

Rdv

Edv

F

F

F

F


133

1) The bearing resistance Fb,Rd for bolts

– in oversized holes is 0,8 times the bearing resistance for bolts in normal clearance holes.

– in slotted holes, where the longitudinal axis of the slotted hole is perpendicular to the direction of the force transfer, is 0,6 times the bearing resistance for bolts in round, normal clearance holes.

2) For countersunk bolt:

– the bearing resistance Fb,Rd should be based on a plate thickness t equal to the thickness of the connected plate minus half the depth of the countersinking.

– for the determination of the tension resistance Ft,Rd the angle and depth of countersinking should conform with .8 Reference Standards: Group 4, otherwise the tension resistance Ft,Rd should be adjusted accordingly.

3) When the load on a bolt is not parallel to the edge, the bearing resistance may be verified separately for the bolt load components parallel and normal to the end.

4.3.3.6. Behaviour of high strength bolts in slip connections

Tightening control refers to the pre-load force Fp,C to be induced in the shank

of the bolt by the twisting moment Mt applied to the nut. Codes generally accept an

empirical relation like the following one:

dF2,0M C,pt ⋅⋅= ( 4.67 )

between the pre-load force Fp,C and the applied twisting moment Mt, where d is the

diameter of the bolt. The preload force is:

sb,uC,p Af7,0F ⋅⋅= ( 4.68 )

The design slip resistance is (Fig. 4.52):

C,p3M

sRd,s F

nkF ⋅

γµ⋅⋅= ( 4.69 )

where:

n – number of friction surfaces;

ks – given in table 4.5 (EN 1993-1-8 [14] Tab. 3.6);

μ – slip factor given in EN 1993-1-8 [14] Tab. 3.7 and in EN 1090-2 [20] Tab. 18;

Table 18 – Classifications that may be assumed for friction surfaces ( EN 1090 – 2) Surface treatment Class Slip factor Surfaces blasted with shot or grit with loose rust removed, not pitted. A 0,50 Surfaces blasted with shot or grit: B 0,40 a) spray-metallized with a aluminium or zinc based product; b) with alkali-zinc silicate paint with a thickness of 50 µm to 80 µm Surfaces cleaned by wire-brushing or flame cleaning, with loose rust removed C 0,30 Surfaces as rolled D 0,20


134

Table 4.5. Values of ks [14] (EN 1993-1-8 [14] Tab. 3.6)

Description ks

Bolts in standard clearance holes. 1,0

Bolts in either oversized holes or short slotted holes with the axis of the slot perpendicular to the direction of load transfer.

0,85

Bolts in long slotted holes with the axis of the slot perpendicular to the direction of load transfer. 0,7

Bolts in either oversized holes or short slotted holes with the axis of the slot parallel to the direction of load transfer.

0,76

Bolts in long slotted holes with the axis of the slot parallel to the direction of load transfer. 0,63

Fig. 4.52. The basic principles of a slip connection

If a slip-resistant connection is subjected to an applied tensile force, Ft,Ed, in addition

to the shear force, Fv,Ed, depending on the category of the connection (Tab. 4.6) the

slip resistance force is:

for category B connections ser,3M

ser,Ed,tC,psRd,s

)F8,0F(nkF

γ−µ

= ( 4.70 )

for category C connections 3M

Ed,tC,psRd,s

)F8,0F(nkF

γ−µ

= ( 4.71 )

Based on the fact that the greater pressure is the greater the friction force is, in order to obtain a maximum capacity of the connection, a maximum pre-load force Nt needs to be applied. According to the Romanian code C133–82 [8], the pre-load force should be: cbt RAkN ⋅⋅= ( 4.50 ) where: k – behaviour factor; k = 0,8 for 8.8 bolt grade; k = 0,7 for 10.9 bolt grade;

Nf Nf

Nf/2

Nf/2

Nf/2

Nf/2

Nt

Nt

friction forces


135

Ab – area of the cross-section of the bolt in the threaded zone; it may be taken from tables or it may be calculated using the approximate formulae:

