CHAPTER 4: LOADS ON BRIDGES Introduction
Bridge structures , like buildings, must be designed to resist various kinds of loads: gravity as well as lateral.
The major components of the loads acting on highway bridges are DEAD LOAD, LIVE LOAD, ENVIRONMENTAL ENVIRONMENTAL LOADS.
Two major components of the bridge design process are the Design of the superstructure and the design of the substructure .
Loads on bridges
Superstructure s
Gravity loads
Substructure
Longitudinal forces
Lateral loads
Gravity loads
Dead load
Live load
Impact
Vehicular loads Pedestrian & other loads
Truck loading
Lane loading
Alternate loading
Extra legal loads
Longitudinal forces
Longitudinal Longitudinal load l oad due to LL
Thermal load
Lateral load
Wind
Seismic Activity
Centrifugal forces
Substructure
Gravity load
Lateral load
Miscellaneous loads
Gravity loads
Dead load
Live load
Loads from superstructures
Loads from substructures
Selfweight
Lateral loads
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Longitudinal load from superstructures Wind load Seismic Load Earth pressure Stream current Ice pressure Thermal load
Miscellaneous loads
Buoyancy
Uplift
Loads on Bridge superstructures
1. Gravity loads - are caused by the deadweight of the bridge itself, the superimposed dead load and the live load. > Dead load – load – consist consist of the weight of the superstructure plus the weight of other items such as utility pipes, conduits and cable. The self weight of the superstructure consist of deck, side walk, curbs, parapets, railings, supporting stringer and the floor beam > Live loads – loads – specified specified in the AASHTO standard specifications . AASHTO highway live loads – highway bridges are subjected to a variety of nonstationary loads, such as those due to vehicles, motorcycles, bicycles, equestrians and pedestrians. “ live loads refers refers to loads due to moving vehicles that are dynamics.” Highway live loads classified as
– the weights of all vehicles are assumed to be concentrated on the wheels 1. Legal loads – the and are transmitted through them to the axles. The maximum permissible weights for wheels and axles and their sizes are as follows:
Single axle weight – total gross weight imposed on the highway by the wheels of any single axle of a vehicle is limited to 20 kips, including any and all weight tolerances. Tandem axle weight - total gross weight imposed on the highway by a tandem axle shall not exceed to 34 kips, including any and all weight tolerances.
Maximum permissible axle group weight - total gross weight imposed on the highway by ant group of two or more consecutive axle on a vehicle or combination. Maximum permissible vehicle gross weight - total gross weight imposed on the highway by a vehicle or a combinations of vehicles with two or more consecutives axles. Maximum sizes Maximum height: 13ft 6 in Maximum overall length of a single truck: 40ft Maximum overall length of a single two axle or three axles bus: 40ft Maximum overall length of a semitrailer: 53ft
2. Design loads – design – design live loads for highways have been and continue to be subject of considerable research. Design vehicular live loads divided into 3 categories categories
1. Design truck loading – referred – referred to as standard truck loading, this originated in the 1920’s , and it has been revised periodically, basic format has remained unchanged. Two systems of loadings are provided: H loading and heavier HS loading ( S refers to semitrailer), there are two standard classes of loadings (AASHTO3.7.2) which is designated (AASHTO3.7.3) as follows:
H15-44 and H20-44
HS15-44 and HS20-44
444 refers to the fact that these loadings were standardized and first published in the 1944 AASHTO specifications. H loading consist of two axle truck, 15 and 20 in the loading classification refer to the gross truck weight in tons ( 1 ton= 2000lb) 2. Design lane loading – lane loading was developed to better model loading on long spans, where a string of light vehicles might be cri tical. 3. Alternate military ( or design tandem) loading – this loading originated in 1956 as a federal highway administration requirement for bridges on the interstate highway system, to provide load carrying capacity for certain heavy military vehicles.
Impact – defined – defined as a suddenly applied load, whose period of application is shorter than the fundamental period for the structure on which the load is applied.
Provision in AASHTO Specifications = AASHTO 3.8.2 specifies that the dynamic effects of moving loads be expressed as a fraction of the loads according to the following fol lowing empirical formula: I = 50/L + 125 Where: I = Impact factor ( maximum 30% or 0.3)
L = length in ft, portion of the span that is loaded to produce the maximum stress in the member Prior this time, various formulas, based primarily on the opinions of bridge engineers or on limited and inconclusive test, were in use. The two most commonly used were. I = L^2 / L + D & I = 300 / L + 300 300 Japanese Specifications for highway bridge uses an impact formula similar format to that AASHTO I = 20/ 50+L ( L = m)
Effect of Vibrations on Pedestrian in Bridges
> Pedestrian bridges are typically designed for pedestrian loads, which are considered static loads. However, walking across pedestrian bridge can be characterized as a moving repetitive force that may cause the bridge to vibrate. Pedestrian Pedestrian Loading > on most bridges, sidewalks and curbs are provided, and the live load imposed on them should be given due consideration in i n design.
