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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 19952
November 2004
ICS 91.010.30; 91.080.20; 93.040
Supersedes ENV 19952:1997
English version
Eurocode 5: Conception et calcul des structures bois  Partie 2: Ponts  Eurocode 5: Bemessung und Konstruktion von Holzbauten  Teil 2: Brucken 
This European Standard was approved by CEN on 26 August 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Uptodate lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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© 2004 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 19952:2004: E
1Foreword  3  
Section 1 General  6  
1.1  Scope  6  
1.1.1  Scope of EN 1990  6  
1.1.2  Scope of EN 19952  6  
1.2  Normative references  6  
1.3  Assumptions  7  
1.4  Distinction between principles and application rules  7  
1.5  Definitions  7  
1.5.1  General  7  
1.5.2  Additional terms and definitions used in this present standard  7  
1.6  Symbols used in EN 19952  9  
Section 2 Basis of design  11  
2.1  Basic requirements  11  
2.2  Principles of limit state design  11  
2.3  Basic variables  11  
2.3.1  Actions and environmental influences  11  
2.4  Verification by the partial factor method  11  
2.4.1  Design value of material property  11  
Section 3 Material properties  13  
Section 4 Durability  14  
4.1  Timber  14  
4.2  Resistance to corrosion  14  
4.3  Protection of timber decks from water by sealing  14  
Section 5 Basis of structural analysis  15  
5.1  Laminated deck plates  15  
5.1.1  General  15  
5.1.2  Concentrated vertical loads  15  
5.1.3  Simplified analysis  16  
5.2  Composite members  17  
5.3  Timberconcrete composite members  17  
Section 6 Ultimate limit states  18  
6.1  Deck plates  18  
6.1.1  System strength  18  
6.1.2  Stresslaminated deck plates  19  
6.2  Fatigue  21  
Section 7 Serviceability limit states  22  
7.1  General  22  
7.2  Limiting values for deflections  22  
7.3  Vibrations  22  
7.3.1  Vibrations caused by pedestrians  22  
7.3.2  Vibrations caused by wind  22  
Section 8 Connections  23  
8.1  General  23  
8.2  Timberconcrete connections in composite beams  23  
8.2.1  Laterally loaded doweltype fasteners  23  
8.2.2  Grooved connections  23  
Section 9 Structural detailing and control  24  
Annex A (informative) Fatigue verification  25  
A.1  General  25  
A.2  Fatigue loading  25  
A.3  Fatigue verification  26  
Annex B (informative) Vibrations caused by pedestrians  28  
B.1  General  28  
B.2  Vertical vibrations  28  
B.3  Horizontal vibrations  28 
This European Standard EN 19952 has been prepared by Technical Committee CEN/TC250 “Structural Eurocodes”, the Secretariat of which is held by BSI.
This European Standard shall be given the status of a National Standard, either by publication of an identical text or by endorsement, at the latest by May 2005, and conflicting national standards shall be withdrawn at the latest by March 2010.
This European Standard supersedes ENV 19952:1997.
CEN/TC250 is responsible for all Structural Eurocodes.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them.
For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980s.
In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement^{1} between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products  CPD  and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).
The Structural Eurocode programme comprises the following standards, generally consisting of a number of Parts:
EN 1990:2002  Eurocode: Basis of structural Design 
EN 1991  Eurocode 1: Actions on structers 
EN 1992  Eurocode 2: Design of concrete structures 
EN 1993  Eurocode 3: Design of steel structures 
EN 1994  Eurocode 4: Design of composite steel and concrete structures 
EN 1995  Eurocode 5; design of timber structures 
EN 1996  Eurocode 6 Design of masonry structures 
EN 1997  Eurocode 7: Geotechnical design 3 
EN 1998  Eurocode 8: Design of structures for earthquake resistance 
EN 1999  Eurocode 9: Design of aluminium structures 
^{1} Agreement between the commision of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89).
Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.
The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes:
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents^{2} referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards^{3}. Therefore, technical aspects arising from the Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving full compatibility of these technical specifications with the Eurocodes.
The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.
The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National annex.
The National annex may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e.:
^{2}According to Art. 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for harmonised ENs and ETAGs/ETAs.
^{3}According to Art. 12 of the CPD the interpretative documents shall:
give concrete form to the essential requirements by harmonising the terminology and the technical bases and indicating classes or levels for each requirement where necessary ;
indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g. methods of calculation and of proof, technical rules for project design, etc. ;
serve as a reference for the establishment of harmonised standards and guidelines for European technical approvals.
