3.4.3 contact wire height distance from the top of the rail or road surface for overhead contact line system for trolleybus applications to the lower face of the contact wire, measured
Systems
The contact line system serves as a support network for delivering electrical energy from substations to traction units powered by electricity This system encompasses both overhead contact line systems and conductor rail systems The electrical boundaries of the system are defined by the feeding point and the contact point connected to the current collector.
NOTE The mechanical system may comprise
supports and any components supporting or registering the conductors,
along-track feeders, reinforcing feeders, and other lines like earth wires and return conductors as far as they are supported from contact line system structures,
any other equipment necessary for operating the contact line,
conductors connected permanently to the contact line for supply of other electrical equipment such as lights, signal operation, point control and point heating
3.1.2 contact line conductor system for supplying traction units with electrical energy via current-collection equipment
NOTE This includes all current-collecting conductors and conducting rails or bars, including the following:
supports that are not insulated from the conductors;
insulators connected to live parts; but excluding other conductors, such as the following:
earth wires and return conductors
EN ISO 1461:1999, Hot dip galvanized coatings on fabricated iron and steel articles – Specifications and test methods (ISO 1461:1999)
HD 578, Characteristics of indoor and outdoor post insulators for systems with nominal voltages greater than
IEC 60050-811, International Electrotechnical Vocabulary (IEV) – Chapter 811: Electric traction
IEC/TR 61245, Artificial pollution tests on high-voltage insulators to be used on d.c systems
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms and definitions given in IEC 60050-811 and the following apply
The contact line system serves as a support network for delivering electrical energy from substations to electrically powered traction units This system encompasses both overhead contact line systems and conductor rail systems The electrical boundaries of the system are defined by the feeding point and the contact point to the current collector.
NOTE The mechanical system may comprise
supports and any components supporting or registering the conductors,
along-track feeders, reinforcing feeders, and other lines like earth wires and return conductors as far as they are supported from contact line system structures,
any other equipment necessary for operating the contact line,
conductors connected permanently to the contact line for supply of other electrical equipment such as lights, signal operation, point control and point heating
3.1.2 contact line conductor system for supplying traction units with electrical energy via current-collection equipment
NOTE This includes all current-collecting conductors and conducting rails or bars, including the following:
supports that are not insulated from the conductors;
insulators connected to live parts; but excluding other conductors, such as the following:
earth wires and return conductors
HD 578 S1, Characteristics of indoor and outdoor post insulators for systems with nominal voltages greater than 1 kV (IEC 60273)
3.1.3 overhead contact line system contact line system using an overhead contact line to supply current for use by traction units
3.1.4 overhead contact line contact line placed above or beside the upper limit of the vehicle gauge, supplying traction units with electrical energy via roof-mounted current collection equipment
3.1.5 conductor rail system contact line system using a conductor rail for current collection
The overhead conductor rail is a rigid overhead contact line, which can be either simple or composite in design It is installed above or alongside the upper limit of the vehicle gauge and provides electrical energy to traction units through current collection equipment mounted on the roof.
3.1.7 conductor rail contact line made of a rigid metallic section or rail, mounted on insulators located near the running rails
3.1.8 supporting assembly assembly of components attached to the main support structure that supports and registers the overhead contact line
3.1.9 static load gauge maximum cross-sectional profile of the vehicles using the railway line
3.1.10 kinematic load gauge static load gauge enlarged to allow for dynamic movements of the vehicle, e.g suspension travel and bounce
3.1.11 kinematic envelope kinematic load gauge further enlarged to allow for possible tolerances in the position of the track
3.1.12 swept envelope kinematic envelope enlarged to allow for centre and end throw of the vehicles on horizontal and vertical curves
3.1.13 tensioning device device to maintain the tension of conductors within the system design parameters
3.1.14 urban mass transportation system light rail, trolleybus and tramway system, operating in urban areas, excluding heavy rail systems
Conductors
3.2.1 along-track feeder overhead conductor mounted on the same structure as the overhead contact line to supply successive feeding points
A reinforcing feeder is an overhead conductor installed alongside the overhead contact line, with frequent direct connections to enhance the effective cross-sectional area of the contact line.
Electrical
3.3.1 nominal voltage voltage by which an installation or part of an installation is designated
NOTE The voltage of the contact line may differ from the nominal voltage by a quantity within permitted tolerances given in EN 50163
3.3.2 feeding section electrical section of the route fed by individual track feeder circuit breakers within the area supplied by the substation
3.3.3 fault current maximum current passed through the overhead contact line system under fault conditions between live equipment and earth, within a short defined time period
A short-circuit refers to an accidental or intentional conductive path that connects two or more points in an electrical circuit, resulting in relatively low voltages between these points This conductive path can occur between conductors or between a conductor and the earth, and is classified as a short-circuit.
3.3.5 short-circuit current electric current flowing through the short-circuit
3.3.6 continuous current rating permanent rated current carrying capacity of the overhead contact line within the system operating parameters
3.3.7 feeding point point at which the feeding system is connected to the contact line
3.3.8 isolation disconnection of a section of overhead contact line from the source of electrical energy, either in an emergency or to facilitate maintenance
Geometrical
3.4.1 tension length length of overhead contact line between two terminating points
The gradient ratio measures the difference in height of the overhead contact line above the top of the rail or road surface at two consecutive supports, relative to the length of the span.
The contact wire height refers to the vertical distance from the top of the rail, or the road surface in the case of overhead contact line systems for trolleybus applications, to the lower face of the contact wire This measurement is taken perpendicular to the track.
The minimum height of the contact wire is crucial to prevent arcing between the contact wires and vehicles under all conditions This ensures safe and efficient operation of the electrical system.
3.4.5 minimum design contact wire height theoretical contact wire height including tolerances, designed to ensure that the minimum contact wire height is always achieved
3.4.6 nominal contact wire height nominal value of the contact wire height at a support in the normal conditions
3.4.7 maximum contact wire height maximum possible contact wire height which the pantograph is required to reach, in all conditions
3.4.8 maximum design contact wire height theoretical contact wire height taking account of tolerances, movements etc, designed to ensure the maximum contact wire height is not exceeded
3.4.9 contact wire uplift vertical upward movement of the contact wire due to the force produced from the pantograph
Foundations
3.5.1 gravity foundation shallow foundation installed by excavation and backfilling
A pile foundation is designed to be flexible, allowing for both rotation and deformation of the pile element when subjected to horizontal loads or overturning moments Its cross-section can be either circular or non-circular, and it is typically installed through boring or ramming methods.
