Post on 16-Oct-2021
Fakultät Bauingenieurwesen, Institut für Massivbau, Prof. M. Curbach
Bridge Loads
Dresden, May 6th, 2019
Dr.-Ing. Patricia Garibaldi
Concrete bridges
Applicable codes:
• Live load on bridges: Eurocode 1-Part 2 (EC1-2)• Temperature: Eurocode 1-Part 1-5 (EC1-1-5)• Snow: Eurocode 1-Part 1-3 (EC1-1-3)• Wind: Eurocode 1-Part 1-4 (EC1-1-4)
Include modifications as required by German Annex: DIN EN 1991-2: 2010 (12), and other applicable annexes.
Including relevant loads for roadway, railway bridges, and pedestrian bridges as well as non-dynamic loads induced by pedestrians and tra.
Folie 2
Concrete bridges
Classification of loads:
Loads can be classified according to the following criteria:
• Situation (normal, extraordinary, earthquake)• Ocurrence (permanent, variable)• Frequency
Folie 3
Concrete bridges
Classification of loads based on frequency of ocurrence:
Frequency
Characteristic value - 1000 yearsNon-often value - 1 year Often value - 1 weekQuasi permanent value - exceeds 50%
probability
Folie 4
Concrete bridges
Permanent loads – Typical values
Dead weight:• Reinforced concrete γ = 25 KN/m3
• Steel γ = 78.5 KN/m3
Additional permanent loads:(usually applied as superimposed loads, at end of construction)
Pavement (asphalt) γ = 24 KN/m3
• Railing (each) 0.5 KN/m• Steel guardrail (each) 0.5 KN/m Cap, parapet, concrete barrier γ = 25 KN/m3
Folie 5
Concrete bridges
Permanent loads – Typical layout (asphalt)
Folie 6
Concrete bridges
Permanent loads – Typical layout (barriers)
Folie 7
Concrete bridges
Permanent loads – Typical values (cont.)
Ground motion:• Probable and possible soil settlements „s“• Difference in soil settlements „Δs• Data are provided by geotechnical experts. Horizontal soil
supports stiffness can be calculated from he modulus of subgrade (horizontal springs), for example, in the case of pile foundations:
ks,k = Es,k / Ds
ks,k = Modulus of horizontal subgrade reaction of soilEs,k = Young’s modulus of soil (provided by geotechnical engineer)Ds = Diameter of pile
Consider also skin friction and ultimate bearing capacity of soil and foundation elements.
Folie 8
Concrete bridges
Live loads for roadway bridges
Scope of DIN EN 1991-2:
• Span lengths <200 m• Roadway widths < 42 m
In other cases, bridge specific load assumptions shall be made, because recommendations according to EC1, may be too conservative.
Impact factors and mutiple presence factors are already included in the live load model definitions.
Folie 9
Concrete bridges
Live loads
• Notional lanes• Live load models
Tandem systemUniform loads
• Horizontal lanesBreaking loadsCentrifugal forces
• Fatigue load models• Railway loads• Pedestrian bridge loads
Folie 10
Concrete bridges
Notional lanes
In general, notional lanes have a width, we = 3 m.
For narrower roadway widths, the notional lanes width are defined according to Table 4.1, below.
Folie 11
Concrete bridges
Notional lanes
For the general case, where wo ≥ 6m, the number of notional lanes, „n“, is defined as:
n = integer (wo/we)
where:
wo: width of roadway (distance between curbs with h≥7 cm)we: width of nomimal lane = 3 m
The reamining area is called the „residual area.“
But, how is the roadway width actually defined?
Folie 12
Concrete bridges
Notional lanes Roadway width definition according to EC1-2, section 4.2.3, (page 32)
Folie 13
Concrete bridges
Notional lanes Roadway width definition according to EC1-2, section 4.2.3, (page 32)
Folie 14
Concrete bridges
Notional lanes
Folie 15
Concrete bridges
Live loads
• Notional lanes• Live load models
Tandem systemUniform loads
• Horizontal lanesBreaking loadsCentrifugal forces
• Fatigue load models• Railway loads• Pedestrian bridge loads
Folie 16
Concrete bridges Folie 17
Live load models
Live load models are composed of a combination of double axle load (tandem system), that represent an idealized design truck, and uniform distributed loads that account for the effect of cars, smaller trucks or crowds of people.
•Loads are further modified by adjustment factors that may be defined by each country. •The applicability of the load models can also be further defined by each country. •In the case of Germany, factors in the Eurocode for the load model 1 are overrided by the values given in the national German annex.•Load models 2 and 3 are not considered in Germany. It is assumed that load model 2 is included in load model 1. •The effect of special trucks on the existing and aging infrastructure, such as those considered in model 3, is still being investigated in Germany, and for now, there are not freely allowed on roads.
