SKILLS_M09E_Trusses_Part1.pdf

SKILLS Project

October 2013

TRUSSES PART 1

Special features for the design of truss structures for single-storey buildings

Design procedure:

Global analysis

Verification of members

Verification of connections

3

LEARNING OUTCOMES

Introduction

Constructional details

Calculation

Preliminary design

Global analysis

Verification of members

Verification of members under compression (and bending)

Verification of members in tension (and bending)

Verification of connections

Bolted connections

Welded connections

Conclusion

4

LIST OF CONTENTS

INTRODUCTION

Definition:

A truss is essentially a triangulated system of (usually) straight interconnected structural elements.

The individual elements are connected at nodes; the connections are often assumed to be nominally pinned.

The external forces applied to the system and the reactions at the supports are generally applied at the nodes.

When all the members and applied forces are in a same plane, the system is a plane or 2D truss.

6

INTRODUCTION

7

INTRODUCTION

The principal force in each element is axial tension or compression.

Members under axial forces in a simple truss

When the connections at the nodes are stiff, secondary bending is introduced.

1 - Compression axial force 2 - Tension axial force

Use of trusses in single-storey buildings

To carry the roof load:

Gravity loads (self-weight, roofing and equipment, either on the roof or hung to the structure, snow loads);

Actions due to the wind (including uplift due to negative pressure).

To provide horizontal stability:

Wind girders at roof level, or at intermediate levels if required;

Vertical bracing in the side walls and/or in the gables.

8

INTRODUCTION

Types of general arrangement of the structure

of single-storey building

9

INTRODUCTION

Lateral stability provided by portal trusses; Longitudinal stability provided by transverse wind girder and vertical

cross bracings (blue); No longitudinal wind girder.

Portal frame arrangement



10

INTRODUCTION

Beam and column arrangement

Vertical trusses are simply supported by columns; Lateral stability provided by longitudinal wind girder and vertical

bracings in the gables (blue); Longitudinal stability provided by transverse wind girder and vertical

bracings (green).



11

INTRODUCTION

Saw tooth roof arrangement

Main beams are trusses (drawn in blue) with parallel chords; their span L is the long side of the column mesh;

Secondary beams (green) are trusses with a triangular shape and a shorter span A (distance between main trusses);

Members in red support the north oriented windows.

12

INTRODUCTION

Main types of trusses

In a Pratt truss, diagonal members are in tension for gravity loads. This type of truss is used where gravity loads are predominant.

In this truss diagonal members are in tension for uplift loads. This type of truss is used where uplift loads are predominant, such as open buildings.

In a Warren truss, diagonal members are alternatively in tension and in compression. This type of truss is also used for the horizontal truss of gantry/crane girders.

All these types of trusses can be used either in portal truss structures or in simple truss structures with long spans, range from 20m to 100m.

13

INTRODUCTION

Main types of trusses (continued)

There are two different types of X truss : if the diagonal members are designed to resist

compression, the X truss is the superposition of two Warren trusses.

if the resistance of the diagonal members in compression is ignored, the behaviour is the same as a Pratt truss.

This shape of truss is more commonly used for wind girders, where the diagonal members are very long.

It is possible to add secondary members in order to : create intermediate loading points; limit the buckling length of members in

compression (without influencing the global structural behaviour).

For any of the forms shown above, it is possible to provide either a single or a double slope to the upper chord of a roof supporting truss. This example shows a duo-pitch truss.

All these types of trusses can be used either in portal truss structures or in simple truss structures

14

INTRODUCTION

Main types of trusses (continued)

Single slope upper chord for these triangular trusses, part of a saw tooth roof.

This type of truss is more commonly used for the roof of houses and for smaller spans (range from 10 to 15 m).

This type of truss can be used for larger spans.

These trusses can be used as simply supported.