3.5.3 sidebearing foundation relatively short, rigid foundation installed by excavation or boring which is subjected to horizontal loading or overturning moments The cross section may be circular or rectangular
Symbols and abbreviated terms
A ins projected area of an insulator
A K characteristic value of accidental actions
A lat effective area of the elements of a lattice structure
A str projected area of a structure
AACSR Aluminium alloy conductor steel reinforced
ACSR Aluminium conductor steel reinforced a.c alternating current
C compression amplitude for dropper test
C ins drag factor for insulators
C lat drag factor for lattice structures
C str drag factor of a structure d.c direct current
E d total design value of actions
F Bmin minimum breaking loadof stranded conductors and ropes
F d design value of an action
F K characteristic value of an action
F L internal force for dropper test
F max maximum or failure force for test specimens
F perm.op permissible operating force
F w permissible tensile loading of stranded conductors & ropes
G C structural response factor for conductors
G ins structural resonance factor for insulator sets
G K characteristic value of permanent actions
G lat structural resonance factor for lattice structures
G str structural resonance factor for a structure
G t terrain factor gIK characteristic ice loads
M dyy, M dzz design bending moments
N dax internal axial force of an element n safety factor for calculating the permissible loading in wires
OCS overhead contact line system
Q CK conductor tensile forces depending on the temperatures and climate related loads
Q K characteristic value of variable actions
Q PK construction and maintenance loads
Q WC wind load on conductors
Q Wt wind load on lattice structures
Q Wstr wind load on structures q K characteristic dynamic wind pressure
R dax axial resistance under tension or compression
R dyy, R dzz design bending resistances
R k characteristic value of the foundation ultimate resistance
R p 0,2 min 0,2 % yield point u variation in elasticity (also named ‘degree of non-uniformity’)
V c wave propagation velocity of the contact wire
V R reference wind velocity v w wind speed
X d design value of a material property
The X K characteristic value represents a material property, while the heat transmission coefficient is denoted by α The angle of incidence for the critical wind direction is indicated by Φ Various partial factors are essential for assessing different loads: γA for accidental loads, γC for conductor tensile forces, γF for actions, γG for permanent actions, γI for ice loads, γM for material properties, γP for construction and maintenance loads, and γW for wind loads The coefficient of friction for bolt connections is represented as àtot Additionally, ρ denotes the density of air, and ρI signifies the unit weight force of ice The minimum failing tensile stress of the contact wire is represented by σmin, while σw indicates the maximum permissible working tensile stress of a contact wire.
General
The overhead contact line system serves a dual purpose: it transmits energy from substations to vehicles and facilitates energy return from vehicles to substations through regenerative braking To achieve this, the design of the contact line system must align with specified requirements, ensuring seamless integration with other interconnected systems, such as the power supply and traction systems.
The requirements for overhead contact lines shall also apply to masts that are erected in connection with the overhead contact line system and used for feeder lines
The effectiveness of the current collection system relies on the integration of overhead contact lines and pantograph equipment, with the performance of each component significantly influencing overall quality It is essential that both systems are meticulously designed to meet their specific functions while ensuring compatibility with one another.
The data listed in 4.2 to 4.7 are normally specified by the purchaser.
Line characteristics
The train service characteristics and operational requirements to be considered in the design shall include
the speed and performance capability of the train/traction units to be employed,
the future performance capability to be anticipated and allowed for in the design, including any allowances for over speeding,
the type and frequency of electrically hauled trains,
the line speed for main and station tracks,
track gradient profile and location of the route; including turnouts and transitions,
Electrical power system design
The overhead contact line system design shall be based upon the consideration of the electrical characteristics of the power supply system design, including
nominal voltage and frequency, in accordance with EN 50163,
required impedance for a.c systems where stated,
required resistance for d.c systems where stated,
earthing and stray current protection in accordance with EN 50122-1 and EN 50122-2,
requirements to mitigate EMI and facilitate EMC in accordance with EN 50121-2,
requirements for over-voltage protection
For urban mass transportation systems the short-circuit current details are not required
Vehicle characteristics
The design of the overhead contact line system must account for clearances for all vehicle types operating on the line Key considerations include determining the static and kinematic load gauge, kinematic envelope, swept envelope, and compliance with national or international structural clearance requirements Additionally, it is essential to assess the number of pantographs in use, their spacing, and whether they are electrically linked or operate independently.
Current collectors
The characteristics of current collectors for line use must be defined, including the head width, length, and profile as per EN 50206-1:1998 and EN 50206-2:1999 Key factors include the number and type of contact strips, mean static contact force based on working height, and details regarding lateral movement of the collector head Additionally, considerations such as mean contact force at maximum line speed, working width, working range, controlled height positions, and a mathematical model of dynamic characteristics are essential The skew of the current collector head and the number, position, and separation of simultaneously used current collectors are also critical factors to address.
NOTE Specific requirements for pantographs for interoperable lines are given in EN 50367.
Environmental conditions
For environmental conditions refer to EN 50125-2.
Design life
The purchaser can specify the desired design life of the system, while consumable components like contact wire are excluded from this design life Additionally, the purchaser may outline specific requirements for the design life of these components.
Design of electrical system
The overhead contact line system must be designed to meet the electrical specifications outlined in sections 4.2 and 4.3, incorporating the return circuit and feeder connections while also accounting for potential short-circuit faults.
The overhead contact line system must be designed to accommodate the electrical load specified in the system design, which includes return circuit and feeder connections, while considering all environmental operating conditions outlined in EN 50125-2.
The rise in temperature of conductors caused by load currents must remain within limits that do not significantly compromise the mechanical properties of the material Refer to sections 7.3 and 7.4 for additional information.
The increase in temperature from current heating, along with ambient temperature and solar gain, must be considered when calculating the mechanical and dimensional allowances for the maximum expansion of the conductor system Additionally, geometrical allowances for electrical clearance and contact wire height should be included in the design, which must also account for pantograph current when at a standstill.
The temperatures above which the mechanical properties might be impaired are given in Table 1 for material compositions used in contact line systems
Table 1 — Temperature limits for material mechanical properties
Up to 1 s (short-circuit current) Up to 30 min
Normal and high strength copper with high conductivity 170 120 80
For temperatures exceeding those listed in Table 1, it is essential to evaluate the potential decrease in conductor strength based on the duration of the elevated temperature If a reduction is identified, adjustments to the conductor's dimensions may be required.