4d

A2s

b

⋅π= ( 4.51 )

d89,0ds ⋅≅ ( 4.52 ) d – nominal diameter of the bolt; Rc – yield strength of the bolt (fyb in table 4.2); The pre-load force Nt may be practically obtained by: • using a dynamometric wrench calibrating the required Mt; • turning-off the nut tightening (after the first snug tight, an additional turning is

applied, representing an amount of a complete turn i.e. 0,25 to 0,75 turn). An important friction appears between plates (Fig. 4.42) as a result of the tightening. Under these circumstances, the slip resistance of a pre-loaded bolt is [8]: tff NfnmN ⋅⋅⋅= ( 4.53 ) where: m – working condition factor (it has the meaning of a partial safety factor); m = 0,95 for static loading; m = 0,85 for dynamic loading; nf – number of friction (slip) interfaces; f – slip factor; according to [8] it generally may be considered as: f = 0,25 for cleaned surfaces without any brushing; f = 0,35 for brushed surfaces using wire brushes or for burnt surfaces; f = 0,50 for blasted surfaces; Nt – the pre-load force. The equation (4.53) shows that the slip resistance of a bolt increases when the pre-load force Nt increases. Following this, a higher strength bolt allows a higher slip resistance. It may be also noticed that the greater the slip factor f is the greater the slip resistance is. A treatment of the surfaces in contact improves friction. Figure 4.53 shows the general behaviour of a shear connection. It can be

noticed that the ultimate load Fu is the same for a given bolt and it corresponds to the

failure of a bearing type connection (which is produced by the lowest value between

the force that causes failure of the plates and the force that causes shear failure of

the bolt). The presence of the pre-load force Fp,C only increases the range of elastic

behaviour and it delays slipping but it has no practical influence on the ultimate

capacity of the connection.


136

Fig. 4.53. General behaviour of a shear connection

4.3.3.5. Design resistance of bolts according to STAS 10108/0–78 [7], C133–82 [8] 1. Bolts in tension connections

bibi,cap RAN ⋅= ( 4.54 )

where: Ab – area of the cross-section of the bolt (from table or using rel. (4.51)); b

iR – tension design strength of the bolt, as given in table 4.3.

2. Ordinary bolts in shear connections ( )p,fg,pf,cap N;NminN = ( 4.55 )

bg,p

ming,p RtdN ⋅⋅= ∑ ( 4.56 )

bfbp,f RAN ⋅= ( 4.57 )

where the terms are explained at relations (4.42) and (4.43) and values of the design strength are given in table 4.3.

3. High-strength bolts in slip connections tff NfnmN ⋅⋅⋅= ( 4.58 )

where the terms are explained at relation (4.53). 4. Bolts used in tension and shear connections

• Shear connections Apart from checks using relations (4.54) and (4.55) for the capable forces, an interaction check is needed. This check is based on the von Mises criterion.

ANL

=σ ( 4.59 )

ANT

=τ ( 4.60 )

normally tightened connection

partially pre-loaded slip connection

pre-loaded slip connection

F

Fu

Nf1

Nf2

ΔL


137

R3 22 ≤τ⋅+σ ( 4.61 ) where: NL – the force acting along the axis of the bolt; NT – the force acting normal to the axis of the bolt; A – area of the cross-section of the bolt; if shear occurs in the threaded zone of the shank the reduced area given by relation (4.51) shall be used. R – design strength of the steel grade of the bolt;

• Slip connections The force NL reduces the pre-load Nt and it unfavourably affects the capacity of the connection. The capable force is in this case:

( )Ltff NNfnmN −⋅⋅⋅= ( 4.62 )

Table 4.3. Design strength for bolts according to STAS 10108/0–78 [7] Design

strength [N/mm 2]

γm

Bolt grade Steel grade of plates 4.6 5.6 6.6*) OL37 OL44 OL52

Shear bfR 0,6 130 160 180 – – –

Bearing bg,pR 1,6 – – – 350 415 500

Tension biR 0,8 170 210 240 – – –

*) They are no longer in fabrication In order to avoid failure of plates between neighbour holes and to prevent corrosion between connected elements, codes usually give some limitations concerning the spacing of holes for bolts and rivets. In the Romanian code STAS 10108/0–78 [7], they are as follows (Fig. 4.45): ( )t12;d8mined3 00 ≤≤ ( 4.63 )

( )t8;d4mined2 010 ≤≤ ( 4.64 )

( )t8;d4mined5,1 020 ≤≤ ( 4.65 )

( )21 t;tmint = ( 4.66 ) where: d0 – diameter of the hole; e – spacing between centres of fasteners on any direction; e1 – end distance from the centre of a hole to the adjacent end of any part, measured parallel to the loading direction; e2 – edge distance from the centre of a fastener hole to the adjacent edge of any part, measured normally to the loading direction; t – minimum thickness of exterior plates.