CONSTRUCTIONAL DETAILS

General geometry of truss for roof structure

Trusses generally give an economic solution for spans over 20 (25)m;

The ratio of span to truss depth should be in the range 10 to 15;

The inclination of the diagonal members in relation to the chords should be between 35 and 55;

Point loads should only be applied at nodes;

The orientation of the diagonal members should be such that the longest members are subject to tension (the shorter ones being subject to compression).

16


Section of the members

Sections should be symmetrical for bending out of the vertical plane of the truss;

For members in compression, the buckling resistance in the vertical plane of the truss should be similar to that out of the plane;

Example proposals for chords: IPE, HEA, HEB, Tees, hollow sections or a section made of 2 channels (UPE), or sections composed of two angles bolted on vertical gusset plates and intermediately battened;

Example proposals for internal members: single or two battened angles, hollow sections.

17


18


Types of connections

Truss connections

via gusset plates

directly to the chord

welded bolted

prefabricated in the workshop

Splices

site connections

bolted

with cover plates

with end plates

19


Chord continuity

The design of bolted connections of truss chord depend on the type of chord section to be connected.

Types of recommended connections:

When the chords are made of:

a single I or H, either of the connections can be used;

two double angle or channel sections, splice connections are generally used;

hollow sections end plate connections are generally used.

with end plates with splice plates

20


Connection of diagonals to chords

When the chords are made of double members (2L or 2UPE sections), common practice is to insert gusset plates (welded or bolted on the chords) between the two component members of the chord. The diagonals and posts are connected to the gussets, usually by bolting.

When the chords are made of IPE or HEA/HEB sections, the most common connection method is also to use a welded gusset plate on the chord. The gusset plate is attached to the flange when the section is upright (vertical web), and to the web when the section is flat (horizontal web).

Frame stability

Frame stability is provided by bracing in both orthogonal directions, and the truss is simply pinned to the supporting columns.

To realise a pinned connection, one of the chord members is redundant (1) and the connection of that redundant member to the column is usually allowed to slip in the direction of the axis of the chord.

In the longitudinal direction, stability is usually provided by vertical bracing.

21


Lateral stability

Truss

Cross bracing between trusses

22


Thick black dots: two consecutive trusses

Blue: the purlin which completes the bracing in the upper region

Green: the longitudinal element which closes the bracing in the lower region

Red: Vertical roof bracing

Lateral stability

The lateral stability of the top chords of trusses is usually provided by the purlins (and by one panel of bracing, as for portal frames) but where stressed skin design is permitted, it may provide the restraint without bracing.

Roof cladding acting as stressed skin in a rigid-framed truss roof

23


CALCULATION

25

CALCULATION GENERAL

DATA

CHOICE OF GLOBAL ANALYSIS

MEMBER RESISTANCE

VERIFICATION

CONNECTIONS RESISTANCE

VERIFICATION EN 1993-1-8

EN 1993-1-1

SLS VERIFICATION

Flowchart for the design of trusses

Contractual data:

Geometrical data Incidence of neighbouring

construction Obligations or restrictions

in choice of sections Nature and position of

permanent loads Nature and position of

imposed loads Stabilising role of

envelope

Regulatory data and Standards: Climatic loads EN 1991 Seismic loads EN 1998 Exploitation loads

26

CALCULATION PRELIMINARY DESIGN

Preliminary design steps

Determine the loading on the truss;

Determine a truss depth and layout of internal members;

Determine the forces in the chords and internal members, assuming the truss is pin-jointed throughout (using software or by simple manual methods);

Select the compression chord member;

Select the tension chord member;

Choose internal members, whilst ensuring the connections are not complicated;

Check truss deflections.

Calculation of forces in a pin-jointed truss

Simple manual methods

Resolving forces at joints

Taking moments around node D determines force CB


27

28


Selection of the compression chord member

The buckling resistance is based on the length between node points for in-plane buckling;

The out-of-plane buckling is based on the length between out-of-plane restraints usually the roof purlins or other members.