Concrete bridges Folie 18
Live load modelsaccording to EC1-2, section 4.3.1, (page 35)
Concrete bridges
Live load models
Live load models shall be applied to create the worse adverse effect.
Different live load models may be combined when required by the geometry of the bridge and the use of the structure (pedestrian loads for example).
Live load model 4 shall only be considered as a transient condition, for global checks.
Folie 19
Concrete bridges
Live load models – Model 1
Folie 20
Concrete bridges
Live load models – Model 1
Folie 21
Concrete bridges
Live load models – Model 1
Characteristic values of axle loads Qik, include each a pair of wheel loads. In the case of model 1, the wheel are assumed to have a tire contact area of 0.4 m x 0.4 m. For load model 2, the tire contact are is assumed to be 0.35 m x 0.6 m. The adjustment factors given in th Eurocode (shown below) are superseded.
Folie 22
Concrete bridges
Live load models – Model 1Adjustment Factors with German national annex:
Tanden System 𝛼𝛼Qi
Lane 1 1.0Lane 2 1.0Lane 3 1.0Other lanes 0.0
Uniform Load 𝛼𝛼qi qi
Lane 1 1.33 (9 kN/m2) = 12 kN/m2
Lane 2 2.40 (2.5 kN/m2)= 6 kN/m2
Lane 3 or more 1.20 (2.5 kN/m2)= 3 kN/m2
Residual area 1.20 (2.5 kN/m2)= 3 kN/m2
Folie 23
Concrete bridges
Live loads – Example layout (UDL system)
Folie 24
Concrete bridges
Live loads – Example layout (Tandem system)
Folie 25
Concrete bridges
Live load models – Model 1
Arrangement of loads to investigate the local effect, for example the transverse analysis of structure.
Folie 26
Concrete bridges
Live load models – Model 2
Folie 27
Concrete bridges
Live load models – Model 3 Special vehicles (example)
Folie 28
Concrete bridges
Live load models – Model 3 Special vehicles (example)
Folie 29
Concrete bridges
Live load models – Model 3 Special vehicles combined with Model 1
Folie 30
Concrete bridges
Live load models – Model 4
Folie 31
Live load models 4 controls for very long bridges, specially in urban areas.
Concrete bridges
Live load models –Tire distribution pressure
Folie 32
Concrete bridges
Live loads
• Notional lanes• Live load models
Tandem systemUniform loads
• Horizontal lanesBreaking loadsCentrifugal forces
• Fatigue load models• Railway loads• Pedestrian bridge loads
Folie 33
Concrete bridges
Horizontal loads – Breaking loads
Loads induced by breaking and accelerating:
60% of the tandem system of lane 110% of the UDL of lane 1
Folie 34
Concrete bridges
Horizontal loads – Breaking loadsExample (all piers have neoprane bearings and can resist the breaking loads)
Folie 35
Distribute QLK along the whole length of the structure, and then, apply a fraction of the total load only to the bearings that are supporting the breaking force. Use the tributary span length corresponding to the pier resisting the loads.
Concrete bridges
Horizontal loads – Centrifugal forces
The centrifugal force Qtk should be taken as a transverse force acting at the finished carriageway level and radially to the axis of the carriageway.Notice the decrease in load as the radius increases.
Folie 36
Concrete bridges
Multi-component actions – Load combinations
Folie 37
38
Accompanying value of a variable action: (ψ Qk)
Source: Leonardo da Vinci Pilot Project CZ/02/B/FP -134007. Development of skills facilitating the implementation of the Eurocodes. Handbook 1- Guide to interpretative document for essential
Slide
Concrete bridges
Live loads
• Notional lanes• Live load models
Tandem systemUniform loads
• Horizontal lanesBreaking loadsCentrifugal forces
• Fatigue load models• Railway loads• Pedestrian bridge loads
Folie 39
Concrete bridges
Fatigue load models (example)
Folie 40
Concrete bridges
Railway loads (Annex D & E, 12 types), as an example:
Folie 41
Concrete bridges
Pedestrian bridge loads
Folie 42
Concrete bridges
Pedestrian bridge loads
Folie 43
Concrete bridges
Pedestrian bridge loads
Folie 44
Concrete bridges
Pedestrian bridge loads
Folie 45
Concrete bridges
Pedestrian bridge loads
Folie 46
Service vehicles are usually maintenance, fire or emergency vehicles.