1. Sidewalk floors, stringers, and their immediate supports:85psf 2 Girder, trusses, arches and other members: (a) span 0-25ft: 85lb/ft^2 (b) span 60-100ft: 60lb/ft^2 (c) span over 100ft :according to P = ( 30 + 3000/L) ( 55-W / 50)
P= live load per square foot ( max. 60 lb) L= loaded length of side walk ( ft) W= sidewalk width (ft)
Note that the sidewalk live load is reducible for members or portions of a bridge superstructure spanning 60 ft or more that receive load from members that directly support the deck. 3. Pedestrian traffic: 85lb/ft^2 4. Bicycle traffic: 85lb/ft^2 There is no min. or max. sidewalk width stipulated in the specifications; widths of 3ft to 6ft are commonly used.
Reduction in live load intensity
The reduction is limited to 40% for members receiving load from one level only 60% for others, or R as determined by the following formula ( UBC 6.2) R = 23.1 ( 1 + D/L ) D = dead load per ft^2 of area supported by the members L = unit live load per ft^2 of area supported by the member R = reduction in percentage Longitudinal Forces
It refers to the forces that act in the direction of the longitudinal axis of the bridge, specifically, in the direction of the traffic. These forces develop as a result of the braking effort, or the tractive effort. In both cases the vehicles inertia iner tia force is transferred to the deck through friction between the deck and the wheels. The magnitude of the longitudinal force can be determined using newton’s second law of motion. The force generated by a particle of mass m, in motion is given by: Force = mass x acceleration F = m( dv/dt dv/dt ) = (w/g) (dv / dt) m= W/g = mass of the particle dv/dt = tangential acceleration or deceleration g = acceleration due to gravity= 32.2 ft sec^2 Centrifugal Force
When a particle of mass m moves along a constrained curved path with a constant speed, there is a normal force exerted on particle by constraint. mv2 W v 2 F r g r Where m=w/g= mass of the particle g= acceleration due to gravity v= particle velocity r= instantaneous radius of Curvature of the path Provision for the centrifugal force in AASHTO 3.10 C
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0.00117( S
D)
S 2 6.68 F
Where C= centrifugal force in percent of the live load, without impact. S= design speed in miles per hour D= the degree of the curve ⁴=5729.65/R R= the radius of the curve in feet F= mv²/r AASHTO-LRFD (AASHTO,1994a) Where v= highway design speed (ft/sec) g= gravitational acceleration, 32.2 ft/sec r= radius of curvature of the traffic lane Curb Loading
AASHTO 3.14.2 stipulates a lateral force not less than 500 pounds per linear foot of curb, applied At the top of of the curb, or At an elevation 10 in. above the floor if the curb is higher than 10 in. In AASHTO 2.5.4 stipulates the minimum width of curb to be 18 in. Railing Loading
Depends on the purpose for which the railing is provided ( e.g., vehicular, bicycle, or pedestrian railing r ailing ) , the geometry and type of parapet provided on the deck. Requirements for designing will covered by AASHTO 2.7 Wind loads
Bridges are frequently built on exposed sites and are subject to wind exposure. Wind loads on bridge superstructures depend on the type of bridge, e.g., slab stringer, truss, arch, cable-stayed, or suspension. Other parameters affect wind loads on bridge are wind velocity, angle attack, the size and shape of the bridge, the terrain, and the gust characteristics. Wind effects on bridge structures may be threefold: 1. Static wind pressures 2. Dynamic ( oscillatory ) wind movements 3. Buffeting between adjacent structures. Static wind pressures are those that cause a bridge to deflect or deform. Dynamic wind movements affect long – span span flexible bridges. Oscillate in a number of different moves at low frequencies. Buffeting is defined as the randomly forced vibration of a structure due to velocity fluctuation Slender towers Deck of suspended-span bridges that exhibit aero elastic effects. Static wind pressure the main wind force acting on a bridge
structures, develop as a result of a steady wind exerts a fairly constant pressure in the general direction of the wind. Bernoulli‘s theorem:
1 2
2
C V