The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.
There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works^{4}. Furthermore, all the information accompanying the CE Marking of the construction products which refer to Eurocodes shall clearly mention which Nationally Determined Parameters have been taken into account.
EN 1995 describes the Principles and requirements for safety, serviceability and durability of timber bridges. It is based on the limit state concept used in conjunction with a partial factor method.
For the design of new structures, EN 19952 is intended to be used, for direct application, together with EN 199511 and EN1990:2002 and relevant Parts of EN 1991.
Numerical values for partial factors and other reliability parameters are recommended as basic values that provide an acceptable level of reliability. They have been selected assuming that an appropriate level of workmanship and of quality management applies. When EN 19952 is used as a base document by other CEN/TCs the same values need to be taken.
This standard gives alternative procedures, values and recommendations with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 19952 should have a National annex containing all Nationally Determined Parameters to be used for the design of bridges to be constructed in the relevant country.
National choice is allowed in EN 19952 through clauses:
2.3.1.2(1)  Loadduration assignment 
2.4.1  Partial factors for material properties 
7.2  Limiting values for deflection 
7.3.1(2)  Damping ratios 
^{4} See Art.3.3 and Art. 12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.
5Section 1:  General 
Section 2:  Basis of design 
Section 3:  Material properties 
Section 4:  Durability 
Section 5:  Basis of structural analysis 
Section 6:  Ultimate limit states 
Section 7:  Serviceability limit states 
Section 8:  Connections 
Section 9:  Structural detailing and control 
European Standards:
EN 1990:2002  Eurocode – Basis of structural design 
EN1990:2002/A1  Eurocode – Basis of structural design/Amendment A1 – Annex A2: Application to Bridges 
EN 199114  Eurocode 1: Actions on structures – Part 14: Wind loads 
EN 19912  Eurocode 1: Actions on structures – Part 2: Traffic loads on bridges 
EN 199211  Eurocode 2: Design of concrete structures – Part 11: Common rules and rules for buildings 
EN 19922  Eurocode 2: Design of concrete structures – Part 2: Bridges 
EN 19932  Eurocode 3: Design of steel structures – Part 2: Bridges 
EN 199511  Eurocode 5: Design of timber structures – Part 11: General – Common rules and rules for buildings 
EN 101381  Prestressing steels – Part 1: General requirements 
EN 101384  Prestressing steels – Part 4: Bars 
Shear connection consisting of the integral part of one member embedded in the contact face of the other member. The contacted parts are normally held together by mechanical fasteners.
NOTE: An example of a grooved connection is shown in figure 1.1.
7Figure 1.1 – Example of grooved connection
Deck plates made of laminations, arranged edgewise or flatwise, held together by mechanical fasteners or gluing, see figures 1.2 and 1.3.
Laminated deck plates made of edgewise arranged laminations with surfaces either sawn or planed, held together by prestressing, see figure 1.2.b, c and d.
Figure 1.2 – Examples of deck plates made of edgewise arranged laminations
a) naillaminated or screwlaminated
b) prestressed, but not glued
c) glued and prestressed glued laminated beams positioned flatwise
d) glued and prestressed glued laminated beams positioned edgewise
Laminated deck plates made of laminations in layers of different grain direction (crosswise or at different angles). The layers are glued together or connected using mechanical fasteners, see figure 1.3.
A permanent effect due to controlled forces and/or deformations imposed on a structure.
NOTE: An example is the lateral prestressing of timber deck plates by means of bars or tendons, see figure 1.2 b to d.
Figure 1.3 – Example of crosslaminated deck plate
For the purpose of EN 19952, the following symbols apply.
