PD6695-2

C Hendy, D Iles, S Chakrabarti page 1

EN1993-2: PD 6695-2: RECOMMENDATIONS FOR THE DESIGN OF STEEL BRIDGES C Hendy, Atkins, London, UK D Iles, The Steel Construction Institute, Ascot, UK S Chakrabarti, consultant, London, UK

Abstract The paper presents the background to the development of the provisions of PD 6695-2:2008

Recommendations for the design of bridges to BS EN 1993. That Published Document was

prepared with the objectives of providing information on topics not covered by BS EN 1993-2

and offering guidance where it was considered further explanation of the Eurocode provisions

was desirable for their correct and consistent application. It explains that the main sources of

this material were BS 5400-3 and Designers Guide to EN 1993-2, Eurocode 3: Design of steel structures. Part 2: Steel bridges.

Introduction The objective of this paper is to give the background to the development of the provisions of

PD 6695-2:2008 Recommendations for the design of bridges to BS EN 1993. The Published

Document was prepared by B525/10 Working Group 3 and is referred to in the National

Annex to BS EN 1993-2 as a source of NCCI. The PD was written with two primary

objectives in mind:

(i) Provision of information on topics not covered by EN 1993. (ii) Provision of guidance where it was considered further explanation of the Eurocode

provisions was desirable for their correct and consistent application.

The first objective was the subject of debate during drafting because the principle-based

approach used in the Eurocodes, together with the wide range of analysis techniques

permitted, combine to ensure that it is usually possible to design all elements of a bridge

utilising the Eurocode methodologies without further information, if a sufficiently powerful

analysis model is used. However, the drafters of the PD considered it undesirable to require

an increase in the level of complexity of analysis over and above that used in previous

practice, although the flexibility to permit such analysis was considered to be beneficial. The

material included to meet (i) is therefore usually in the form of design rules that can be

applied by hand methods of calculation with a similar level of complexity as required by

previous practice to BS5400. Much of the PD draws on recommendations in BS 5400-3,

where they are non contradictory, as they are perceived by many to be more user friendly than

Eurocodes. Clarification of Eurocode provisions also draws on guidance in Reference 2.

The paper deals with each principal PD clause in turn and provides explanation for the

recommendations given. References to clauses in EN 1993-2 have been abbreviated below.

For example, 3-2/6.3.4.2(5) is a reference to clause 6.3.4.2(5) of EN 1993-2. The PD clause

mndiayeRectangle


numbers are given in parenthesis in each heading. It should be noted that the clause

numbering in the PD does not follow that in EN 1993-2.

Global analysis (4)

Joint modelling (4.2) The statement that semi-rigid (or semi-continuous joints as termed in EN 1993-1-8) should

not be used for bridge structures has been included because such details are difficult to assess

for fatigue performance, are likely to have relatively short life and are not included in the

various detail categories of EN 1993-1-9.

Truss connections (4.3) The recommendations given for the considerations of truss connections in global analysis

have been imported from the requirements in BS 5400-3[1]

. They essentially assume that joint

moments arising purely from joint stiffness and compatibility are shed at ULS, as was

previous practice. This is in line with EN 1993-1-8 provisions.

Main beam splices and bracing member connections (cl 4.4) According to 3-1-1/5.2.1(6), bolt slip needs to be included in analysis where it is significant

but no specific guidance is given in EN 1993-2. The PD therefore provides guidance.

The PD requires that bolt slip should be taken into account at the connections of bracing

systems because a sudden loss of stiffness arising from bolt slip leads to an increase in

deflection of the main member and an increased force on the bracing member, which could

lead to overall failure. Ideally, connections of bracing members should be designed as non-

slip at ULS (Category C to EN 1993-1-8) to avoid the need to evaluate the effects of slip.

The PD permits bolt slip at main beam splices to be ignored in global analysis. It has been

UK practice to design splice bolts to slip at ULS (Category B to EN 1993-1-8) without

consideration of slip in global analysis. This is justifiable as, although slip could alter the

moment distribution in the beam, splices are usually positioned near to points of contraflexure

and therefore slip will not shed significant moment to either adjacent hog or sag zones. Also,

the loading that gives maximum moment at the splice will not be fully coexistent with that for

either the maximum hogging moment or maximum sagging moment in adjacent regions.

Corresponding recommendations are given in clause 19 of the PD for the design of the

connections.