When calculating the temperature rise in a conductor the following contributions should be considered:
the heating caused by the current;
the heating caused by the environmental conditions;
the radiant heat emitted from the conductor;
the heat lost from the conductor by convection depending on the wind speed
The values of the environmental parameters (ambient temperature, wind speed and temperature rise caused by solar gain) shall be given in the purchaser specification
NOTE A wind speed of 1 m/s is often used for this calculation
The overhead contact line system must be engineered to accommodate the electrical load specified in the system design, which includes return circuit and feeder connections, while adhering to all environmental operating conditions outlined in EN 50125-2.
The rise in temperature of conductors caused by load currents must remain within limits that do not significantly compromise the mechanical properties of the material Refer to sections 7.3 and 7.4 for additional information.
The temperature increase from current heating, along with ambient temperature and solar gain, must be considered when calculating the mechanical and dimensional allowances for maximum conductor system expansion, as well as for electrical clearance and contact wire height Additionally, the design should account for pantograph current when stationary.
The temperatures above which the mechanical properties might be impaired are given in Table 1 for material compositions used in contact line systems
Table 1 — Temperature limits for material mechanical properties
Up to 1 s (short-circuit current) Up to 30 min
Normal and high strength copper with high conductivity 170 120 80
For temperatures exceeding those listed in Table 1, it is essential to assess the potential decrease in conductor strength based on the duration of the elevated temperature If a reduction is identified, the dimensions of the conductor should be adjusted accordingly.
When calculating the temperature rise in a conductor the following contributions should be considered:
the heating caused by the current;
the heating caused by the environmental conditions;
the radiant heat emitted from the conductor;
the heat lost from the conductor by convection depending on the wind speed
The values of the environmental parameters (ambient temperature, wind speed and temperature rise caused by solar gain) shall be given in the purchaser specification
NOTE A wind speed of 1 m/s is often used for this calculation
For temperatures exceeding those listed in Table 1, it is essential to evaluate the potential decrease in conductor strength based on the duration of the elevated temperature If required, adjustments should be made by either increasing the dimensions of the conductor(s) or reducing the working load.
The temperature of the contact wire at the interface with the contact strips shall not exceed the appropriate value given in Table 1
5.1.3 Clearances between live parts of contact lines and earth
The recommended air clearances between earth and the live parts of the overhead contact line system are stated in Table 2
Static Dynamic d.c 600 V a 100 50 d.c 750 V 100 50 d.c 1,5 kV 100 50 d.c 3,0 kV 150 50 a.c 15 kV 150 100 a.c 25 kV 270 150 a Only for existing systems
Probabilistic assessments justify the distinction between clearances for "static" and "dynamic" scenarios For instance, the likelihood of an over-voltage surge coinciding with a pantograph traversing a narrow tunnel is low Therefore, employing a dynamic clearance in this temporary situation is warranted.
Table 2 values are not applicable to section insulators, as lower values may be used to maintain acceptable dynamic performance for the pantograph and overhead contact line system For reduced electrical clearances specific to section insulators, please refer to EN 50122-1.
The clearance values in Table 2 can vary based on factors such as absolute humidity, ambient temperature, air pressure, pollution, relative air density, and the shape and material of both energized and grounded structures, as outlined in EN 50125-2 Each situation must be assessed on a case-by-case basis.
The clearance values given in Table 2 should also be applied for clearances between adjacent live parts of contact lines of different electrical sections of the same voltage and phase
In regions prone to over-voltage from lightning or other sources, it is essential to utilize surge arrestors when electrical clearances to grounded structures are inadequate to prevent flashovers.
5.1.4 Clearances between adjacent live a.c contact lines of differing voltage phases
In an overhead contact line system, a phase difference can occur between various components, leading to a phase-to-phase voltage that exceeds the nominal voltage Specifically, in 15 kV and 25 kV autotransformer systems, there exists a 180° phase difference between all live parts linked to the feeder line and those connected to the overhead contact line.
For single phase a.c systems, the phase difference between 120° and 180° at neutral section locations results in a similar effect
Table 3 provides recommendations for the air clearance which should be achieved between live parts of an a.c contact line system of differing phases
Table 3 — Clearance between differing phases
Nominal voltage Phase difference Relative voltage Recommended clearance
Static Dynamic kV degrees kV mm mm
Design of current collection systems
The design of both the overhead contact line system and pantograph shall take into account the required relevant speed
The performance of overhead contact lines and pantographs must take into account both geometric and static characteristics Dynamic behavior can be anticipated during the design phase through computer simulations, which should be validated according to EN 50318 Additionally, these simulations must be verified with measurements taken from the installed overhead contact line system.
For a train with multiple pantographs, the performance of each pantograph both separately and with the pantographs used collectively shall be assessed
For urban mass transportation systems the dynamic behaviour need not be considered
NOTE Technical criteria for the interaction between pantograph and overhead contact line to achieve free access to rail infrastructure are given in EN 50367
The design of the overhead contact line must ensure minimal variation, denoted as \$u\$, in elasticity, represented by \$e\$ (measured in millimeters per Newton, mm/N) Elasticity is defined as the uplift divided by the force applied at the contact wire Each span features both maximum and minimum elasticity values, which should remain static, effectively characterizing the variation \$u\$.
NOTE 1 The value u is also named ‘degree of non-uniformity’
NOTE 2 Low values of elasticity do not always give a small variation
The elasticity and its variation depend upon the configuration of the overhead contact line For the overhead contact system the following main factors shall be taken into account:
number of contact and catenary wires;
tension of contact and catenary wires;
Table 3 — Clearance between differing phases
Nominal voltage Phase difference Relative voltage Recommended clearance
Static Dynamic kV degrees kV mm mm
When a pantograph crosses the overlap of a phase separation section, a temporary phase-to-phase voltage occurs between the contact lines Consequently, the clearances between these lines must adhere to the dynamic clearances specified in Table 3 and must be consistently maintained.
5.2 Design of current collection systems
The design of both the overhead contact line system and pantograph shall take into account the required relevant speed
The performance of overhead contact lines and pantographs must take into account both geometric and static characteristics Dynamic behavior can be anticipated during the design phase through computer simulations, which should be validated according to EN 50318 Additionally, these simulations must be verified with measurements taken from the installed overhead contact line system.