Where p= wind pressure p= the mass density of air (0.00233 slug/ft³ sea level 15°c V= wind velocity wind velocity in ft/sec C= coefficient of proportionally, shape factor, Aerodynamic instability means the effect of a steady wind, acting on a flexible structure of conventional cross section, to produce a fluctuating force automatically synchronizing in timing and direction with the harmonic motion of those structures so as to cause a progressive amplification of these motions to dangerous destructive amplitudes. Wind uplift or the vertical component of wind, known in aeronautics as lift. Variation of wind speed with height and terrain roughness Characteristically , the velocity of wind increases from zero at ground surface to a certain maximum at height of approximately 0.5 to 1.0 km above the ground
Retard wind flow
Boundary layer of atmosphere
free atmosphere
Gradient height
Gradient velocity
Aerodynamics Aerodynamics Considerations •
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The literature is replete with the discussion of aerodynamics of an aircraft structures, specifically for the airfoil. The interaction between the wind and the bridge deck and a great deal of research is in progress
– cross section of an airplane’s wing Airfoil – cross
Baytown bridge (482, 1250, and 482 ft ) Houston ship channel Texas 100 year old design wind speed calculated as 110 mph at 30 ft elevation, 160 mph Deck elevation 176 ft above water level in the channel195 mph at tower tops (266 ft above the deck15 % additional gust load Vortex theory
Bridge deck is essentially bluff (i.e., a non- streamlined object), as an compared with and airfoil. Wake - When a steady wind blows perpendicularly across the width of such an object, a zero turbulent flow. Whose number depends on the Reynolds number, Created leeward side past or past the railing edge of the air-foil, On Karman vortex trailvortices trail behind the cylinder in two rows. Mackinac suspension bridge Flutter theory
Flutter refers to an oscillating motion in which two or more modes of oscillation, usually bending and torsion, are usually combined. As wind velocity increases, a critical value is reached, which triggers the flutter motion. It is characterized by rapid build-up of amplitude with little or no further increase in wind speed. Aeroelastic stability considerations 1. Geometry of bridge deck – over-all – over-all cross section shape of the bridge structure 2. Frequency of vibration of the bridge – superstructure – superstructure profiles may be torsionally soft or torsionally stiff. Mechanical damping of the bridge – aeroelastic stability of the bridge can be enhanced by increasing the mechanical damping ration of the bridge Vibration Effects Wind induce vibration is much more pronounced on flexible bridges, such as suspension, short-span rigid and slab stringer bridges. Note that dangerous bridge vibration can be generated due to loads other than vehicular impact and wind. Rhythmical human body motions lasting up to 20 seconds or more lead to almost periodic dynamic forces. Normal walking rate – varies – varies up to 2.3 paces per second or 2.3 Hz (about 4 mph).Note that bridge vibrations within a certain range of frequencies also tend to affect humans (pedestrians) adversely, both physiologically and psychologically. Provision in the AASHTO Specifications for wind loads
AASHTO 3.15, basic wind velocity 100 mph and elevation at 90° longitudinal axis.
Wind load on the structure (superstructure and substructure )
Wind load on the moving load (vehicles on the bridge.
Wind load on superstructure.
Group II and V loadings:
Trusses and arches - 75 psf > 300 – 300 – 500 500 lbs./ linear foot in the plane leeward and windward chords, respectively. Girders and beams – beams – 50 50 psf, > 300 lbs. / linear foot.
Group III and and VI loadings:
Reduced 70 % load of 100 lbs/ linear foot applied at right angles to the longitudinal axis of the bridge, applied 6 ft above the deck as wind load on the moving live load. Wind Load on Substructure Substructure (AASHTO 3.15.2)
Forces transferred from the superstructure these forces depend on the type of superstructure, the skew angle (angle between the assumed wind direction and the normal to the longitudinal axis of the bridge), and the load group combinations. For usual girders and slab bridges of spans not exceeding 125 ft, which constitute most shortshort span bridges? AASHTO 3.15.2.1.3
On the substructure: 50 psf traverse and 12 psf longitudinal
On the live load: 100 lbs/ linear foot traverse and 40 lbs./ linear foot.
Forces applied directly to the substructure. •
On assumed wind pressure of 40 psf, based on the basic wind speed of 100 mph. mph. in the case of skewed wind loading, the analysis can be performed by resolving the applied applied load into components components perpendicular to the end and and the front elevations of the substructure.