Imperfections (cl 4.5) The PD introduces a recommendation that imperfections in common planarity of bearings

should be allowed for in the analysis of torsional moments and reactions for torsionally stiff


superstructures. Whilst such imperfections are permitted by the tolerances in EN1090-2,

there is no explicit requirement for their consideration in design in EN 1993-2. It is however

necessary because if the structure is stiff (for example a box girder with rigid diaphragms at

supports) then an error in level of the bearings could induce significant torsion in the structure

and an uneven load distribution on the bearings. This is primarily a problem at SLS but it

could also trigger failure at ULS if there is inadequate ductility in the system (including

bearings and supporting structures). The recommendations are consistent with the approach in

BS 5400-3.

The PD also clarifies how to treat forces from imperfections in bracing systems comprising

both torsional restraints and plan bracing. Where the restraint forces are to be transmitted to

end supports by a system of plan bracing, the plan bracing system should be designed to resist

the more onerous of the forces EdF from each restraint within a length equal to the half

wavelength of buckling and the forces generated by an overall flange bow in each flange

according to clause 5.3.3 of EN 1993-1-1. In the latter case, for a very stiff bracing system

with zero first order transverse deflection, each flange applies a total force of mEd

.

N

562

uniformly distributed to the plan bracing, where m is the reduction factor for the number of

interconnected beams in BS EN 1993-1-1 clause 5.3.3(1).

Non-dimensional Slenderness for Beams With Different Restraints (cl 5 to 8) The basic definition of slenderness for lateral torsional buckling in 3-1-1/6.3.2.2 requires

calculation of the elastic critical buckling moment, Mcr. Formulae for the elastic critical

moment are not provided so the designer must find a way of determining this value. To do

this, there are three basic means: refer to theoretical texts; determine a value directly from an

elastic finite element model; use empirical formulae. It is not realistic to expect to find a

suitable formula for crM from a text book; real bridge problems are too complex so the other

methods must be considered.

It is becoming increasingly easy to calculate crM directly from a computer elastic critical

buckling analysis, using a shell finite element model, and many engineers will find this the

quickest and most accurate method. Some experience is required however to determine crM

from the output as often the first buckling mode observed does not correspond to the required

global buckling mode; there may be many local plate buckling modes for the web and flanges

before the first global mode is found.

To avoid the need for computer analysis, it was decided to provide empirical rules in the PD

that enable calculation of the slenderness for lateral torsional buckling without explicit

calculation of crM . The rules have been adapted from those in BS 5400-3 and take advantage

of the fact that for a Class 1 or 2 cross section

E

f

2

yLTLT


and for a beam with Class 3 or 4 cross section

Rkpl,

Rkel,

2

yLTLT

M

M

E

f

where LT is the slenderness in BS 5400-3. Derivation of this equivalence is given in reference 2. Clauses 5 to 8 effectively import the rules from BS 5400-3 clause 9.7, covering

situations without effective intermediate restraints, with effective intermediate restraints and

with flexible intermediate restraints, transcribed into Eurocode terminology. These rules

derive a value of slenderness from evaluation of effective length, which is a concept that is not needed when deriving Mcr from a theoretical analysis or from an elastic buckling analysis.

There is a semi-empirical approach to the determination of slenderness based on the use of the

general method in 3-2/6.3.4.2. See further discussion below in relation to clause 9 of the PD.

The general method cannot be used for cases where only torsional bracing is provided (e.g.

paired beams during construction of the deck slab); in such cases, either the rules in PD clause

8 should be followed or Mcr determined from elastic critical buckling analysis.

Simplified Method for Verification of Lateral Buckling of Truss Chords and Flanges in Compression (9) When an empirical approach is taken, rather than an FE analysis, the complexity of the PD

formulae in clauses 5 to 8 mean it will often be preferable to use the simple compression

chord model of 3-2/6.3.4.2. This is particularly applicable for U-frame bridges or completed

steel and concrete composite bridges with a deck slab and with or without intermediate

bracings in the span. The simplified method in 3-2/6.3.4.2 is intended for use for beams where one flange is held in

position laterally. The method is based on representing lateral torsional buckling (actually

lateral distortional buckling, since one flange is assumed to be held in position) by lateral

buckling of the compression flange. The method is primarily intended for U-frame type

bridges but can be used for other flexible bracing systems as well. It can also be applied to

lengths of girder compression flange between rigid restraints, as found in hogging zones in

steel and concrete composite construction. For this method, the St Venant torsional stiffness

of the beam is ignored. This simplification may be significantly conservative for shallow

rolled steel sections but is generally not significant for most fabricated bridge girders.