Latin upper case letters
A  Area of bridge deck 
E_{0,mean}  Mean modulus of elasticity parallel to grain 
E_{90,mean}  Mean modulus of elasticity perpendicular to the grain 
F  Force 
F_{t,Ed}  Design tensile force between timber and concrete 
F_{v,Ed}  Design shear force between timber and concrete 
G_{0,mean}  Mean shear modulus parallel to grain 
G_{90,mean}  Mean shear modulus perpendicular to grain (rolling shear) 
M  Total mass of bridge 
M_{beam}  Bending moment in a beam representing a plate 
M_{max,beam}  Maximum bending moment in a beam representing a plate 
N_{obs}  Number of constant amplitude stress cycles per year 
R  Ratio of stresses 
Latin lower case letters
a  Distance; fatigue coefficient 
a_{hor,1}  Horizontal acceleration from one person crossing the bridge 
a_{hor,n}  Horizontal acceleration from several people crossing the bridge 
a_{vert,1}  Vertical acceleration from one person crossing the bridge 
a_{vert,n}  Vertical acceleration from several people crossing the bridge 
b  Fatigue coefficient 
b_{ef}  Effective width 
b_{ef,c}  Total effective width of concrete slab 
b_{bef,1}; b_{ef,2}  Effective width of concrete slab 9 
b_{lam}  Width of the lamination 
b_{w}  Width of the loaded area on the contact surface of deck plate 
b_{w,middie}  Width of the loaded area in the middle of the deck plate 
d  Diameter; outer diameter of rod; distance 
h  Depth of beam; thickness of plate 
f_{c,9o,d}  Design compressive strength perpendicular to grain 
f_{fat,d}  Design value of fatigue strength 
f_{k}  Characteristic strength 
f_{m,d,deck}  Design bending strength of deck plate 
f_{v,d,deck}  Design shear strength of deck plate 
f_{m,d,lam}  Design bending strength of laminations 
f_{v,d,lam}  Design shear strength of laminations 
f_{vert}, f_{hor}  Fundamental natural frequency of vertical and horizontal vibrations 
k_{c,90}  Factor for compressive strength perpendicular to the grain 
k_{fat}  Factor representing the reduction of strength with number of load cycles 
k_{hor}  Coefficient 
k_{mod}  Modification factor 
k_{sys}  System strength factor 
k_{vert}  Coefficient 
ℓ  Span 
ℓ_{1}  Distance 
m  Mass; mass per unit length 
m_{plate}  Bending moment in a plate per unit length 
m_{max,plate}  Maximum bending moment in a plate 
n  Number of loaded laminations; number of pedestrians 
n_{ADT}  Expected annual average daily traffic over the lifetime of the structure 
t  Time; thickness of lamination 
t_{L}  Design service life of the structure expressed in years 
Greek lower case letters
α  Expected percentage of observed heavy lorries passing over the bridge 
β  Factor based on the damage consequence; angle of stress dispersion 
γ_{M}  Partial factor for timber material properties, also accounting for model uncertainties and dimensional variations 
γ_{M,c}  Partial factor for concrete material properties, also accounting for model uncertainties and dimensional variations 
γ_{M,s}  Partial factor for steel material properties, also accounting for model uncertainties and dimensional variations 
γ_{M,v}  Partial factor for shear connectors, also accounting for model uncertainties and dimensional variations 
γ_{M,fat}  Partial safety factor for fatigue verification of materials, also accounting for model uncertainties and dimensional variations 
k  Ratio for fatigue verification 
p_{mean}  Mean density 
μ_{d}  Design coefficient of friction 
σ_{d.max}  Numerically largest value of design stress for fatigue loading 
σ_{d,min}  Numerically smallest value of design stress for fatigue loading 
σ_{p,min}  Minimum longterm residual compressive stress due to prestressing; 
ζ  Damping ratio 
Note 1: The relevant parts of EN 1991 for use in design include:
EN 199111  Densities, selfweight and imposed loads 
EN 199113  Snow loads 
EN 199114  Wind loads 
EN 199115  Thermal actions 
EN 199116  Actions during execution 
EN 199117  Accidental actions due to impact and explosions 
EN 19912  Traffic loads on bridges. 
NOTE: Examples of loadduration assignments are given in note to 2.3.1 of EN 199511. The recommended loadduration assignment for actions during erection is shortterm. The National choice may be given in the National annex.
NOTE: For fundamental combinations, the recommended partial factors for material properties, γ_{M}, are given in table 2.1. For accidental combinations, the recommended value of partial factor is γ_{M} = 1,0. Information on the National choice may be found in the National annex.
111. Timber and woodbased materials  
– normal verification  
– solid timber  γ_{M} = 1,3 
– glued laminated timber  γ_{M} = 1,25 
– LVL, plywood, OSB  γ_{M} = 1,2 
– fatigue verification  γ_{M} = 1,0 
2. Connections  
– normal verification  γ_{M} = 1,3 
– fatigue verification  γ_{M,fat} = 1,0 
3. Steel used in composite members  γ_{M,s} = 1,15 
4. Concrete used in composite members  γ_{M,c} = 1,5 
5. Shear connectors between timber and concrete in composite members  
– normal verification  γ_{M,v} = 1,25 
– fatigue verification  γ_{M,v,fat} = 1,0 
6. Prestressing steel elements  γ_{M,s} = 1,15 
NOTE 1: The effect of direct weathering by precipitation or solar radiation of structural timber members can be reduced by constructional preservation measures, or by using timber with sufficient natural durability, or timber preservatively treated against biological attacks.