Selection of the tension chord member

The critical design case is likely to be an uplift case, when the lower chord is in compression;

The out-of-plane buckling is likely to be critical. It is common to provide a dedicated system of bracing at the level of the bottom chord, to provide restraint in the reversal load combination.

29

CALCULATION GLOBAL ANALYSIS

In reality, truss structures deviate from this theoretical behaviour and their global analysis involves consideration of the deviations.

In particular, the deviations include the occurrence of bending in the members (secondary moments), in addition to the axial forces, which can cause significant additional stresses in the members which make up the truss.

The deviations in design: the members which make up the truss are not usually articulated at their

original node and their end node;

the members are not always strictly aligned on their original and end nodes;

Loads are not always strictly applied to the nodes.

30


Modelling of a truss

A truss can even be modelled without its supporting columns when it is articulated to the columns;

If separate models are used, it may be necessary, in order to verify the resistance of certain elements, to combine the results of several analyses (example: the upper chord of a truss also serves as chord of the wind girder);

If a global 3D model is used, parasitic bending can be observed, which often only creates an illusory precision of the structural behaviour process. That is why 2D models are generally preferable.

Modelling of a truss

For trusses, the model is commonly represented as either:

Continuous chords (and therefore chord members rigidly connected at both ends);

Truss members (diagonals and verticals) pin jointed to the chords.


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Simplified global analysis

A triangulated beam, with a constant depth, can be equated to an I-beam. This equivalence is possible and provides a good approximation, for example, for a truss with parallel chords.

The global shear force Vglobal and the global bending moment Mglobal in the equivalent beam vary very little along a panel and can be equated with the mean values in the panel. Therefore the axial load can be assessed using the following expressions:

In the chords

In a diagonal


32

hMN /globalch

cos/globald VN

Simplified global analysis

An estimate can also be made for the deflection of the truss beam by calculating that for an equivalent beam, for the same loading. In order to do this, the classic approach is to use elementary beam theory, giving the equivalent beam a second moment of area equal to:

where:

Ach,i is the section area of the chord i

di is the distance from the centroid of both chords to the centroid of the chord i

In order to take into account global shear deformations, not dealt with in elementary formulae, a reduced modulus of elasticity is used.


33

2

1i

2iich, dAI

Secondary forces

There are bending moments and shear forces due to:

influence of chord rigidity

assumption of rigid truss connections

added to the axial loads in the members calculated assuming the nodes are pined (primary forces).

It is routine in design to use continuous chord members and to pin the truss members.


34

Influence of secondary forces

Transforming pinned connections into rigid nodes hardly leads to any modification to the axial forces in the members;

Bending of the member due to secondary bending moments only causes a slight variation in the distance between the ends of this member compared to the difference in length due to axial force;

The greater the stiffness of the chords (which are usually continuous), compared to the global stiffness of the truss beam, the bigger the moments developed in the chords => secondary bending should be taken into account in the chord design;

Comparing the trusses with rigid connections of diagonals to the pinned connections, the end moments are in the same range as the moments resulting from the self-weight of the diagonals => assumption of bi-hinged diagonals is acceptable.


35

Effect of clearance of deflection

When the connections between elements which make up a truss beam are bolted connections, with bolts in shear (category A in EN 1993-1-8), the clearance introduced into these connections can have a significant effect on displacement of the nodes.


36

The effect of slack under load


The deflection of a truss due to the slack can be evaluated by considering the effect of a unit load applied at mid span, using the Bertrand Fontviolant equation:

where:

N1,i is the axial force produced in the member i by a unit force applied at the point where the deflection is required

li is the length of the member i

Si is the section area of the member i

b is the number of the members with bolted connection(s)

is the variation in length of member i due to the slack recovery, equal to 4mm according to whether the chord is in compression or tension.


37

bi

1i i

iii1,ES

lFN

i

ii

ES

lF


It is therefore essential, where truss structures are concerned, to control the effect of connection slack on the displacements.

In order to do this, it is often necessary:

either to limit slack in category A connections: drilling at +1 mm, even +0,5 mm and using shear bolts on a smooth bolt shank (to limit the increase in slack by deformation) of the threads and pieces; or

to use fit bolts; or

to use preloaded bolts (category C connections); or

to use welded connections instead of bolted connections.


38

Modification of a truss for the passage of equipment

It frequently occurs that it is necessary to modify the form of a truss in order to allow equipment to pass (a large section duct for example).

Several solutions can be provided:

either to increase the passage area available by an eccentricity in the connection of one of the chords (case 1); or

break the straight form of a diagonal, by triangulating the breakage point (case 2).

Local modification of the truss due to the passage of duct


39

case 1 case 2

VERIFICATION OF MEMBERS

41

VERIFICATION OF MEMBERS UNDER COMPRESSION

The resistance of a member to compression is evaluated by taking into account the different modes of instability:

Local buckling of the section is controlled using section classification, and when necessary, effective section properties (class 4);

Buckling of the member is controlled by applying a reduction coefficient in the calculation of resistance (obtained from the slenderness of the member, which depends on the elastic critical force Ncr);

In most truss members, only flexural buckling of the compressed members in the plane and out of plane of the truss structure need to be evaluated.

42


Verification of the design resistance of the cross-section

for uniform compression

where:

for class 1, 2, 3 cross sections

for class 4 cross sections

NEd is the design value of the compression force

A is the area of a cross-section

Aeff is the effective area of a cross-section, according to EN 1993-1-5

fy - yield strength

M0 - partial factor for resistance of cross-sections whatever the class is

M0 = 1,00

1Rdc,

Ed N

N EN 1993-1-1 6.2.4(1)

EN 1993-1-1 6.2.4(2) 0M

y

Rdc,

AfN

M0

yeff

Rdc,

fAN

43


Verification of the design buckling resistance

of the compression member

where:



Nb,Rd the design buckling resistance of the compression member

the reduction factor for the relevant buckling mode

M1 partial factor for resistance of members

M1 = 1,00

1Rdb,

Ed N

N

EN 1993-1-1 6.3.1.1

1M

y

Rdb,

AfN

M1

yeff

Rdb,

fAN

44


Calculation of the reduction factor

where:

is the appropriate non-dimensional slenderness, determined from the relevant buckling curve

is an imperfection factor corresponding to the relevant buckling curve

11

22

EN 1993-1-1 6.3.1.2

])2,0(1[5,02

Buckling curve a0 a b c d

Imperfection factor 0,13 0,21 0,34 0,49 0,76

EN 1993-1-1 6.3.1.2

Table 6.1

Selection of the buckling curve for a cross-section

45


EN 1993-1-1 6.3.1.2 Table 6.2

46


Calculation of the appropriate non-dimensional slenderness



where:

Lcr is the buckling length in the buckling plane considered

i is the radius of gyration about the relevant axis, determined using the properties of the gross cross-section

EN 1993-1-1 6.3.1.2

1

cr

cr

y 1

i

L

N

Af

1

eff

cr

cr

yeff

A

A

i

L

N

fA

9,93y

1 f

E

y

235

f

47


Determination of the buckling length

where:

L is the in plane system length (distance between nodes)

Ls is the out of plane system length (segment between lateral supports)

EN 1993-1-1 Annex BB BB.1

CHORDS

in plane out of plane

I or H sections

other open sections

hollow sections

I or H sections

open sections

hollow sections

0,9L 1,0L 0,9L 1,0Ls 1,0Ls 0,9Ls

48


Determination of the buckling length

L is the system length (distance between nodes)

TRUSS MEMBERS

in plane (except angle sections) out of plane

appropriate fixity and end restraint

(with at least 2 bolts or by welding)

inappropriate end restraint (with 1 bolt)

all cases

0,9L 1,0L 1,0L

EN 1993-1-1 Annex BB BB.1

49


Angles as web members

Provided that the chords supply appropriate end restraint to web members of angles and the end connections of such web members supply appropriate fixity (at least 2 bolts if bolted), the eccentricities may be neglected and end fixities allowed for in the design of angles as web members in compression.

The effective slenderness ratio may be obtained as follows:

for buckling about v-v axis

for buckling about y-y axis

for buckling about z-z axis

where is as defined in EN 1993-1-1 6.3.1.2

When only one bolt is used for end connections of angle web members the eccentricity should be taken into account and the buckling length Lcr should be taken as equal to the system length L.

EN 1993-1-1 Annex BB BB.1.2

yyeff, 7,050,0

zeff,z 7,050,0

vveff, 7,035,0

50


Determination of the compression resistance of built-up members

It is quite common to make up members from a truss structure using two angles, or two channels (UPE);

It is not specified in EN 1993-1-1 Annex BB if the particular rule as for angle truss members also concerns members made up to two pairs of angles: by way of simplification, it is recommended that Lcr = 0,9L of the axis be retained;

In order to ensure that such built-up members will behave as sole members in the flexural buckling mode, the two components are connected by small battens.

1 - Batten 2 - Gusset

Members composed of two angles

51


Built-up members must be connected without slack;

The gap between the angles, and the thickness of the battens, should be the same as the thickness of the gusset to which the built-up member is connected;

The maximum spacing of the connections between members is limited by EN 1993-1-1 to 15imin (imin - the minimum radius of gyration of the isolated component). Otherwise a more complex verification needs to be carried out, by taking into account the shear stiffness of the composed member.

52

VERIFICATION OF MEMBERS UNDER COMPRESSION AND BENDING

Verification of the design resistance of the cross-section

for bending

where:

for class 1 or 2 cross sections



MEd is the design value of the bending moment

Wpl plastic section modulus respectively

Wel,min minimum elastic section modulus

Weff,min minimum effective section modulus

1Rdc,

Ed M

M EN 1993-1-1 6.2.5

0M

ypl

Rdpl,Rdc,

fWMM

0M

yminel,

Rdel,Rdc,

fWMM

0M

ymineff,

Rdc,

fWM

correspond to the fibre with the max. elastic stress

53


Bending and axial force

For class 1 or 2 cross sections:

MN,Rd is the design plastic moment resistance reduced due to the axial force NEd,

For cross-sections where bolt holes are not to be accounted for, the following approximations may be used for standard rolled I or H sections and for welded I or H sections with equal flanges:

but

for n a:

for n > a:

where: n = NEd/Npl,Rd a = (A-2btf)/A but a 0,5

For other cross-sections see EN 1993-1-1 6.2.9(5)

RdN,Ed MM

EN 1993-1-1 6.2.9

)5,01/()1(Rdy,pl,Rdy,N, anMM

Rdpl,z,RdN,z, MM Rdy,pl,Rdy,N, MM

2

Rdpl,z,RdN,z,1

1a

anMM

54


Bending and axial force

For class 3 or 4 cross sections:

x,Ed is the design value of the local longitudinal stress due to moment and axial force taking into account of bolt holes where relevant (see EN 1993-1-1 6.2.4 and 6.2.5);

For class 4 cross-sections x,Ed is calculated using the effective cross sections and following criterion should be met:

where:

eN is the shift of the relevant centroidal axis when the cross-section is subjected to compression only

M0

y

Edx,

f

EN 1993-1-1 6.2.9

1/// M0ymineff,z,

NzEdEdz,

M0yminy,eff,

NyEdEdy,

M0eff

Ed

fW

eNM

fW

eNM

fA

N

y

55

Verification of the design resistance of the cross-section for shear

in the absence of torsion and for plastic design:

For verifying the design elastic shear resistance:

or for I- or H-sections: if Af/Aw0,6

where: VEd is the design value of the shear force

Av is the shear area according to

S is the first moment of the area above examined point

I is the second moment of area of the whole cross section

t is the thickness at the examined point

Af is the area of one flange

Aw is the area of the web: Aw = hwtw hw, tw is the height and thickness of the web, respectively

1Rdc,

Ed V

VEN 1993-1-1 6.2.6

0,1)3/( 0My

Ed

f


0M

yv

Rdpl,Rdc,

)3/(

fAVV

EN 1993-1-1 6.2.6(3)

tI

SV

EdEd

wA

VEdEd

56

Influence of the shear force on the resistance of the cross-section under bending moment and axial force

Provided that VEd 0,5Vpl,Rd and hw/tw 72/ (for see or conservatively: = 1,0), no reduction of the resistances defined for bending and axial force in need be made.

Where VEd > 0,5Vpl,Rd the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength (1-)fy for the shear area, where:

EN 1993-1-1 6.2.10


EN 1993-1-1 6.2.9

EN 1993-1-5

2

Rdpl,

Ed 12

V

V

57

Verification of the buckling resistance of the member under compression and bending

where:

NEd, My,Ed and Mz,Ed are the design values of the compression force and the maximum moments about the y-y and z-z axis along the member, respectively

My,Ed, Mz,Ed are the moments due to the shift of the centroidal axis according to EN 1993-1-1 6.2.9.3 for class 4 sections

y and z are the reduction factors due to flexural buckling from 6.3.1

LT is the reduction factor due to lateral torsional buckling from 6.3.2

kyy, kyz, kzy, kzz are the interaction factors

EN 1993-1-1 6.3.3


1

M1

Rkz,

Edz,Edz,yz

M1

Rky,LT

Edy,Edy,

yy

M1

Rky

Ed

M

MMk

M

MMk

NN

1

M1

Rkz,

Edz,Edz,zz

M1

Rky,LT

Edy,Edy,

zy

M1

Rkz

Ed

M

MMk

M

MMk

NN

58

Values for NRk = fyAi, Mi,Rk = fyWi and Mi,Ed

The interaction factors kyy, kyz, kzy, kzz have been derived from two alternative approaches. Values of these factors may be obtained from EN 1993-1-1 Annex A (alternative method 1) or from EN 1993-1-1 Annex B (alternative method 2). The National Annex may give a choice from alternative method 1 or alternative method 2.

EN 1993-1-1 6.3.3


Class 1 2 3 4

Ai A A A Aeff

Wy Wpl,y Wpl,y Wel,y Weff,y

Wz Wpl,z Wpl,z Wel,z Weff,z

My,Ed 0 0 0 eN,yNEd

Mz,Ed 0 0 0 eN,zNEd

59

VERIFICATION OF MEMBERS IN TENSION

Verification of members in tension

where:

Nt,Rd - design tension resistance

For welded joints:

For bolted joints: according to connection type

Category A connections: Bearing type

Category B connections: Slip resistant at service limit state

Category C connections: Slip resistant at ultimate limit state

1Rdt,

Ed N

N

0M

yRdpl,Rdt,

AfNN

EN 1993-1-1 6.2.3

EN 1993-1-8 3.1.1(4)

60


Resistance of tension members with bolted connections

A particular feature is the existence of criteria which bring into play the net section of the member.

For sections with holes, for category A and B connections, the design tension resistance Nt,Rd:

In category C connections the design resistance Nt,Rd:

where:

A cross-sectional gross area

Anet net area of a cross section

M2 =1,25 - partial factor for resistance of cross-sections in tension to fracture

M2

unetRdu,

M0

y

Rdpl,

Rdt, 9,0min

fA

N

AfN

N

the design plastic resistance of the gross cross-section

the design ultimate resistance of the net cross-section at holes for fasteners

M0

ynet

Rdnet,Rdt,

fANN

EN 1993-1-1 6.2.3

0net tndAA t is the thickness of the leg

n is the number of vertically aligned holes

d0 is the diameter of the hole

with 1 bolt with 2 bolts with 3 or more bolts

61


M2

u02Rdu,

)5,0(0,2

ftdeN

M2

u2Rdu,

fAN net

M2

u3Rdu,

fAN net

EN 1993-1-8 3.10.3

Resistance of tension members with bolted connections Angles connected through one leg

A single angle in tension connected by a single row of bolts in one leg, may be treated as concentrically loaded over an effective net section for which the design ultimate resistance should be determined as:

where:

2 and 3 are reduction factors dependent on the pitch p1 Anet is the net area of the angle. For an unequal-leg angle connected by its smaller leg, Anet should be taken as equal to the net section area of an equivalent equal-leg angle of leg size equal to that of the smaller leg

fu is the ultimate tensile strength

Resistance of tension members with bolted connections Angles connected through one leg

For intermediate values of p1 the value of may be determined by linear interpolation

Similar consideration should also be given to other type of sections connected through outstands.

62


(a) 1 bolt

(b) 2 bolts

(c) 3 bolts

EN 1993-1-8 3.10.3

Pitch p1 2,5d0 5,0d0

2 bolts 2 0,4 0,7

3 bolts 3 0,5 0,7

EN 1993-1-8 3.10.3 Table 3.8

63

VERIFICATION OF MEMBERS IN TENSION AND BENDING

Verification of members in tension and bending

where:

Nt,Rd - design tension resistance

Mc,Rd - design moment resistance considering fastener holes

Consideration of fastener holes in the design moment resistance

Fastener holes in the tension flange may be ignored provided that for the tension flange:

where: Af is the area of tension flange

Fastener holes in tension zone of the web need not be allowed for, provided that the above limit given is satisfied for the complete tension zone comprising the tension flange plus the tension zone of the web

1Rd,

Ed

Rdt,

Ed cM

M

N

N EN 1993-1-1 6.2.1(7) EN 1993-1-1 6.2.3

EN 1993-1-1 6.2.5

M0

yf

M2

unetf, 9,0

fAfA

VERIFICATION OF CONNECTIONS

65

VERIFICATION OF CONNECTIONS - BOLTED CONNECTIONS

Categories of bolted connections

Category Criteria Remarks

Shear connections

A bearing type Fv,Ed Fv,Rd

Fv,Ed Fb,Rd

No preloading required. Bolt classes from 4.6 to 10.9 may be used.

B slip resistance at SLS Fv,Ed,ser Fs,Rd,ser

Fv,Ed Fv,Rd Fv,Ed Fb,Rd

Preloaded 8.8 or 10.9 bolts should be used. For slip resistance at serviceability see EN 1993-1-8 3.9.

C slip resistance at ULS Fv,Ed Fs,Rd

Fv,Ed Fb,Rd

Fv,Ed Nnet,Rd

Preloaded 8.8 or 10.9 bolts should be used. For slip resistance at ultimate see EN 1993-1-8 3.9; Nnet,Rd see EN 1993-1-1.

Tension connections

D non-preloaded Ft,Ed Ft,Rd

Ft,Ed Bp,Rd

No preloading required. Bolt classes from 4.6 to 10.9 may be used.

E preloaded Ft,Ed Ft,Rd

Ft,Ed Bp,Rd

Preloaded 8.8 or 10.9 bolts should be used.

EN 1993-1-8 Table 3.2

66


Design resistances of individual bolts subjected to shear

Fv,Rd - Shear resistance per shear plane

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

- v = 0,6 for classes 4.6, 5.6. 8.8

- v = 0,5 for classes 4.8, 5.8. 10.9

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

Fb,Rd Bearing resistance

M2

ubvRdv,

AfF

M2

ub1Rdb,

dtfkF

5,2;7,18,2;7,14,1min

0

2

0

21

d

e

d

pk

0,1;;

3min

0

1b

u

ub

f

f

d

e

for end bolts

for inner bolts

0,1;;

4

1

3min

0

1b

u

ub

f

f

d

p

5,2;7,14,1min

0

21

d

pk

67


Symbols for end and edge distances and spacing of bolts

Staggered spacing - compression 1 outer row, 2 inner row Spacing in tension members mm200,14min2,2 10 tpd

mm200,14min4,2 20 tpd

mm200

14min0,1

tp

mm400

28mini,1

tp

125mm or 8t

mm4042,1

2

1

0

t

e

ed

For structures made of steels confirming to EN 10025 except steels confirming to EN 10025-5

For structures made of steels confirming to EN 10025-5

Design for block tearing

Block tearing consists of failure in shear at the row of bolts along the shear face of the hole group accompanied by tensile rupture along the line of bolt holes on the tension face of the bolt group.

For a symmetric bolt group subject to concentric loading the design block tearing resistance:

For a bolt group subject to eccentric loading the design block shear tearing resistance:

68


1 small tension force 2 large shear force 3 small shear force 4 large tension force Ant is net area subjected to tension Anv is net area subjected to shear

M0nvyM2ntuRdeff,1,Ed /3/1/ AfAfVV

M0nvyM2ntuRdeff,2,Ed /3/1/5,0 AfAfVV

69


Design resistances of individual bolts subjected to tension

Bp,Rd punching shear resistance

where: dm is the mean of the across points and across flats dimensions of the bolt head or the nut, whichever is smaller,

tp is the thickness of the plate under the bolt or the nut;

Ft,Rd tension resistance

where: k2 = 0,63 for countersunk bolts otherwise k2 = 0,9.

Combined shear and tension

M2upmRdp, /6,0 ftdB

M2

ub2Rdt,

sAfkF

0,14,1 Rdt,

Edt,

Rdv,

Edv, F

F

F

F

70


Design slip resistance

where:

n is the number of the friction surfaces

Fp,C is the preloading force

is the slip factor

ks is the factor from

M3 =1,25 - partial factor for slip resistance

subp,C 7,0 AfF

p,C

M3

sRds, F

nkF

EN 1993-1-8 Table 3.7

EN 1993-1-1 3.9.1

Class of friction surfaces

(see EN 1090)

Slip factor

A 0,5

B 0,4

C 0,3

D 0,2

Description ks

Bolts in normal holes 1,0

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

0,85

Bolts in long slotted holes with axis of the slot perpendicular to the direction of load transfer

0,7

Bolts in short slotted holes with axis of the slot parallel to the direction of load transfer

0,76

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

EN 1993-1-8 Table 3.6

71

VERIFICATION OF CONNECTIONS - WELDED CONNECTIONS

Design resistance of fillet welds

A uniform distribution of stress is assumed on the throat section of the weld, leading to the normal stresses and shear stresses:

is the normal stress to the throat plane

is the shear stress perpendicular to the axis of the weld

is the shear stress parallel to the axis of the weld

The normal stress parallel to the axis is not considered when verifying the design resistance of the weld.

The design resistance of the fillet weld is sufficient if the following conditions are both fulfilled:

and

where: w is the appropriate correlation factor from

M2wu2II22w /3 f

EN 1993-1-8 4.5.3.2(6)

EN 1993-1-8 Table 4.1

M2u /9,0 f

72

VERIFICATION OF CONNECTIONS - WELDED CONNECTIONS

EN 1993-1-8 Table 4.1

CONCLUSION

The use of the truss form of construction allows buildings of all sizes and shapes to be constructed.

This presentation provides guidance on the design of trusses for single-storey buildings including issues connected with constructional details, global analysis as well as verification of members (chords and truss members: posts and diagonals) and connections (splices, truss member to chord connections).

74

CONCLUSION

REFERENCES

EN 1993-1-1 Eurocode 3 Design of steel structures Part 1-1: General rules and rules for buildings

EN 1993-1-8 Eurocode 3 Design of steel structures Part 1-8: Design of joints.

76

REFERENCES

SKILLS training modules have been developed by a consortium of organisations whose logos appear at the bottom of this slide. The material is under a creative commons license

The project was funded with support from the European Commission. This module reflects only the views of the

authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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