The PD includes guidance on two aspects not covered by EN 1993-2. First, the expressions

for U-frame stiffness in 3-2/Annex D do not contain a contribution from the flexibility of the

joints between U-frame members. The PD offers suggested values of joint flexibility, in the

absences of specific calculation. The values have been imported from BS 5400-3 (and are

based on research by British Railways in the 1960s) and are acknowledged to be fairly

conservative. Second, the expression for Ncr = mNE in 3-2/6.3.4.2(6) requires there to be rigid

bracings at supports. In conventional U-frame decks, the end U-frames are normally not

sufficiently stiff to be classed as rigid and hence an alternative expression for Ncr is required.

The PD therefore provides a modified expression for m in this case. The expression has been


derived from coefficients provided in BS 5400-3 (which were derived from consideration of

beam on elastic foundation theory) which fulfilled the same purpose.

Restraints at Supports Effects Due to Restraint of Main Beams (10) Bracing providing torsional restraint at supports experience forces arising from imperfections

such as lack of verticality of beams, lack of straightness in the flanges and bearing

eccentricity. The PD provides simplified guidance on the design of torsional restraints at

supports because EN 1993-1-1 only covers the subject indirectly through second order

analysis of the main beams and bracing system with modelled imperfections. EN 1993-2

provides little guidance on this analysis although flange bow and lack of verticality

imperfections are covered by 3-1-1/5.3.3 and would therefore allow a suitable analysis to be

carried out. The rules provided derive from previous UK practice through BS 5400-3. Further

commentary on this is given in reference 3.

Intermediate Restraints Effects Due to Restraint of Main Beams (cl. 11) Clause 11 of PD 6695-2 is intended as a clarification of the 3-2/6.3.4.2(5) requirements for

design forces for intermediate bracings see also the comments made in relation to PD clause 4.2 above. The expression for FEd in 3-2/6.3.4.2 does not cover torsional restraints without

the presence of plan bracing, so the PD provides additional expressions to cover this situation.

They are needed for the design of paired beams during construction. The formulae provided

have been brought in from BS 5400-3, with modifications to notation to suit the Eurocode

format.

The remainder of clause 11 treats the additional forces generated in U-frame bridges

(including the flanges) by local loading on the cross girders. Loading on a transverse member

will cause that transverse member to deflect and rotate at its connection to the vertical

stiffener. The stiffener will therefore try to deflect inwards. If all cross girders are not loaded

similarly, the tendency is to produce differential deflections at the tops of the stiffeners but

this differential deflection is resisted by the flanges in transverse bending. A transverse force

is therefore generated at the top of the stiffener and a moment My is produced in the flange.

Simplified expressions for the force, Fc, and moment, My, are provided in the PD. They have

been imported from BS 5400-3 and further background on their origins can be found in

reference 3.

The method provided in the PD is simple to carry out but can give conservative results.

Second order analysis carried out on a suitable 3-D model will produce more accurate results.

Further guidance and background on this approach is given in reference 2.


Buckling Resistance of Plates With Out of Plane Loading (cl 12) Where there is out of plane loading on a plate, as occurs for example in a longitudinally

stiffened deck plate subjected to traffic loading, 3-2/6.5 can be used but it is far from

comprehensive. The PD therefore provides two alternative methods of analysis; one in clause

12.2 based on the effective section method in 3-1-5/4 and one in clause 12.3 based on the

reduced stress method of 3-1-5/10. In both cases, the rules have been set out so that as the

transverse loading reduces to zero, the same result is obtained as would be derived from the

use of the expressions in EN 1993-1-5 for in-plane loading alone. The expressions originate

from reference 2.

The method in clause 12.2 is similar to that proposed in EN 1993-1-7 but ensures

compatibility with EN 1993-1-5 which EN 1993-1-7 does not achieve. EN 1993-2 does not

reference EN 1993-1-7.

The UKs decision on the use of 3-1-5/4 and 3-1-5/10 is discussed in the paper on the NA to EN 1993-1-5.

Generally the effective section method will be the more economic and thus the use of clause

12.2 will generally be the more economic when transverse load is present.

The reduced stress method provided in clause 12.3 has some limitations, notably that the

minimum load amplifier cr (in 3-1-5/10) can legitimately be less than 1.0 due to the post-

buckling reserve of plates, whereupon the amplification factor, ( )/11/(1 cr ) in PD clause

12.3 will become negative and the expressions become invalid. They will in any case become

very conservative as cr approaches 1.0. This method is therefore not recommended unless

the criteria for the use of 3-1-5/4 cannot be met.

Resistance of Members With Flanges Curved Out of Plane (cl. 13) No guidance is given in EN 1993-1-1 on the design of beams with flanges continuously

curved in elevation, mainly because it involves out of plane bending in plate panels, which is

not explicitly covered by either EN 1993-2 or EN 1993-1-5. EN 1993-1-7 covers transverse

loading (not curved beams specifically) but is not fully applicable to bridge members as

discussed under clause 12 above.