Overturning wind loads in AASHTO 3.15.3
20 psf of the deck and sidewalk plan area for group II and V loading combinations
6 psf of the deck and side walk plan area for group III and VI loading combinations
3.10.7 Investigation of Aerodynamic Structural Structural Response by Wind Tunnels Test
3.10.7.1 Application of wind tunnel test
The response of structures to wind-induced forces depends on the characteristic of the coming wind loads and on the geometry and mechanical properties of structures. Wind tunnels test are conducted extensively for aircraft structures. To determine the effects of snow drifts, test power plant, chemical plants, and factories. Types of Wind Tunnels
According to ASCE (1987) classified into four basic categories: 1. Long tunnels 2. Short tunnels 3. Tunnels with passive devices 4. Tunnels with active devices Wind tunnels can be classified as open or closed circuit Tunnels used for civil engineering purpose have cross section that rarely exceed 3 m x 3 m. notable exception is the 9 m x 9 m tunnel of the national research Council of Ottawa, Canada. Types of Wind Tunnels
Model test of the full bridge 1. It represents the proper interaction of the bridge deck, piers, abutments, towers, and cables. 2. It can represent the proper flow distortions on all parts of the bridge if the surrounding topography is modeled as well as the bridge itself 3. In certain cases, the model scale permits the proper turbulent structure of the wind to be modeled as well. Taut Strip Model Test
It was developed to study the behavior of suspension bridges at a larger scale than that which is possible with full models. Section Models Test
Sections model test are quite useful for making initial assessment, based on simple test, of the extent to which a bridge deck shape is aero elastically stable. They can built to scales on the order of 1:50 to 1:25 Advantage Advantage of the allowing the measurement of the fundamental aerodynamic characteristics of the bridge deck. It consist of representative span wise of the deck built to scale, spring supported at the ends to permit both vertical and torsional motion.
Temperature Induced Forces
1. Traditionally the longitudinal movements induced by maximum expected temperature variations, typically + 20°c or - 20°c. 2. Thermal response of the bridge deck is a complex transient phenomenon influenced by many factors 3. Time-dependent solar radiation 4. Ambient temperature 5. Wind speed fluctuations 6. Material properties, heat transfer coefficient for reinforced and prestressed concrete and steel 7. Variation in ambient temperature between the maximum and the minimum during 24 hrs period 8. Type of span-simple or continuous c ontinuous 9. Deck configuration, T-beams, single or multicell reinforced or prestressed concrete girders, concrete deck-steel girder composite, orthotropic bridge 10. Geometrical configuration of the deck, overhang-to-web depth ratio 11. Surface characteristics of the deck Current AASHTO 3.16 provisions specifies the following ranges of temperature Metal structures: Moderate climate
0-120°F
Cold climate
30-120°F
Concrete structures: –
Moderate climate 30°F rise
40°F fall
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Cold climate
45°F fall
35°F rise
Forces on Pier
Stream Current
Floating Ice
Pier - The main support for a bridge, upon which the bridge superstructure rests; Stream current on piers:
While designing bridges if any portion of the structure is submerged in flowing water then it is to be also designed to safely resist the horizontal force due to the water current. Importantly bridge substructures constructed in a region of flowing water should be designed to withstand withst and water pressure which could cause the pier to slide sl ide or overturn. Scour around the bottom of the piers is of great concern in the bridge design. The design for every bridge over a stream should involve a careful study of possible stream velocities. Past flow records are helpful to determine velocities. If this information is lacking, the design engineer should make the best estimate possible with the available data. Intensity of pressure should be calculated from 2
P = KV
(from AASHTO 3.18.1)
P = Intensity of pressure in kg/m^2 due to the water current. K = a coefficient whose value depends depends upon the different shapes the piers V = the velocity of the current in meters/sec Shape of Piers , K value Square ended piers, 1.50
Circular piers or piers with semi circular ends, 0.66 Piers with triangular cut and case waters, the angle included between the faces being 30degrees or less, 0.50
Ice on Piers:
In snow bound areas floating ice generally causes high forces to work against piers. In some cases bridges have been completely demolished by the pressure of floating ice. The interaction between ice and bridges can result to static ice pressure and dynamic ice pressure. Static ice pressure is due to thermal movements of continuous stationary ice sheets or ice jams while the dynamic ice pressure results from moving ice sheets carried by stream flow, wind or current. The horizontal force resulting from the pressure of moving ice depends on the effective ice strength (usually 100 to 400 psi), the thickness of the contact ice sheet, and the inclination of the pier nose to the vertical. The actual value of the horizontal ice pressure to be used will depend on the condition of the ice at that time of movement, including the temperature, the size of the moving ice sheets and floes, and the velocity at contact. Since the last two conditions cannot be determined with a reasonable certainty, it is recommended that a conservative approach be used in es timating the ice conditions. From AASHTO 3.18.2.2, the recommended formula is used for calculating horizontal forces due to ice pressure: F = CnPtw
F = horizontal force due to ice pressure, lb Cn = coefficient for nose angle P = effective ice strength, psi t = thickness of ice in contact with pier w = width or diameter of pier at the level of ice action, in Earth Pressure on Bridges:
Abutments and wing walls are portions of substructure that retain earth or the backfill. Consequently, both are subjected subjected to lateral loads due to earth pressure. There are three kinds of earth pressure.