NOTE 2: Where a partial or complete covering of the main structural elements is not practical, durability can be improved by one or more of the following measures:
NOTE 3: The risk of increased moisture content near the ground, e.g. due to insufficient ventilation due to vegetation between the timber and the ground, or splashing water, can be reduced by one or more of the following measures:
NOTE: An example of especially corrosive conditions is a timber bridge where corrosive deicing cannot be excluded.
NOTE: In an advanced analysis, for deck plates made of softwood laminations, the relationships for the system properties should be taken from table 5.1. The Poisson ratio v may be taken as zero.
Type of deck plate  E_{90,mean}/E_{0,mean}  G_{0,mean}/E_{0,mean}  G_{90,mean}/G_{0,mean} 

Naillaminated  0  0,06  0,05 
Stresslaminated  
– sawn  0,015  0,06  0,08 
– planed  0,020  0,06  0,10 
Gluedlaminated  0,030  0,06  0,15 
where:
b_{w}  is the width of the loaded area on the contact surface of the pavement; 
b_{w,middle}  is the width of the loaded area at the reference plane in the middle of the deck plate; 
β  is the angle of dispersion according to table 5.2. 
Figure 5.1 – Dispersion of concentrated loads from contact area width b_{w}
Pavement (in accordance with EN 19912 clause 4.3.6)  45° 
Boards and planks  45° 
Laminated timber deck plates:  
– in the direction of the grain  45° 
– perpendicular to the grain  15° 
Plywood and crosslaminated deck plates  45° 
b_{ef} = b_{w,middle} + a (5.1)
where:
b_{w,middle}  should be calculated according to 5.1.2(2); 
a  should be taken from table 5.3. 
Deck plate system  a m 

Naillaminated deck plate  0,1 
Stresslaminated or glued laminated  0,3 
Crosslaminated timber  0,5 
Composite concrete/timber deck structure  0,6 
NOTE: See clause 8.2
b_{ef,c} = b + b_{ef,1} + b_{ef,2} (5.2)
where:
b  is the width of the timber beam; 
b_{ef,1,} b_{ef,2}  are the effective widths of the concrete flanges, as determined for a concrete T section according to EN 199211, subclause 5.3.2.1. 
f_{m,d,deck} = k_{sys} f_{m,d,lam} (6.1)
f_{v,d,deck} = k_{sys} f_{v,d,lam} (6.2)
where:
f_{m,d,lam}  is the design bending strength of the laminations; 
f_{v,d,lam}  is the design shear strength of the laminations; 
k_{sys}  is the system strength factor, see EN 199511. For decks in accordance to Fig. 1.2d EN 199511 figure 6.14 line 1 should be used. 
For the calculation of k_{sys,} the number of loaded laminations should be taken as:
with:
b_{ef}  is the effective width; 
b_{lam}  is the width of the laminations. 
where:
M_{max,beam}  is the maximum bending moment in a beam representing the plate; 
m_{max,plate}  is the maximum bending moment in the plate calculated by a plate analysis. 
NOTE: In 5.1.3 a simplified method is given for the determination of the effective width.
Figure 6.1 – Example of bending moment distribution in the plate for determination of effective width
F_{v,ED} ≤ μ_{d} σ_{p},_{min}h (6.5)
where:
F_{v,Ed}  is the design shear force per unit length, caused by vertical and horizontal actions; 
μ_{d}  is the design value of coefficient of friction; 
σ_{p,min}  is the minimum longterm residual compressive stress due to prestressing; 
h  is the thickness of the plate. 
Lamination surface roughness  Perpendicular to grain  Parallel to grain  

Moisture content ≤ 12 % 
Moisture content ≥ 16 % 
Moisture content ≤ 12 % 
Moisture content ≥ 16 % 

Sawn timber to sawn timber  0,30  0,45  0,23  0,35 
Planed timber to planed timber  0,20  0,40  0,17  0,30 
Sawn timber to planed timber  0,30  0,45  0,23  0,35 
Timber to concrete  0,40  0,40  0,40  0,40 
where:
d  is the distance between the prestressing elements; 
t  is the thickness of the laminations in the direction of prestressing. 
Figure 6.2 — Butt joints in stresslaminated deck plates
NOTE 1: A fatigue verification is normally not required for footbridges.
NOTE 2: A simplified verification method is given in annex A (informative).
