cap 4 2015
DESCRIPTION
Steel, Bogdan StefanescuTRANSCRIPT
4. CONNECTING DEVICES
92
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
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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
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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
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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
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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:
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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
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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”
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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
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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.
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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
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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
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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
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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
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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*
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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
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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
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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
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• 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
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• 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
4. CONNECTING DEVICES
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.
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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).
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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:
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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:
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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]:
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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.
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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.
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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)
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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):
4. CONNECTING DEVICES
142
ser,Rd,sser,Ed,vmax,i FFF ≤= ( 4.89 )
Rd,vEd,vmax,i FFF ≤= ( 4.90 )
Rd,bEd,vmax,i FFF ≤= ( 4.91 )
• for category C shear connections (slip-resistant at ultimate LS):
Rd,sEd,vmax,i FFF ≤= ( 4.92 )
Rd,bEd,vmax,i FFF ≤= ( 4.93 )
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.
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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
4. CONNECTING DEVICES
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 )
4. CONNECTING DEVICES
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:
4. CONNECTING DEVICES
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.