For a train with multiple pantographs, the performance of each pantograph both separately and with the pantographs used collectively shall be assessed
For urban mass transportation systems the dynamic behaviour need not be considered
NOTE Technical criteria for the interaction between pantograph and overhead contact line to achieve free access to rail infrastructure are given in EN 50367
The design of the overhead contact line must ensure minimal variation, denoted as \( u \), in elasticity \( e \) Elasticity \( e \), measured in millimeters per Newton (mm/N), is defined as the uplift divided by the force at the contact wire Each span has defined maximum and minimum elasticity values, which should remain static to accurately represent the variation \( u \).
NOTE 1 The value u is also named ‘degree of non-uniformity’
NOTE 2 Low values of elasticity do not always give a small variation
The elasticity and its variation depend upon the configuration of the overhead contact line For the overhead contact system the following main factors shall be taken into account:
number of contact and catenary wires;
tension of contact and catenary wires;
The design of the overhead contact line must ensure minimal variation, denoted as \( u \), in elasticity \( e \) Elasticity \( e \), measured in millimeters per Newton (mm/N), is defined as the uplift divided by the force at the contact wire Each span has specific maximum and minimum elasticity values, which are static and represent the variation \( u \).
type, number and the position of droppers
If dynamic simulations are not undertaken, elasticity and variation may be specified by the purchaser
The elasticity should normally be calculated with a value of force equal to either the mean contact force at maximum speed or double the static contact force
5.2.3 Vertical movement of contact point
The contact point is the point of the mechanical contact between a contact strip and a contact wire
The design of the overhead contact line must ensure that the vertical height of the contact point remains consistent above the track throughout the span length, which is crucial for effective current collection.
The maximum permissible difference between the highest and the lowest dynamic contact point height within one span shall be as specified by the purchaser
Verification will be conducted through measurements or simulations, focusing on the maximum line speed permitted by the overhead contact line This assessment will take into account the average contact force and the longest span length.
This need not be verified for overlap spans or for spans over switches
Waves generated by pantograph forces on contact wires travel at a specific velocity To ensure safety and efficiency, the overhead contact line must be designed so that the operational speed does not exceed 70% of the wave propagation velocity, denoted as V_c, of the contact wire.
∑z is the sum of the working tensile loads of contact wire(s) (in N);
∑m is the sum of the linear mass of the contact wire(s) (in kg/m)
For urban mass transportation systems the calculation of the wave propagation velocity may be omitted
Pantographs and overhead contact lines shall be designed and installed to ensure acceptable current collection performance at all operating speeds and whilst at standstill
The life cycle of the contact strips and contact wires essentially depends on
dynamic behaviour of the overhead contact line and the pantograph,
contact areas and the number of contact strips,
material of contact strips and contact wire,
speed of the train, the number of pantographs in operation and the distances between them,
geometry of the contact line,
pantograph design and contact force
Overhead contact line equipment must be engineered to withstand the maximum allowable contact forces between the pantograph and the contact wire, while also considering the aerodynamic effects that arise at the vehicle's maximum permissible speed.
The minimum contact force shall be positive to ensure that there is no loss of contact between the pantograph and the overhead contact line
Force values differ based on the combinations of pantographs and overhead contact systems The simulated or measured contact forces between the contact wire and contact strip must remain within the limits specified in Table 4.
Where contact forces are used to define the current collection, the mean value and standard deviation of contact force shall be the criteria for current collection quality
The mean contact force, when increased by three standard deviations, must not exceed the maximum value listed in Table 4 Additionally, the mean contact force, when decreased by three standard deviations, should remain a positive value.
For rigid components such as section insulators in overhead contact line systems up to 200 km/h the contact force can increase up to a maximum of 350 N
In urban mass transportation systems, the dynamic behavior is not a critical factor, and the static contact force must be a minimum of 60 N Specific values for trolleybus systems are outlined in section 5.13.5.
NOTE Requirements for contact forces for interoperable lines are given in EN 50367
Maintaining a high quality of current collection relies on the uninterrupted mechanical contact between the contact wire and contact strip Any disruption in this contact can lead to arcing, which significantly accelerates wear on both the contact wire and the contact strip.
In defining current collection through loss of contact, the quality is determined by the frequency and duration of arcing When applying these criteria, the parameters and assessment tests must align with the specifications provided by the purchaser.
NOTE Requirements for interoperable lines are given in EN 50367.
Mechanical design of contact wire loads
The maximum permissible working tensile stress σw of a contact wire depends on the parameters defined in
The minimum tensile failing stress (\(\sigma_{min}\)) of the contact wire must be adjusted by multiplying it with individual weighting factors and a safety factor (\(n\)) that does not exceed 0.65 This calculation determines the maximum permissible working tensile stress for the wire.
The values in Table 5 and Table 7 may be interpolated
The maximum permissible working tensile stress to be applied to unworn contact wire shall be determined using the following equation: joint clamp eff wear temp min w = σ × n × K × K × K icewind × K × K × K σ
The tensile strength and creep behaviour of contact wires depends on the maximum working temperature
The factor K temp expresses the relationship between the permissible tensile stress and the maximum working temperature of a contact wire and is given in Table 5
Table 5 — Factor K temp for contact wires
For max temperature ≤ 80 °C For max temperature = 100 °C
For conductor temperatures exceeding 100 °C, the decrease in wire strength throughout its lifespan must be assessed through type tests The temperature factor K must be modified based on the wire's residual strength.
When addressing permitted tensile stress, it is crucial to also consider the contact wire material's resistance to creep To enhance this resistance, it is advisable to adopt a lower permissible tensile stress and/or working temperature.
Provision shall be made for allowable wear by applying a factor appropriate to the permissible wear
K wear = 1 – x where x is the permissible wear in percent / 100
5.3.4 Wind and ice loads K icewind
The maximum tensile strength of contact wires is influenced by wind and ice loads, which are determined by the design of overhead contact lines The factor \( K_{icewind} \) varies based on these loads and the specific type of overhead contact line, as detailed in Table 6.
Table 6 — Factor K icewind for contact wires
Type of overhead contact line Wind and ice load Wind load
Contact and catenary wire automatically tensioned 0,95 1,00 Contact wire automatically tensioned and catenary wire fixed termination 0,90 0,95
Single contact wire automatically tensioned 0,90 0,95
Contact and catenary wire fixed termination 0,70 0,80
5.3.5 Efficiency of tensioning devices K eff
The efficiency of tensioning devices is represented by the factor \( K_{\text{eff}} \) For proper design and installation, \( K_{\text{eff}} \) is typically assumed to match the efficiency values provided and verified by the supplier.