138

Fig. 4.45. Spacing of holes

4.3.4. Categories of bolted connections according t o EN 1993-1-8 [14]

Table 4.6 shows a classification of bolted connections given in EN 1993-1-8

[14]:

Table 4.6. Categories of bolted connections (EN 1993-1-8 [14] Tab. 3.2)

Shear connections

Category Criteria Remarks

A bearing type

Fv,Ed ≤ Fv,Rd Fv,Ed ≤ Fb,Rd

No pre-loading required. Bolt classes from 4.6 to 10.9 may be used.

B slip-resistant at serviceability

Fv,Ed.ser≤Fs,Rd,ser Fv,Ed ≤ Fv,Rd Fv,Ed ≤ Fb,Rd

Preloaded 8.8 or 10.9 bolts should be used. No slip at serviceability limit state Surfaces treatment

C slip-resistant at

ultimate

Fv,Ed ≤ Fs,Rd Fv,Ed ≤ Fb,Rd

Fv,Ed ≤ Nnet,Rd

Preloaded 8.8 or 10.9 bolts should be used. No slip at ultimate limit state Surfaces treatment

Tension connections

D non-preloaded

Ft,Ed ≤ Ft,Rd Ft,Ed ≤ Bp,Rd

No pre-loading required Bolt classes from 4.6 to 10.9 may be used.

E Ft,Ed ≤ Ft,Rd Preloaded 8.8 or 10.9 bolts should be used.

e e e

e

t1

t2

e2

e2

e1 e1


139

preloaded Ft,Ed ≤ Bp,Rd No slip at ultimate limit state Surfaces treatment

4.3.5. Examples of calculation

4.3.5.1. General aspects

Checking a fastened connection generally consists of the following steps:

1. Establishing the design cross-section of the connection, that consists of points;

2. Reducing loads in the centre of gravity of the cross-section;

3. Establishing the load distribution on the cross-section;

4. Checking the most loaded fastener.

A force acting on any direction in the centre of gravity of the connection

uniformly distributes its effects on all fasteners in the connection. A moment acting in

the centre of gravity of the connection distributes its effects on each fastener

proportionally to the distance from that fastener to the centre of rotation. The first

three steps of the checking procedure are the same for all types of fastened

connections (rivets, bolted connections, slip connections). The influence of the type

of fastener appears only in the final step, when establishing the capable force.

4.3.5.2. Connection loaded only in its plane (Fig. 4.54)


140

Fig. 4.54. Fastener connection loaded only in its plane

The force produced in a fastener i by the moment M (Fig. 4.54) is proportional

to the displacement δi. This displacement is normal to the radius of the point, r i, and

it is proportional to that radius, considering a rotation θ.

irθδi ⋅= ( 4.72 )

As all fasteners are identical, they have the same stiffness K. The force Ni produced

by the moment in a fastener can be expressed as:

iii rKKF ⋅θ⋅=δ⋅= ( 4.73 )

The moment is resisted by all the fasteners in the connection:

∑=

⋅=n

1jjjEd rFM ( 4.74 )

where n is the number of fasteners in the connection.

Using relation (4.73) in relation (4.74), the following relations can be written:

∑=

⋅θ⋅=n

1j

2jEd rKM ( 4.75 )

∑=

=θ⋅n

1j

2j

Ed

r

MK ( 4.76 )

Following this, the force Fi produced by the moment in the fastener i is:

NEd

VEd MEd

z

x x x

z

design cross-section

ri

M,iF xN,iF x

M,iF

zV,iF

zM,iF


141

in

1j

2j

Edi r

r

MF ⋅=

∑=

( 4.77 )

Based on the following notations:

2i

2i

2i zxr += ( 4.78 )

i

ii

xM,i r

zFF ⋅= ( 4.79 )

i

ii

zM,i r

xFF ⋅= ( 4.80 )

it can easily be proved that:

( )∑

=

+⋅=

n

1j

2j

2j

iEd

xM,i

zx

zMF ( 4.81 )

( )∑

=

+⋅=

n

1j

2j

2j

iEd

zM,i

zx

xMF ( 4.82 )

( ) ( )2zM,i

2xM,ii FFF += ( 4.83 )

It is obvious that the most loaded fastener is the one situated at the greatest distance

from the centre of gravity of the connection.