Concrete bridges
Temperature
Folie 47
Eurocode 1 – Part 1-5. Effect are dependant of location, seasonal changes, and boundary conditions. The following cases are considered:
Concrete bridges
Temperature Coefficients of linear expansion
Folie 48
Concrete bridges
Temperature
Folie 49
Three diferent types of bridge decks are considered:
Concrete bridges
Temperature
Temperature ranges - linear expansion – case (a) (expansion shall be measured using the length from the point of zero movement in the structure, to the point of interest):
Folie 50
Te, max Te,min
Group 1 +51°C -26°C
Group 2 +41°C -20°C
Group 3 +37°C -17°C
Air temperature +37°C -17°C
Mean temperature +10°C
Concrete bridges
Temperature
Folie 51
Linear temperature variation along height (case c):
Concrete bridges
Temperature Gradient case (d)(Example, not eurocode values)
Folie 52
Concrete bridges
Temperature Gradient
Folie 53
Concrete bridges
Temperature Gradient
Folie 54
Concrete bridges
Temperature Gradient
Folie 55
Concrete bridges
Snow Loads – Eurocode 1 Part 1-4Wind Loads - Eurocode 1 Part 1-5
Folie 56
Concrete bridges
Inter-relationship between design and construction
Folie 57
Concrete bridges Folie 58
Inter-relationship between design and construction
Concrete bridges Folie 59
Time Dependent Effects (creep and shrinkage)
T = INITIAL
T = INFINITYsay (10000 days)
Concrete bridges Folie 60
Time Dependent Effects (creep and shrinkage)
Typical parameters, (example):
Concrete bridges Folie 61
Worst live load effects
Live load effects are ussually maximized (or minimized) by proper placement of live load to create maximum (or minimum) effects.
This is usually done with the help of influence lines
Concrete bridges Folie 62
Muller Breslau Principle
The influence line follows the profile of the deflected shape of a structure generated by releasing the restraint corresponding to the action and applying a unit displacement or rotation in the direction of the action.
Concrete bridges Folie 63
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Application and Live Load to Produce Maximum Positive Moment – Longitudinal Direction
Concrete bridges Folie 64
Application and Live Load to Produce Maximum Negative Moment – Longitudinal Direction
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load Distribution (AASHTO Example)
Folie 65
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load – Influence Lines
Folie 66
Concrete bridges Folie 67
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load – Influence Lines
Concrete bridges Folie 68
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load – Influence Lines
Concrete bridges Folie 69
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load Distribution
Concrete bridges Folie 70
Design Example by Parsons and Brickerhoff , Proposed AASHTO-PCI-ASBI Standard Box Girder, 1996
Live Load – Influence Lines
Concrete bridges Folie 71
Worst live load effects
Live load effects are ussually maximized (or minimized) by proper placement of live load to create maximum or minimum effects.
Notice the difference between the following terms (as related for example to moment)
Moment Diagram – Moment at every point in the structure when a load is placed at a fixed location.
Influence line for maximum moment at a given point – Moment at a single pointcreated by a unit load moving along the length of the structure.
Moment envelope – Compilation of all maximum load effects along the length of the structure, created by various load combinations that maximize the effect at each point.
Concrete bridges Folie 72
Worst live load effectsMoment diagram, when a unit load is place at 0.4 L of span 1
Concrete bridges Folie 73
Worst live load effectsinfluence diagram at 0.4 L of span 1Example: Span 1= 12 m, Span 2 = 14.4 m
Concrete bridges Folie 74
Worst live load effectsMoment envelope for a uniform distributed unit lane load
Concrete bridges Folie 75
Worst live load effectsUsing influence charts to estimate the profile and value of influence ordinates.
Concrete bridges Folie 76
Worst live load effectsUsing influence charts to estimate the profile and value of influence ordinates.(Tables give a influence coefficient)
Moment diagramLoad at 0.4 of span 1
Influence diagram for momentat 0.4 of span 1
Moment Envelope due to lane load
In this table, coefficient values have been normalized, with respect to the shortest length span L1, and by the use of a unit load. Therefore, the actual resulting in a given structure, with a shortest span = L1, longest span L2= 1.2 . L1due to a:concentrated load =P, or uniform load = wis given by:
Moment:M= P.(coefficient). L1
M=w.(coefficient).L12
ShearV= P.(coefficient)V= w. (coefficient)
Concrete bridges Folie 77
Self-study
Give it a try!!
Find the moment envelopes and shear envelopes for a continuous double span bridge. Each span measures 12 m. Consider live load model 1 only.