Where fixed terminations are used, K eff shall be equal to 1,0
The termination fittings' impact is determined by the K clamp factor, which is set to 1.00 when the clamping force meets or exceeds 95% of the contact wire's tensile strength If the clamping force is lower, the K clamp value is calculated as the ratio of the clamping force to the tensile strength.
5.3.7 Welded or soldered joints K joint
The factor K joint assesses the impact of welded or soldered joints, equating to 1.00 when no joints are used If joints are present, K joint is determined by the ratio of the tensile strength of the welded or soldered joints to the higher tensile strength of the contact wire Compliance with EN 50149 dictates the minimum tensile strength required for the joint.
Mechanical design of catenary wire loads
The maximum permissible working tensile load of catenary wire is determined by specific parameters outlined in sections 5.4.2 to 5.4.7, each weighted by an individual factor To calculate this load, the minimum breaking load \( F_{B_{\text{min}}} \) of the catenary wire is multiplied by the product of these factors and a factor \( n \), which must not exceed 0.65.
The maximum permissible working tensile load shall be determined from: load clamp eff ice wind temp
The K temp factor is set to 1.0 when the maximum working temperature remains within the limits specified in Table 1 If the working temperature exceeds these values, the factor will be decreased based on the percentage reduction in tensile strength.
5.3.4 Wind and ice loads K icewind
The maximum tensile strength of contact wires is influenced by wind and ice loads, which are determined by the design of overhead contact lines The factor K icewind, reflecting these loads and the specific type of overhead contact line, is detailed in Table 6.
Table 6 — Factor K icewind for contact wires Type of overhead contact line Wind and ice load Wind load
Contact and catenary wire automatically tensioned 0,95 1,00 Contact wire automatically tensioned and catenary wire fixed termination 0,90 0,95
Single contact wire automatically tensioned 0,90 0,95
Contact and catenary wire fixed termination 0,70 0,80
5.3.5 Efficiency of tensioning devices K eff
The efficiency of tensioning devices is represented by the factor \( K_{\text{eff}} \) For proper design and installation, \( K_{\text{eff}} \) is typically assumed to match the efficiency values provided and verified by the supplier.
Where fixed terminations are used, K eff shall be equal to 1,0
The termination fittings' impact is determined by the K clamp factor, which is set to 1.00 when the clamping force meets or exceeds 95% of the contact wire's tensile strength If the clamping force is lower, the K clamp value is calculated as the ratio of the clamping force to the tensile strength.
5.3.7 Welded or soldered joints K joint
The factor K joint assesses the impact of welded or soldered joints, equating to 1.00 when no joints are used If joints are present, K joint is determined by the ratio of the tensile strength of the welded or soldered joints to the higher tensile strength of the contact wire Additionally, the minimum tensile strength of the joint must comply with EN 50149 standards.
5.4 Mechanical design of catenary wire loads 5.4.1 Permissible tensile loading F w
The maximum permissible working tensile load of catenary wire is determined by specific parameters outlined in sections 5.4.2 to 5.4.7, each weighted by an individual factor To calculate this load, the minimum breaking load \( F_{B_{\text{min}}} \) of the catenary wire is multiplied by the product of these factors and a factor \( n \), which must not exceed 0.65.
The maximum permissible working tensile load shall be determined from: load clamp eff ice wind temp
The K temp factor is set to 1.0 when the maximum working temperature remains within the limits specified in Table 1 However, if the working temperature exceeds these values, the factor must be decreased in proportion to the potential percentage reduction in tensile strength.
5.3.4 Wind and ice loads K icewind
The maximum tensile strength of contact wires is influenced by wind and ice loads, which are determined by the design of overhead contact lines The factor K icewind, reflecting these loads and the specific type of overhead contact line, is detailed in Table 6.
Table 6 — Factor K icewind for contact wires Type of overhead contact line Wind and ice load Wind load
Contact and catenary wire automatically tensioned 0,95 1,00 Contact wire automatically tensioned and catenary wire fixed termination 0,90 0,95
Single contact wire automatically tensioned 0,90 0,95
Contact and catenary wire fixed termination 0,70 0,80
5.3.5 Efficiency of tensioning devices K eff
The efficiency of tensioning devices is represented by the factor \( K_{\text{eff}} \) For proper design and installation, \( K_{\text{eff}} \) is typically assumed to match the efficiency values provided and verified by the supplier.
Where fixed terminations are used, K eff shall be equal to 1,0
The termination fittings' impact is determined by the K clamp factor, which is set to 1.00 when the clamping force meets or exceeds 95% of the contact wire's tensile strength If the clamping force is lower, the K clamp value is calculated as the ratio of the clamping force to the tensile strength.
5.3.7 Welded or soldered joints K joint
The factor K joint determines the effect of welded or soldered joints, equating to 1.00 when no joints are used If joints are present, K joint is calculated as the ratio of the tensile strength of the welded or soldered joints to the higher tensile strength of the contact wire Additionally, the minimum tensile strength of the joint must comply with EN 50149 standards.
5.4 Mechanical design of catenary wire loads 5.4.1 Permissible tensile loading F w
The maximum allowable working tensile load of catenary wire is determined by the parameters outlined in sections 5.4.2 to 5.4.7, each weighted by an individual factor To calculate this load, the minimum breaking load \( F_{B_{\text{min}}} \) of the catenary wire is multiplied by the product of these factors and a factor \( n \), which must not exceed 0.65.
The maximum permissible working tensile load shall be determined from: load clamp eff ice wind temp
The K temp factor is set to 1.0 when the maximum working temperature remains within the limits specified in Table 1 If the working temperature exceeds these values, the factor will be decreased based on the percentage reduction in tensile strength.
5.3.4 Wind and ice loads K icewind
The maximum tensile strength of contact wires is influenced by wind and ice loads, which are determined by the design of overhead contact lines The factor \( K_{icewind} \), which varies based on these loads and the specific type of overhead contact line, is detailed in Table 6.