For the problem in figure 4.54:

n

NF Edx

N,i = ( 4.84 )

n

VF Edz

V,i = ( 4.85 )

Based on relations (4.82), (4.83), (4.84) and (4.85), the resultant force in the most

loaded fastener is obtained for the maximum value of the distance r i:

( ) ( )2zM,i

zV,i

2xM,i

xN,imax,i FFFFF +++= ( 4.86 )

This force must be less than the design resistance capable force of the for individual

fastener:

• for category A shear connections (bearing type):

Rd,vEd,vmax,i FFF ≤= ( 4.87 )

Rd,bEd,vmax,i FFF ≤= ( 4.88 )

• for category B shear connections (slip-resistant at serviceability LS):


142

ser,Rd,sser,Ed,vmax,i FFF ≤= ( 4.89 )

Rd,vEd,vmax,i FFF ≤= ( 4.90 )


• for category C shear connections (slip-resistant at ultimate LS):

Rd,sEd,vmax,i FFF ≤= ( 4.92 )


Rd,netEd,vmax,i NFF ≤= ( 4.94 )

Depending on the type of fastener, Ncap may be calculated using relation (4.55) for

rivets and bolts in ordinary shear connections or relation (4.58) for high-strength

bolts in slip connections.

4.3.5.3. Connection loaded normally on its plane (Fig. 4.55)

The model accepted by the Romanian code STAS 10108/0–78 [7] assumes

the end-plate as infinitely rigid. A force acting on any direction in the centre of gravity

of the connection uniformly distributes its effects to all fasteners in the connection.

The model used for calculating the efforts produced by a bending moment M

resembles to the one used for a reinforced concrete cross-section. A moment

equation should be written by the centre of compressions (Fig. 4.47b):

∑=

⋅=n

1jjj rNM ( 4.83 )

Based on the infinite rigidity of the end plate assumption, efforts in each fastener are

proportional to the distance ei from that fastener to the neutral axis (Fig. 4.47b).

ieKNi ⋅= ( 4.84 )

where K is a constant.


143

Fig. 4.47. Fastener connection loaded normally on its plane

A force acting on any direction in the centre of gravity of the connection in

figure 4.55 uniformly distributes its effects to all fasteners in the connection. If a

support is attached on the column by welding right under the end-plate, than the

shear force VEd is transferred to the column by means of this support and no longer

loads the fasteners. The model used for calculating the efforts produced by a

bending moment MEd resembles to the one used for a reinforced concrete cross-

section. A moment equation is written about the centre of compression (Fig. 4.55b):

( a ) ( b ) ( c ) ( d ) ( e )

N

M T

ei ri

hi

x

z

xN,iN

zT,iN

xM,iN

( a ) ( b ) ( c ) ( d ) ( e )

hr

x NEd

MEd

VEd

xN,trF

zV,vrF

xM,trF

CM


144

Fig. 4.55. Fastener connection loaded normally on its plane

There are several possible failure modes of this connection and they must be taken

into account when checking the resistance:

• failure of the bolt in tension;

• failure of column flange in bending;

• failure of end-plate in bending;

• failure of column web in tension;

• failure of beam web in tension;

• failure of beam flange in compression;

• failure of column stiffener in compression.

The models used in EN 1993-1-8 [14] are based on the equivalent T-stub (Fig. 4.56).

Three possible failure modes of the T-stub are taken into account:

• Mode 1: Complete yielding of the flange (plastic hinges) (Fig. 4.57)

• Mode 2: Bolt failure with yielding of the flange (Fig. 4.58)

• Mode 3: Bolt failure (Fig. 4.59)

1 End bolt row adjacent to a stiffener 2 End bolt row 3 Inner bolt row 4 Bolt row adjacent to a stiffener

Fig. 4.56. The equivalent T-stub


145

Fig. 4.57. Mode 1: Complete yielding of the flange

Fig. 4.58. Mode 2: Bolt failure with yielding of the flange

Fig. 4.59. Bolt failure

Based on these models, considering several bolt-rows and bolt-groups, the capable

force Ftr,Rd on each row of bolts is established and the capable (resistant) bending

moment of the connection is calculated as:

Prying force Prying force

Prying force Prying force


146

∑=

⋅=n

1rrRd,trRd,j hFM ( 4.95 )

where hr is the distance from the bolt-row r to the centre of compression. The centre

of compression is considered to be in the centre of gravity of the compressed flange

of the beam. The distribution of forces on bolt-rows (Fig. 4.55(b)) is not a simple one.

The procedure is complicated and requires a lot of calculation.

In the following, a simplified procedure (not always a safe one) is presented,

as a first step in learning how to check such a connection and not as one to be used

in practice. This simplified approach presumes the end-plate (and the column flange)

as infinitely rigid.

These equations are hard to be handled, so a simplified approach is used: the

compression centre is on the same line with the rotation axis, which is situated on

the last line of fasteners (Fig. 4.47e). In this case:

iii her == ( 4.85 )

where h i is the distance from fastener i to the line of least tensioned fasteners (Fig.

4.47e). Under these circumstances, the force produced in a fastener i by the

moment MEd (Fig. 4.55e) is proportional to the fastener elongation Δl i. This

elongation is proportional to the distance hi, considering a rigid body rotation θ.

ii hθl ⋅=∆ ( 4.96 )

As all fasteners are identical, they have the same stiffness K. The tension force Ni

produced by the moment in a fastener can be expressed as:

iix

M,Ed,ti hKlKF ⋅θ⋅=∆⋅= ( 4.97 )

The moment is resisted by all the fasteners in the connection:

∑=

⋅=n

1jj

xM,Ed,tiEd hFM ( 4.98 )

where n is the number of fasteners in the connection. Replacing (4.97) in (4.98), it

can easily be proved that:

∑=

⋅θ⋅=n

1j

2Ed j

hKM ( 4.99 )

∑=

=θ⋅n

1j

2j

Ed

h

MK ( 4.100 )


147

Following this, the force Fti,Ed,M produced by the moment in the fastener i is (Fig.

4.55e):

in

1j

2j

Edx hh

MF

M,Ed,ti⋅=

∑=

( 4.101 )

and it has the maximum value for the maximum distance hi. The forces produced by

the axial force NEd (Fig. 4. 55c) and by the shear force VEd (Fig. 4.55d) are:

n

NF Edx

N,Ed,ti = ( 4.102 )

n

VF Edz

V,Ed,i = ( 4.103 )

When solving the problem in figure 4.55a, there are basically three groups of

checks that need to be done:

A. Check in the longitudinal direction of the fastener (Fig. 4.55c), (Fig. 4.55e):

xmaxM,Ed,ti

xN,Ed,timax,Ed,ti FFF += ( 4.104 )

Rd,tmax,Ed,ti FF ≤ ( 4.105 )

Rd,pmax,Ed,ti BF ≤ ( 4.106 )

where Ft,Rd and Bp,Rd are calculated using the relations given in table 4.4.

where Ncap is calculated using relation (4.54).

B. Check in the plane of the connection (Fig. 4.55d):

capzT,i NN ≤ ( 4.96 )

Rd,vz

V,Ed,v FF ≤ ( 4.107 )

Rd,bz

V,Ed,v FF ≤ ( 4.108 )

Rd,sz

V,Ed,v FF ≤ ( 4.109 )

where the transverse capable force Ncap is calculated using relation (4.55) for

rivets and bolts in ordinary shear connections. For high-strength bolts in slip

connections the following interaction checks apply. The relations (4.107),

(4.108), (4.109) are chosen depending on the corresponding situation in table

4.4.

C. Interaction check, depending on the type of fastener:


148

• Shear connections

A check based on the von Mises criterion is used. The normal stress σ and

the tangential stress τ are calculated in the shared cross-section of the

fastener. Relations (4.59), (4.60) and (4.61) are used. Relation (4.66) is used.

• Slip connections

The longitudinal force in the bolt reduces the pre-load Nt and it unfavourably

affects the capable force. The capable force is in this case:

( )[ ]xM,i

xN,itff NNNfnmN +−⋅⋅⋅= ( 4.97 )

Relation (4.70) or (4.71) is used, depending on whether it is a category B or

category C connection (Tab. 4.6).

If the end-plate stands on a support that is welded on the column, it is

considered that the shear force is directly transferred to this support and in-plane

checks are no longer necessary, as the fasteners do not carry this force.

When checking a spliced connection of a beam, efforts are distributed

between the flanges and the web connection proportionally to the stiffness

characteristic of the cross-section for that effort:

• the axial force – proportional to the area;

• the shear force – to the web (proportional to the shear area);

• the bending moment – proportional to second moment of the area.

Following this, the connection of the web and the connections of the flanges are

checked separately.

cap 4 2015

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