Active earth pressures - are considered to ensure that the abutment is stable. At rest earth pressures - are considered to ensure that the structural elements are adequate. Passive earth pressures - are only considered for integral abutments or where shear keys are provided.
Both the abutments and wing walls should be designed to withstand earth pressure. By Rankine’s formula the active earth pressure can be calculated as: P = K awh
P = Rankine’s Active Earth Pressure, lb Ka = coefficient of active earth pressure = minimum of 30 lb/ft 3 (AASHTO 3.20.1) w = unit weight of soil, lb/ft3 h = height of backfill, ft Seismic Loads
Historical Background •
First codification of seismic forces on bridges Japan, 1926 Due to the result of the Kanto Earthquake In United States, 1961 edition of AASHTO Earthquake forces were required to be applied in bridge structures in proportion to its weight, depending on the foundation conditions, but independent of its response characteristics BUT…. In Feb. 8, 1971 San Fernando Earthquake in California (M6.6) 42 bridges damaged, 5 collapsed –
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Thus, the pre-1971 AASHO was reviewed and revised
Factors that were chiefly considered: –
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Dynamic response characteristics of the structure Dynamic response characteristics of the soil Proximity of the site to known active faults Intensity of seismic events
The AASHTO standard [1991b] treats the seismic design of bridges in two ways: •
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Calculation of design seismic forces Detailing requirements based on required bridge performance in accordance with the seismic risk associated with its location
AASHTO detailing requirements for seismic resistance of bridges are specified in the AASHTO standard 1991b. The fundamental features of these specifications are as follows: –
Importance Classification (IC) IC one – one – for for essential bridges Bridges that must continue to function after an earthquake IC two – two – for for all other bridges •
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Seismic Performance Categories (SPC) SPC A to D A =lowest level of seismic performance D = highest level of seismic performance Analysis and Detailing Requirements: Analysis Procedure Regular Bridge No abrupt or unusual changes in mass, stiffness, or geometry along its span and has no large differences between adjacent supports Irregular Bridge –
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Design Requirements Design for horizontal seismic force Design for adequate lengths at bearing seats •
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For Specific Performance Category A bridges: •
No elastic analysis is required
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Connection of superstructure to substructure should resist horizontal seismic force equal to 20% of the dead load reaction in t he restrained direction Minimum requirement support lengths are as required by AASHTO Div. 1-A, Seismic Design, 4.9.1 Dimension for Minimum Support Length Requirements N = 8 + 0.02(L) + 0.08(H) 0.08(H) , in N = 203 + 1.67(L) 1.67(L) + 6.66(H) , mm
For Specific Performance Category B bridges: •
Elastic Seismic Forces Load Case 1: Design Force = absolute value of elastic seismic force in the longitudinal direction + 0.3(absolute value of elastic seismic force in the transverse direction) Load Case 2: Design Force = absolute value of elastic seismic force in the transverse direction + 0.3(absolute value of elastic seismic force in the longitudinal direction) Modified Elastic Seismic Force (EQM) EQM = DF / R R = response modification modificati on factor (found in AASHTO, 1992) Group Loading Combination Group Load = 1.0(D + B + SF + E + EQM) » D = dead load » B = Buoyancy » SF = Stream Flow Pressure » E = Earth Pressure » EQM = Modified Elastic seismic Force Each bridge component should withstand forces resulting from each combination Seismic Design Displacement Should be larger than the minimum requirement support lengths are as required by AASHTO Div. 1-A, Seismic Design, 4.9.1 –
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For Specific Performance Category C and D bridges: •
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Deals with designs in the inelastic range Seismic Design Displacement N = 12 + 0.03(L) 0.03(L) + 0.12(H)
Miscellaneous Loads Construction, handling and erection Loads Deformation Effects •
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Forces or displacements due to shrinkage of conventionally reinforced concrete should be evaluated assuming a coefficient of 0.0002 (According to AASHTO 8.5.3)
Combination of Loads for Design Group ( N ) D D L ( L I ) C CF E E B B S SF wW WLWL L LF R ( R S T ) EQ EQ ice ICE
N = group number number ϒ = load factor β = coefficient D = dead load L = live load I = live load (impact) E = earth pressure B = buoyancy W = wind load on live load LF = longitudinal force from live load CF = centrifugal force R = rib shortening S = shrinkage T = temperature EQ = earthquake SF = stream flow pressure ICE = ice pressure