Table 6 — Factor K icewind for contact wires Type of overhead contact line Wind and ice load Wind load
Contact and catenary wire automatically tensioned 0,95 1,00
Contact wire automatically tensioned and catenary wire fixed termination 0,90 0,95
Single contact wire automatically tensioned 0,90 0,95
Contact and catenary wire fixed termination 0,70 0,80
5.3.5 Efficiency of tensioning devices K eff
Mechanical design of other stranded conductor loads
For stranded conductors, other than catenary wires, the requirements of 5.4.1 to 5.4.7 shall only apply if the working load exceeds 40 % of the calculated breaking load of the stranded conductor.
Mechanical design of solid wire loads
Solid wires in overhead contact line systems other than contact wires shall not be loaded over 40 % of the minimum breaking load.
Mechanical design of ropes of non-conducting materials
Ropes made from non-conductive materials should only be utilized within their specified working load limits It is crucial to consider factors such as shearing loads, bending radius, termination arrangements, and elongation These guidelines are applicable to synthetic fiber ropes that feature an external synthetic sheath for fiber protection For more information, please consult EN 50345.
The maximum permissible working tensile load of a rope is determined by multiplying the minimum breaking load \( F_{B_{\text{min}}} \) of the combined fibers by specific individual factors (refer to sections 5.7.3 to 5.7.7) and a factor \( n \) that does not exceed 0.45.
The maximum permissible working tensile load shall be determined from
F w = F Bmin x n x K wind x K ice x K clamp x K load x K radius
Wind load is considered by the factor K wind depending on the wind speed:
K wind = 1,00 for wind speed ≤ 100 km/h;
K wind = 0,90 for wind speed > 100 km/h
The effects of ice loads shall be taken into consideration:
The effect of termination fittings shall be considered by the factor K clamp:
K clamp = 1,00 for cone end termination fittings;
The effect of vertical loading shall be considered using the factor K load:
K load = 0,7 when vertical loads attached;
NOTE Examples of vertical loads to be considered are direction indicators or feeding cables for traffic lights or for the overhead contact line
The effect of the radius on the ropes shall be considered by the factor K radius according to Table 10
Table 10 — Factor K radius for ropes of non-conducting materials
Suspension systems
Automatically tensioned equipment shall be suspended from supports which allow longitudinal movement Fixed termination equipment may be supported from fixed supports Where line speeds are greater than
100 km/h or where high operational currents demand it, a catenary wire type suspension should be used.
Tensioning systems
To maintain optimal performance, the tensions in the contact and catenary wires must adhere to system design parameters For effective current collection at speeds exceeding 100 km/h, automatic tensioning of the contact wires is essential Additionally, the catenary wires will also be automatically tensioned as required by system parameters At speeds above 225 km/h, both the catenary and contact wires will be automatically tensioned independently.
Automatically tensioned equipment can experience variations in local tension within the overhead contact line due to the movement of registration arms or cantilever frames along the track It is essential to consider the maximum acceptable tension variation in the overhead contact line.
Geometry of overhead equipment
5.10.1 Horizontal deflection of contact wire
Under specific environmental conditions and mechanical tolerances, the horizontal deflection of the contact wire and pantograph must prevent the contact wire from sliding off the pantograph head, except at designated contact wire takeover points Each project should specify a minimum stagger value to ensure sufficient mechanical clearances and reduce wear on both the contact wire and pantograph strip Additionally, the contact wire should remain within the pantograph's working width during normal operational conditions.
The wind force acting on conductors must be evaluated, and the maximum cross track deflection in either direction should be determined This assessment of wind force on each conductor should comply with established guidelines.
Clause 6, for individual spans, or applying special national conditions where applicable
For calculation of deflection of the contact wire, wind forces shall be applied to the contact and catenary wires Dropper wires may also be considered
The movement of the contact wire, combined with structural deflection, must ensure that the contact wire deviation remains within the maximum limits set by the system design This deviation, when considered alongside the contact wire stagger in still air, should be maintained at all points along the track.
Mechanical and electrical clearances of conductors to other parts of the railway infrastructure, when subject to wind, shall similarly be verified
The design uplift of the contact wire at the support, considering the maximum span length under normal operating conditions, must be assessed through calculation, simulation, or measurement It is essential to ensure that the space for the free and unrestricted uplift of the contact wire at the support is at least twice the design uplift If the design incorporates restrictions to the uplift of the contact wire, a minimum factor of 1.5 should be applied.
5.10.3 Variation in contact wire height
In cases where local conditions, such as bridges, necessitate a change in contact wire height, it is essential to implement this adjustment with the minimal gradient possible The design specifications for gradients and gradient changes must adhere to the maximum values outlined in Table 11, which are determined based on speed.
Speed up to Maximum gradient Maximum change of gradient km/h ‰ ‰
The minimum height of the contact wire must exceed the swept envelope, ensuring adequate electrical clearance in the air and accommodating the minimum working height of the pantograph This is essential to prevent arcing between the contact wire and the grounded components of vehicles.
See Figure 1 for the relationship between contact wire heights and pantograph working heights
5.10.5 Minimum design contact wire height
The minimum design contact wire height shall be calculated by adding all downwards movements of the contact wire to the minimum height Consideration shall be given to
vertical tolerance on the track position,
downwards installation tolerance for the contact wire,
downwards dynamic movements of the contact wire,
effects of ice load and temperature on the conductors
It is permissible to set the nominal height for an overhead contact line in the range between the minimum and the maximum design heights of the contact wire
NOTE Specific requirements for contact wire heights for interoperable lines are given in EN 50367
5.10.7 Maximum design contact wire height
The maximum design contact wire height is determined by subtracting the potential upward movements of the contact wire from the maximum working height of the pantograph This calculation ensures optimal performance and safety in overhead line systems.
vertical tolerance of the track,
uplift of the contact wire by the pantograph,
upwards dynamic movement of the contact wire,
uplift of the contact wire due to wear,
uplift of the contact wire due to any effect of temperature changes in the conductors
LPupp upper operating position of pantograph or collector (see EN 50206-1:1998, 3.2.12)
LPlow lower operating position of pantograph or collector (see EN 50206-1:1998, 3.2.11)
WR working range of pantograph or collector (see EN 50206-1:1998, 3.2.13)
KE/KLG kinematic envelope / kinematic load gauge height
HCWmin minimum contact wire height
HCWmax maximum contact wire height
HCWd,min minimum design contact wire height
HCWd,max maximum design contact wire height
HCWnom nominal contact wire height
DA1 design allowances exceed the minimum height clearance (HCWmin) and include a vertical tolerance for the track, a downward installation tolerance for the contact wire, allowances for downward dynamic movements of the contact wire, and considerations for the effects of ice load and temperature on conductors.