NOTE: The range of limiting values for deflections due to traffic load only, for beams, plates or trusses with span ℓ is given in Table 7.1. The recommended values are underlined. Information on National choice may be found in the National annex.
Action  Range of limiting values 

Characteristic traffic load  ℓ/400 to ℓ/500 
Pedestrian load and low traffic load  ℓ/200 to ℓ/400 
NOTE 1: For specific structures, alternative damping ratios may be given in the National annex.
NOTE 2: A simplified method for assessing vibrations of timber bridges constructed with simply supported beams or trusses is given in Annex B.
Figure 8.1 – Intermediate layer between concrete and timber
F_{t,Ed} = 0,1 F_{v,Ed} (8.1)
where:
F_{t,Ed}  is the design tensile force between the timber and the concrete; 
F_{v,Ed}  is the design shear force between the timber and the concrete. 
(informative)
NOTE: More advanced fatigue verification for varying stress amplitude can be based on a cumulative linear damage theory (PalmgrenMiner hypothesis).
where:
σ_{d,max}  is the numerically largest design stress from the fatigue loading; 
σ_{d,min}  is the numerically smallest design stress from the fatigue loading; 
f_{k}  is the relevant characteristic strength; 
γ_{M,fat}  is the material partial factor for fatigue loading. 
N_{obs} = 365 n_{ADT} α (A.2)
where:
N_{obs}  is the number of constant amplitude stress cycles per year; 
n_{ADT}  is the expected annual average daily traffic over the lifetime of the structure; the value of n_{ADT} should not be taken less than 1000; 25 
α  is the expected fraction of observed heavy lorries passing over the bridge, see EN 19912 clause4.6 (e.g. α = 0,1); 
σ_{d,max} ≤ f_{fat,d} (A.3)
where:
σ_{d,max}  is the numerically largest design stress from the fatigue loading; 
f_{fat,d}  is the design value of fatigue strength. 
where:
f_{k}  is the characteristic strength for static loading; 
k_{fat}  is a factor representing the reduction of strength with number of load cycles. 
where:
R = σ_{d,min}/σ_{d,max} with –1 ≤ R ≤ 1; (A.6)
σ_{d,min}  is the numerically smallest design stress from the fatigue loading; 
σ_{d,max}  is the numerically largest design stress from the fatigue loading; 
N_{obs}  is the number of constant amplitude stress cycles as defined above; 
t_{L}  is the design service life of the structure expressed in years according to EN 1990:2002 (e.g. 100 years);β is a factor based on the damage consequence for the actual structural component; 
a, b  are coefficients representing the type of fatigue action according to table A.1. 
The factor β should be taken as:
a  b  

Timber members in  
– compression, perpendicular or parallel to grain  2,0  9,0 
– bending and tension  9,5  1,1 
– shear  6,7  1,3 
Connections with  
– dowels with d ≤ 12 mm ^{a}  6,0  1,2 
– nails  6,9  1,2 
^{a} The values for dowels are mainly based on tests on 12 mm tightfitting dowels. Significantly larger diameter dowels or nonfitting bolts may have less favourable fatigue properties. 
(informative)
NOTE: Corresponding rules will be found in future versions of EN 19912.
where:
M  is the total mass of the bridge in kg, given by M = mℓ; 
ℓ  is the span of the bridge; 
m  is the mass per unit length (selfweight) of the bridge in kg/m; 
ζ  is the damping ratio; 
f_{vert}  is the fundamental natural frequency for vertical deformation of the bridge. 
a_{vert,n} = 0,23 a_{vert,1} n k_{vert} (B.2)
where:
n  is the number of pedestrians; 
k_{vert}  is a coefficient according to figure B.1; 
a_{vert,1}  is the vertical acceleration for one person crossing the bridge determined according to expression (B.1). 
The number of pedestrians, n, should be taken as:
where f_{hor} is the fundamental natural frequency for horizontal deformation of the bridge.
a_{hor,n} = 0,18 a_{hor,1} n k_{hor} (B.5)
where:
k_{hor} is a coefficient according to figure B.2.
The number of pedestrians, n, should be taken as:
–  n = 13  for a distinct group of pedestrians; 
–  n = 0,6 A  for a continuous stream of pedestrians, 
where A is the area of the bridge deck in m^{2}.
Figure B.1 – Relationship between the vertical fundamental natural frequency f_{vert} and the coefficient k_{vert}
Figure B.2 – Relationship between the horizontal fundamental natural frequency f_{hor}and the coefficient k_{hor}