Beams with vertical curvature develop out of plane bending moments in the flanges as shown

in Figure 1. For I beams, this flange transverse bending is sometimes referred to as flange curling. PD 6695-2 provides methods for calculating the stresses from curvature (similar to the rules in BS 5400-3) and then for combining them with other effects and verifying the

section; reference is made back to section 12 for the latter purpose. For beams with

longitudinal flange stiffeners, the main out of plane bending effect in the flanges is

longitudinally between transverse restraints. Two options are provided in the PD to account

for this. Either the effects from curvature can be represented by a transverse load or the

curvature can be modelled as in increased imperfection in the stiffener which is included via

the term . The expressions originate from reference 2.


Figure 1. Forces and moments from flange curvature

Design of Flanges and Webs With Large Openings (14) Clause 14 of PD 6695-2 has been added in order to ensure that openings in webs and flanges

do not compromise post-buckling strength and fatigue performance and that designers

consider secondary stresses that develop around openings. The principal recommendation

here is that if the dimensional limits do not satisfy those in 3-1-5/2.3(1), the hole must be

framed by stiffening and the surrounding area designed for secondary bending effects. This

addresses the issue that large unstiffened edges of plates significantly reduce the post buckling

strength and ductility of the section which could compromise the adequacy of many of the

rules in EN 1993-1-5 which assume that such post-buckling strength is available.

a) Radial force from curved flange

b) Transverse moments

in outstand flange

c) Transverse moments in

internal flange

c

b

fF

fF

TP


Design of Intermediate Transverse Web Stiffeners (15) Intermediate transverse web stiffeners are designed to 3-1-5/9. However, the clauses give

only a description of the required performance of the stiffeners, which must satisfy a

maximum deflection requirement and must not yield under all the design effects including

second order effects. Also, EN 1993-1-5 does not provide a list of all the effects to consider

acting on the stiffener, as was provided in BS5400-3.

To rectify the latter omission, the PD imports the list of effects listed for transverse stiffeners

in BS 5400-3. It should be noted that this may not be an exhaustive list for all situations,

which was the main reason for not including a list in EN 1993-1-5. For the strength and

stiffness design, it had been intended to include formulae in the PD for calculating the

deflections and stresses incorporating second order effects; paragraph a) in clause 15 of the

PD refers to this intention. These formulae however were inadvertently omitted from the

published version of the PD. They can be found in reference 2.

Design of Bearing Stiffeners (16) The design of bearing stiffeners is also carried out according to 3-1-5/9. As for intermediate

transverse stiffeners, the guidance provided in EN 1993-1-5 is much less comprehensive than

the equivalent in BS 5400-3. As a result, the PD includes the following additional material,

mostly imported from BS 5400-3:

(i) List of effects to consider in the design of stiffeners (ii) Recommendations for bearing eccentricity values for different types of bearings (iii)General detailing recommendations.

One important effect within (i) which was not imported from BS 5400-3 is the formula for

web membrane force, NH, which must be considered for the design of bearing stiffeners acting

as rigid end posts. Reference 2 shows that the membrane force is given by:

02.1/2.1/

2

cr

cr

wwH thN

where hw and tw are the height and thickness of the web panel respectively, cr is the elastic critical shear stress for the web panel and is the shear stress. This formula has been derived from the assumptions underpinning the rotated stress theory used in shear design.

As with clause 15, for strength and stiffness design, it had been intended to include formulae

for calculating the deflections and stresses incorporating second order effects but they also

have inadvertently been omitted from the published version of the PD. They can be found in

reference 2.

Connections Design of Beam Splices (cl 17) Splices in bridges are not explicitly covered by BS EN 1993-1-8, though general rules on the

design of groups of bolts are provided. The additional guidance provided in the PD has, in the

main, been imported from BS 5400-3 and has been included to bring a consistent approach to


the design of splices. Of particular note are to the provisions of PD clause 17.5.4 which sets

out how the forces and moments in each component part of a web splice should be derived

from the overall moment, shear and axial force.

The specification of the Von Mises yield criterion in PD clause 17.4.2 as the means of

verifying spliced plates and cover plates is also made for compatibility with existing practice

to BS 5400-3. The PD recommedation is the same as the yield criterion is referred to in 3-1-

1/6.2.1 as a general verification where no other rule is givenI.

Connections Design of Gusset Plates (18) Gusset plates are also not explicitly covered by BS EN 1993-1-8. Therefore guidance has

been provided on the proportioning and verification of gusset plates to promote consistency.

The detailing rules are based on design guidance previously provided in BS 5400-3 and the

strength criterion is based on the Von Mises yield criterion, as discussed under clause 17

above.

Bolted Connections (19) The guidance provided in this clause of PD 6695-2 is based on the same assumptions as

outlined under clause 4.3 above.

Welded Connections (20) Welded connections are extensively covered by EN 1993-1-8 but some additional non-

contradictory recommendations were imported to the PD from BS 5400-3. The main

recommendations are:

that, for the fatigue design of welds connecting two parts in contact, all the force should be assumed to pass through the welds. This is because although at ULS the

welds will deform as required to ensure that the two parts are in full contact (and thus

the force can be transmitted in bearing), this condition cannot be assumed for fatigue

because it cannot be assumed that the SLS loading has been exceeded, which would be

necessary to bring the parts into full contact.

that if weld leg length is specified, the throat used in calculations should not be assumed to exceed 0.71 times the leg length. If a bigger throat is required, it should be

specified together with the leg length.

Cross Beams and Other Transverse Members in Flanges (21) As for transverse stiffeners, cross beams and other transverse members in flanges should be

designed to BS EN 1993-1-5. Guidance on loadings for determining design effects is

provided in PD 6695-2. However, the means of calculating the deflections and stresses due to

these loadings, together with second order effects, that is promised in clause 21 paragraph a)

has been inadvertently omitted in the published version of the PD. Suitable formulae can be

found in reference 2.


Shape Limitations for Stiffener Outstands ( 22) Stiffener outstands may buckle locally in a torsional buckling mode transverse to the plane of

the parent plate, possibly in combination with an overall global buckling of the stiffener out of

the plane of the parent plate. Previous UK design practice (in BS 5400-3) provided guidance

on shape limits for stiffener outstands which, when met, would be deemed to ensure torsional

buckling could not occur. Such simple geometrical limits are not given in EN 1993-1-5.

Instead, calculations are required to 3-1-5/9.2.1(8) and (9) to demonstrate that torsional

buckling does not occur. Since some of these provisions require calculation of the critical

stress, cr, for torsional buckling, a formula for cr has been provided. As this formula contains the warping constant, Cw, formulae for Cw for common stiffener types have also been

provided.

For flat stiffeners only, it is possible to determine a simple shape limitation by following the

EN 1993-1-5 rules, so this has been provided, namely that 9.12235

y

s

sf

t

h.

Box Girder Design (23, 24 and 25) These clauses of PD 6695-2 introduce methods based on BS 5400-3 for evaluating torsional

and distortional actions in box girders and for designing diaphragms. The recommendations

are not strictly required because the general principles of EN 1993 can be applied to properly

calculated effects that have been determined taking account of all structural behaviour.

It is likely that FE models using 2D shell elements will be used by designers to determine

stresses for use in verifications. However, elastic FE analysis merges the longitudinal stresses

due to axial force, bending (as modified by shear lag), torsional warping and distortional

warping. When evolving a design, knowledge of the relative magnitudes of the separate

components is useful because certain effects may be neglected at the ultimate limit state due

to the occurrence of plasticity (effects such as torsional warping and much of the shear lag

effects). The algebraic expressions provided in the PD allow these effects to be separated and

are imported directly from BS 5400-3. They also provide a useful check on the output from

FE analysis. A further alternative would be the use of non-linear FE analysis with modelled

imperfections. This could automatically account for the effects of plasticity but is a much

more involved and laborious process.

No attempt has been made to make the rules on diaphragms compatible with the Eurocode

buckling curves and analysis methods; it was simply too great a task. Instead, the method has

been described as a self-contained procedure for hand methods. This has been justified on the basis that diaphragms are not explicitly covered by EN 1993.

Web Breathing (26) Clause 26 of PD 6695-2 was added as to clarify the requirements for web breathing in

longitudinally stiffened sections provided in EN 1993-2. The clarification is simply that two

verifications are required; one for the overall stiffened panel and one for the sub-panels

between longitudinal stiffeners.


Acknowledgements

The work described in this paper was carried out by the authors with the support of and

review by Working Group WG3 of the BSI Committee B525/10. Thanks are expressed to all

contributors.

References

[1] BS 5400-2000 Design of steel bridges. British Standards Institution, London.

[2] Hendy C.R. and Murphy C.J. (2007) Designers Guide to EN1993-2, Eurocode 3: Design of steel structures. Part 2: Steel bridges. Thomas Telford, London. ISBN

9780727731609

[3] Brown, C.W and Iles, D.C. Commentary on BS 5400-3: 2000 - Code of Practice for the

design of Steel Bridges (P295), SCI, 2000, England.

Documents

PD6695-2