The DA2 design allowances specify that the maximum height of the contact wire (HCWmax) must accommodate a vertical tolerance of 5 units for the track, an uplift of 6 units caused by the pantograph's dynamic movement, and an upward installation tolerance of 7 units for the contact wire Additionally, the design must account for an uplift of the contact wire due to wear and temperature fluctuations in the conductors.
Contact line arrangement above turnouts and crossings
Contact lines above turnouts and track crossings must be designed to allow traversal in all directions at the intended speeds, while ensuring compliance with the permissible range of contact forces as specified in Table 4.
The design of crossing points must ensure that no contact wire slips below the pantograph contact strips, taking into account the sway and skew of the pantograph Additionally, considerations for contact wire uplift and lateral deflection caused by wind are essential It is important that both incoming contact wires are positioned on the same side of the pantograph head in relation to its central axis.
To ensure effective operation, it is essential to use appropriate remedies like cross contact bars and cross droppers, which help lift both contact wires when a pantograph passes over them Additionally, it is important to account for the temperature-related longitudinal expansions of the contact wires when implementing these solutions.
To avoid the use of cross contacts alternative equipment arrangements may be used to prevent the effects of a significant dynamic uplift of the pantograph.
Overlap arrangements
Overlaps are essential for allowing the pantograph to transition smoothly between tension lengths without reducing speed or interrupting power supply to the traction unit The design must consider the number and lengths of spans, as well as the variations in adjacent span lengths and contact wire gradients within overlaps, ensuring compliance with permissible contact forces and elasticity differences Additionally, it is crucial to account for maximum running speeds and track radii in the design process.
Uninsulated overlaps in automatically tensioned equipment must have supports that allow for the free movement of the contact line, accommodating temperature-related longitudinal expansion.
For insulated overlaps the minimum dynamic electrical clearance of parallel conductors shall, under the specified environmental conditions, be maintained The required static electric clearance in air shall be met
Uninsulated overlaps should be permanently connected by a jumper Insulated overlaps should be connected, during operational conditions, by a disconnector or via a substation.
Specific requirements for overhead contact lines for trolleybus systems
The typical characteristic of an overhead contact line system for trolleybus applications is twin contact wires that are electrically separate
The overhead contact line in trolleybus systems is essential for transmitting energy from electric substations to the trolleybus units while ensuring safe return To achieve this, the electrical system, comprising cables and feeding/return wires, must be designed according to the specifications outlined in sections 5.13.2 to 5.13.6.
The trolleybus service characteristics and operational requirements should be taken from National Standards
When installing overhead contact lines, it is essential to consider the environmental operating conditions and the urban area involved, while paying special attention to national requirements for structural clearances.
The trolleybus characteristics and operational requirements include
right-of-way types: the types of road or rail alignments (e.g., street, reserved, grade-separated, etc.) commonly used for each different mode,
average speed: the average origin-to-destination speed for each mode in revenue service This includes time spent; at station stops, in traffic and due to other delays,
maximum speed: the top speed the vehicle is capable of reaching on a straight, level right-of-way way with no curves, gradients, stops, traffic signals or other delays,
right-of-way dimensions: the width and height of right-of-way needed to accommodate the vehicle in dynamic mode according to modern standards of safe operation,
minimum curves: the tightest curves that may be used for a given transit mode, measured as the radius of the curve to the centre line of the transit vehicle,
road surface gradients: the steepest gradients that may be used for a given transit mode without compromising reliability or safety of operations
The distance between the feeding and return contact wires shall be either 0,60 m or 0,70 m, with a maximum tolerance of ± 15 mm
In a d.c system, when one pole is earthed or linked to the return circuit of a tram or light rail system, the contact wire for that pole must be positioned outside the right-of-way.
2 overhead contact line: (−) return wire
3 axis of right of way
Figure 2 — Position of return wire in relation to right-of-way
The assemblies of an overhead contact line (wires, suspension, switches and crossing) shall be so positioned as to allow
a regular vehicle circulation along the route,
a correct approach to platform stops,
overtaking of another vehicle of the maximum admissible dimensions for road vehicles
The following characteristics shall be determined and incorporated into the system design:
nominal voltage of the overhead contact line;
type of trolleybus and road characteristics;
maximum and minimum road gradient of the route;
maximum and permanent current of the vehicle;
type of traction (by resistance, chopper, inverter, etc.);
type of braking (by resistance, energy saving, etc.);
environmental characteristics of the vehicle;
trolleybus horizontal displacement from overhead contact line
In particular, the following information shall be considered for the current collector:
current collector dimension and type;
construction characteristics of the current collector and all equipment that comprises the overhead contact line, such as switching and crossing points;
static contact force between the current collector and contact wire;
range of the contact forces related to the dynamic movement of the vehicle and variation of the height of the overhead contact line;
NOTE CLC/TS 50502 provides information regarding safety requirements and connection systems for electric equipment in trolley buses
The range of static contact force applied to feeding and return wires shall be between 70 N and 120 N for each wire
5.13.6 Trolleybus in the vicinity of tramways
In urban areas, it is common for trolleybuses and trams to operate using a shared supporting system, where the overhead contact lines for both modes of transport are suspended from the same infrastructure.
The distance between the contact wires for trolleybus and tramways shall not be less than the distance between the feeding and return wires
In any case the following shall be determined and incorporated into the system design:
the static and kinematic load gauge of the trolleybus and tram;
The distance between the return wire and the tramway's overhead contact line must be at least equal to the distance between the feeder and return contact wires of the trolleybus overhead contact line.
Overhead contact lines for trolleybuses and tramways are generally supplied by separate feeding sections to facilitate maintenance activities.
Tolerances and limits
Construction-influenced parameters must adhere to specific tolerances and limits, which vary based on the type of contact line These tolerances and limits are determined by safety requirements, current collection quality, interface compatibility, and aesthetic considerations It is essential to account for the interdependencies among these values, as well as the impact of external factors such as climate, pantograph design, and power supply.
Operational limits must be established for parameters that can change during operation, such as track position shifts, as they impact system performance It is essential to account for the relationship between construction tolerances and operational limits, considering potential parameter changes over time between inspections and maintenance.
The limits for interoperable lines are specified in the TSI Energy, serving as a guideline for various applications as determined by the purchaser and system designer.
The tolerances and limits shall be implemented in the design and kept during construction and operation
Table 12 outlines the parameters that require defined tolerances and limits, categorized into four main groups based on their significance to the system Each group includes examples related to construction and operation, with specific values to be determined by the system designer.
Table 12 — Important parameters to assist in the definition of tolerances and limits
Type of parameter Tolerances Limits To be defined for:
Construction Operation Type A, safety related dimension of foundations, position of foundations perpendicular to track, rotation angle of masts, contact wire stagger
X X safety clearance, electrical clearances, contact wire height (minimum/maximum), maximum deviation of contact wire due to wind, maximum contact wire wear
Type B pertains to the quality of the current collection system, which is influenced by factors such as the height and distance between droppers, the positioning of foundations along the track, the inclination of droppers, and the maximum and minimum contact forces Additionally, variations in elasticity (u) play a crucial role in the overall performance of the system.
X X X contact wire gradient, change of gradients, inclination of droppers perpendicular to track X X
Type C, compatibility related geometrical tolerances of component interfaces X X
Type D, aesthetics related mast height X X inclination of poles, inclination of horizontal cantilever tubes X X
Basis of design
Structures for overhead contact lines may be designed in accordance with the general principles contained in 6.1.2 to 6.1.6 or as described in EN 1990:2002
Structures for overhead contact line shall be designed and constructed in such a way that during their intended life
they will perform their purpose under a defined set of conditions with acceptable levels of reliability and in an economic manner This refers to aspects of reliability requirements,
they will not be liable to progressive collapse if a failure is triggered in a defined component This refers to aspects of security requirements,
they will not be liable to cause human injuries or loss of life during construction and maintenance This refers to aspects of safety requirements
An overhead contact line must be designed, constructed, and maintained with a strong emphasis on public safety, durability, robustness, maintainability, and environmental factors.
To meet the outlined requirements, it is essential to select appropriate materials, implement effective design and detailing, and establish control procedures for design, production, construction, and usage tailored to the specific project.
6.1.3 Design with regard to structural limits
Generally, a distinction is made between ultimate failure limit and serviceability limit
Ultimate failure limit states refer to conditions leading to structural collapse or similar failures caused by excessive deformation, instability, overturning, rupture, or buckling These failure limits are crucial for ensuring the reliability and safety of supports, foundations, conductors, and equipment, as well as protecting the safety of individuals.
Serviceability limit states refer to specific conditions where the operational requirements for an overhead contact line are not fulfilled These requirements focus on the mechanical performance of supports, foundations, conductors, and equipment, ensuring the seamless transmission of electric energy to vehicles.
Serviceability limits must account for deformations and displacements that impact the functionality of the overhead contact line, as well as any potential damage that could negatively affect the durability and performance of the supports and equipment.
Serviceability limits may be given in the purchaser specification
Design with reference to ultimate failure and serviceability limit states shall be carried out by
setting up structural and load models for relevant ultimate and serviceability limits to be considered in the various design conditions and load cases,
Design values are typically derived from characteristic or combination values as specified in this European Standard, along with the partial factors outlined in the same standard.
EN 1992 series, EN 1993 series, EN 1995 series, EN 1997 and EN 1998 series or in purchaser specifications,
verifying that the limits are not exceeded when design values for actions, material properties and geometrical data are used in the model,
reference to Eurocodes, alternative standards or experimental data for materials not covered by this standard
Actions can be classified by their variation in time or by their nature and/or structural response:
NOTE For the definition of an ‘action’, reference can be made to EN 1990:2002, 1.5.3.1
Permanent actions (G) encompass the self-weight of supports, foundations, fittings, and fixed equipment, as well as the self-weight of conductors and the impact of tensile loads on conductors, excluding ice and wind effects Typically, the characteristic value of these permanent actions can be represented as a single value, G K, due to the minimal variability associated with G.
Variable actions (Q) include wind loads, ice loads, and other imposed loads, which can be evaluated through probabilistic methods, deterministic approaches, or relevant standards like EN 50125-2 The effects of conductor tensile loads from wind, ice, and temperature variations are also considered variable actions, influenced by the design of the contact line The characteristic value Q K represents a nominal value for deterministic actions or an upper limit with a specified probability of not being exceeded, as well as a lower limit with a defined probability of not being lower during a reference period.
Accidental actions (A) refer to loads associated with failure containment, typically represented by a characteristic value A K that corresponds to a specified value Dynamic actions occurring after the operation of a fall arresting device or the failure of a contact or catenary wire can be treated as equivalent static actions.
Construction and maintenance loads (Q PK) encompass various factors such as working procedures, temporary guying, and lifting arrangements The characteristic values of Q PK are predetermined to ensure the safety of individuals involved in these operations.
Overhead contact lines can be engineered to meet specific reliability levels concerning variable loads, which are governed by probabilistic laws The reliability level is quantified by the return period \( T \) associated with climatic actions.
6.1.6 Models for structural analysis and resistance
Calculations must utilize suitable design models that incorporate relevant variables to accurately predict structural behavior, serviceability, and failure limits These models should be grounded in established engineering theories and practices, and should be experimentally verified when necessary.
When analyzing the interaction between foundations and soil, it is crucial to consider the loads from supports, active soil pressure, the permanent weight of the foundation and soil, and the buoyancy effects of groundwater These factors, along with the reaction forces from the soil strata, must be included in foundation calculations Additionally, it is important to establish criteria for acceptable foundation settlements, imposed deformations on supports, and the contact lines and inclinations of the supports.
For urban mass transportation systems the calculations described in this subclause are not required
6.1.7 Design values and verification methods
Reliability in this standard is attained through the use of partial factors and suitable return periods for climatic actions, grounded in a statistical approach, alongside partial factors for deterministic actions and material properties The partial factor method ensures that the impacts of design actions remain within the design resistance at the failure limit, while also meeting performance requirements related to the serviceability limit.
The design value F d of an action is expressed in general terms as:
F =γ × (1) where γF is the partial factor for actions;
F K is the characteristic value of an action
The partial factor for actions, denoted as γF, is influenced by the chosen reliability level and considers potential adverse deviations, modeling inaccuracies, and uncertainties in evaluating action effects In deterministic calculations that involve accidental loads, this partial factor can be applied to the effects of characteristic action values, such as the tensile load on conductors, which includes the impacts of wind and ice.
The design value X d of a material property is generally defined as: