The bridge engineer must first list all the possible loads on the superstructure; to wit,
A) Permanent Loads:
B) Temporary Loads:
04. Vehicle Live Loads
05. Earthquake Forces
06. Wind Forces
07. Channel Forces
08. Longitudinal Forces
09. Centrifugal Forces
10. Impact Forces
11. Construction Loads
C) Deformation and Response Loads:
01. Dead Loads
02. Superimposed Dead Loads
03. Pressures (earth, water, ice, etc.)
16. Thermal Forces
D) Group Loading Combinations.
A Brief History of Highway Loading.
The primary design parameter for highways are truck loadings. The American Association
of State and Highway Transportation Officials (AASHTO), founded in 1914 as AASHO,
developed the concept of a train of trucks in the 1935 that imitated the railroad industry’s
standards. However, as the weight of the trucks grew, the bridges were overstressed.
In 1944, AASHTO developed a new concept: hypothetical trucks, called the H (with twoaxles) and the HS (with three-axles) classes of trucks. These were fictitious trucks, used
only for design and they did not resemble any real truck on the road.
In 1975, the federal DOT upgraded the allowable gross weight for trucks from 73,280 lb to
80,000 lb (although some states increased them to 90,000 lb).
A similar standard exists for Canada (the Ontario Highway Bridge Design Code, OHBDC),
or the United Kingdom, the BS5400 code. Europe has higher bridge loads, because they are
designed to carry heavier loads than the US, primarily military loads.
Permanent loads are always on the bridge throughout its life.
1. Dead Loads (DL). The dead loads of a bridge are all the loads from the superstructure,
such as, the wearing surface, the deck, the stay-in-place forms, parapets, sidewalks,
railings, bracing, connection plates, stiffeners, signing and utilities. The table below shows
some of the dead load unit weights that are used to calculate the superstructure.
2. Superimposed Dead Loads (SDL).
In a typical composite superstructure, the deck is formed by an 8 inch thick slab of reinforced concrete,
placed upon steel stringers or box girders. The top chord of this composite is in compression, which is
ideal for concrete, and the bottom chord is in tension, which is ideal for steel. The superimposed dead
loads are those loads placed on the superstructure after the deck has cured, and thus has begun to work
with the primary members. These are sidewalks, railings, parapets, signing, utilities and the wearing
In general, earth pressures upon the back-wall of the abutment is part of the substructure. The same is
true of the water pressure (and ice) upon the pier. However, part of the earth pressure can end up
affecting the superstructure, and this must be checked in all designs.
4. Vehicle Live Loads (LL).
A live load is any load that moves along a bridge. AASHO in 1935 came up with the concept of a train
of trucks, which is seen below, and identified as the H-20-35 and H-15-35. In 1944, the much heavier
trucks (due to WWII) were the new five truck categories were, the H10-44 (20,000 lb), the H15-44
(30,000 lb), the H20-44 (40,000 lb), the HS15-44 (54,000 lb) and the HS20-44 (72,000 lb). All of these
are still valid except for the H10-44, which has been dropped.
H20-44 8,000 LB
H15-44 6,000 LB
:s: . f - - - - - - - ' - - ' - - - - ' ' - - - - - --.;' ~
-- 1 0.1
- - - - - I 0.1 w 1
---- ~ 0.4 w ~ ---- ------- ---- I 0.4 w ~ I
o.j w 1-
- - -- - - - - - - 1 w 1 -o.4 --
W =TOTAL WEIGHT OF
TRUCK AND LOAD
----- I 0.1' w 1
o.4 w ~ ----- --------- - I o.4 w ~ -
W =COMBINED WEIGHT ON THE FIRST TWO AXLES, WHICH IS THE
SAME AS FOR THE CORRESPONDING H TRUCK.
V =VARIABLE SPACING-14FT TO 30FT INCLUSIVE. SPACING
TO BE USED IS THAT WHICH PRODUCES MAXIMUM STRESSES.
Standard H T.-ucks
lt+--=-'-=--" - - + 11
Standard HS T.-ucks
AASHTO Standard H & HS Design Trucks. (Adapted from Standard Specifications for Highway Bridges, 15th Ed., Ref 3.3.)
The loading is now performed by placing one HS-20-44
truck, for example, per lane, per span. The truck is moved
along the span, to determine the point where it produces the
Some state have very heavily loaded roads (for example,
California and Texas, due to NAFTA). These states are
using a semi-official class, called the HS25, with a gross
vehicle weight of 90,000 lb.
Notice the position of the axles of the HS20-44. The two
rear axles have a variable spacing, that ranges from 14 to 30
feet. This is varies to induce a maximum positive moment in
a span. For a simply supported bridge span, that spacing of
the axles will be 14 feet. For continuous spans, however, the
position of the axles at adjacent supports are varied to create
the maximum negative moment.
To model the train of trucks, two components are used: (1) a
uniformly distributed load, plus (2) a concentrated load.
Concentrated loadings generally govern for short simple spans. Lane loading governs for long and
continuous span bridges. The concentrated load is moved along the span to determine the point of
To determine the maximum positive moment in continuous spans, only one concentrated load is used
(which is also true for a simple span bridge). To determine the maximum negative moment in a
continuous span, two concentrated loads are used.
A reduction of the live load is permitted for bridges with three or more lanes, that have maximum stress
caused by fully loading each lane. A reduction to 90% is allowed for three lane structures and to 75% for
bridges with four or more lanes (AASHTO 3.12). Reduction is justified on the premise that it is unlikely
that all the lanes will be fully loaded to the maximum at the same time.
Two additional classes of loading are used by some agencies.
One is the AASHTO 3.7.4, which was developed in 1975 by the FHA (Federal Highway Administration),
and is known as the Alternative Military Loading. It is represented by two axles separated by only 4 feet,
and each carry 24,000 lb. All bridges on the United States Interstate system are required to compare the
HS20-44 loading with the Alternative Military Loading, with the configuration that produces the greatest
stress being chosen as the design criterion.
The second is the P Load class. States like California, that experience a large number of over-loaded
trucks, use the P loads (from permit design). The P load design vehicle has a single steering axle in front,
and between two to six pairs of loaded axles in tandem.
· · 48K
fiE Em fiE~ tmfm
tmtm Em fiE EfE,fm fiE Em
1 o·-o· clearance
Caltrans permit truck. (AASHTO LRFD Bridge Design Specifications 2nd. ed., American Association
of State Highway and Transportation Officials. Washington, D.C., 1998. With permission.)
5. Earthquake Forces (EQ).
Earthquake forces are a natural force, that depends on the geographical location of the bridge. These
forces are temporary, and act for a short duration of time. The application of these forces to the bridge
is usually studied with their effect upon piles, pile caps and abutments, via the Mononobe-Okabe
analysis method. These will be studied later.
There are four factors that are taken into consideration to determine the magnitude of the seismic
1) The dead weight of the entire bridge;
2) The ground acceleration (all three axes);
3) The period of vibration, and
4) The type of soils or rocks serving as bearing for the bridge.
The sum of these factors are reduced to an equivalent static force, which is applied to the structure in
order to calculate the forces and the displacements of each bridge element.
The first step is to ascertain what is the seismic performance category (SPC), via AASHTO I-A, 3.3
(next two slides). The next step is to determine the type of analysis required, via AASHTO, I-A, 4.2,
which are either Method 1 (Single-Mode Spectral Analysis) or Method 2 (Multi-mode Spectral
Analysis). Method 1 is the simpler of the two, and can be done by hand-calculations. Method 2 is
complex, and requires specialized software. The single-mode spectral analysis uses the same procedure
for calculating the longitudinal as the transverse loading. This is done via the principle of virtual
displacements, in order to develop a mode shape model for the bridge. An arbitrary uniform static force
po = 1, is applied to the length of the structure in order to produce an initial displacement vs. This
displacement, combined with the dead load weight of the superstructure, and part of the substructure, is
used to determine the earthquake force.
I I I
I I I
I I I
I I I
$.., / I
.; .; I
Horizontal acceleration (A) values. Divide values on map by 100 to obtain the coefficient used in calculations. (Adapted from
Standard Specifications for Highway Bridges, 15th Ed., Ref 3.3.) Consult map in the AASHTO specificationsfor more detail.
3.3 IMPORTANCE CLASSIFICATION
3.4 SEISMIC PERFORMANCE
Essential bridges with an acceleration
coefficient greater than 0.29 are assigned
an importance classification (IC) of "I."
All other structures have an IC of "II."
An essential bridge is one that is determined to be critical to "social/survival
and security/defense" needs (MSHTO,
I-A, 3.3). Based on the ICand the acceleration coefficient at the bridge site, a
seismic performance category (SPC) can
be determined from the table below
(MSHTO, 1-A, 3.4).
Seismic Performance Categories
3.5 SITE COEFFICIENT
As stated at the beginning of this section, the type of soil present at the
bridge site plays an important role in
the forces an earthquake exerts on a
structure. The site coefficient is determined by selecting one of three soil
profile types that best fits the conditions at the site. (A
ASHTO, 1-A, 3.5.1).
SOIL PROFILE TYPE 1:
S = 1.0
If rock of any type is present, this profile
type applies. S Iike orcrystall inetypes
with a shear wave velocity greater than
2,500 ft/s (762 m/s). Stiff soil on top of
rock with adepth less than 200ft (61 m)
consisting of stable deposits of sands,
gravels, or stiff clays.
SOIL PROFILE TYPE II:
For stiff clay or deep cohesionless soil
conditions along with sites where the
soil depth on top of rock is greater than
200 ft (61m) consistingof stable deposits of sands, gravels, or stiff clays. If the
soil type is unknown or the soil properties do not fit any of the three types, this
site coefficient (S =1.2) is used for all
SOIL PROFILE TYPE Ill: S = 1.5
Soft to medium-stiff clays and sands
with adepth of 30ft (9.1m) or greater of
soft to medium-stiff clay with or without
intervening layers of sand or other cohesion less soils.
3.6 RESPONSE MODIFICATION
FACTORS (R FACTOR)
For bridges with a SPC = B, C, or D, the
seismic design forces for individual members are calculated by dividing the elastic
forces by the appropriate Rfactor.
Cone. Pile Bent (Vertical Piles)
Cone. Pile Bent (1+ Batter P
Steel Pile B (Vertical Piles)
Steel Pile Bent (1+ Batter Piles)
Multiple Column Bent
Superstructure to Abutment
Exp. Joints within Span of Super. 0.8
Columns, Piers, or Pile Bents to
Cap Beam or Superstructure
Colums or Piers to Foundations 1.0
4.2 CHOOSING THE APPROPRIATE
SEISMIC ANALYSIS METHOD
Once a seismic performance category
(SPC) has been assigned, the type of
analysis required is identified based on
the SPC and whether the bridge is regular
or irregular. Regular bridges are those
with an unchanging bridge cross section, similar supports, and a uniform
mass and stiffness. Bridges which do not
satisfy these criteria are irregular. The two
methods are applicable to multispan
bridges only (AASHTO, 1-A, 4.2).
Method 1 = Single-Mode Spoctral Analysis
Method 2 =Multimode Spectral Analysis
SPC Regular Bridge Irregular Bridge
Bridges with 2 or More Spans O
The next step is to calculate the dead weight value w(x) from the superstructure and part of the substructure. It can also include some live load if the bridge is in a heavily traveled urban area. From these
two values, vs and w(x), we can find the fundamental period T of the bridge and the seismic force pe(x).
UJ(:X)V 5 (:X)d:x;
length of bridge
"WTith.. iliese factors kno'QV"ll, the fundamental period of the bridge
can be computed 'QV'"ith the follo'QV'"i:ng:
g = acceleration of gravity (length/tirr1e 2 )
Cs = y 213
where A = Acceleration Coefficient
S = Site Coefficient
( Table 4 . 6 . 2 . 2 . 1-1 )
per 4.6 . 3 . 8
per 4 . 6 .3. 7
per 4.6.2. 4
per 4 . 6 . 3 . 5 ,6
Refined analysis required ;
put load coeficients on plans
per 4 . 6 . 3 . 1
4 .6 .2 . 3
May not be
Refined analysis required; put
load coefficients on plans per
4 .6 . 3.1
Refined analysis required;
o r put load coefficients on
plans per 4 . 6 . 3 . 1
Ok to use load distribution factor tables ;
Table 4.6.3. 3 .3a to 3f for moment;
Table 4 .6.2 . 2.3a to 3c for shear;
Dynamic load allowance per 3 .6 . 2
Number of design lanes per 3 . 6 . 1 . 1 . 1 ;
Dynamic load allowance per 3 .6 . 2 ;
Multi presence per 3 . 6 . 1 . 1 . 2
Decimal number of lanes from Table
(above) ; Dynamic load allowance per
3 .6.2; Multi presence always included
L ive- load distribution for s upers truc ture design.
6. Wind Forces (W and WL).
Similar to the earthquake forces, wind forces are extremely complicated, but through a series of
simplifications are reduced to an equivalent static force applied uniformly over the exposed faces of the
bridge (both super and sub-structures) that are perpendicular to the longitudinal axis.
AASHTO specifies that the assumed wind velocity should be 100 mph. For a common slab-on-stringer
bridge this is usually a pressure of 50 psf, and a minimum of 300 p/lf. Truss and arch bridges require a
pressure of 75 psf, and a minimum of 300 p/lf on the windward and 150 p/lf on the leeward sides.
These forces are applied at the center of gravity of the exposed regions of the structure.
AASHTO recommends the following for common slab-on-stringer bridges:
1) Wind force on structures (W):
a) transverse loading = 50 psf
b) longitudinal loading = 12 psf
2) Wind force on live load (WL):
a) transverse loading = 100 psf
b) longitudinal loading = 40 psf
The transverse and longitudinal loads are placed simultaneously for both the structure and the live load
AASHTO also requires an additional 20 psf of overturning force, to be applied at quarter points on the
The design wind pressure PD can also be calculated from,
For this equation, in S.I. units, VDZ is the design wind velocity at the designated elevation Z in km/h.
VDZ is a function of the friction velocity Vo, also in km/h, multiplied by the ratio of the actual wind
velocity to the base wind velocity both at 10 m above grade, and the natural logarithm of the ratio of
height to a meteorological constant length for given surface conditions.
v;, and Z
v., ( km/h)
for Various Upstream
Z , ( mm)
Source: AASHTO LRFD Bridge Design Specifications,
2nd. ed., American Association of State Highway and
Transportation Officials. Washington, D.C. , 1998. With
Temperature Ranges, ° C
Steel or Aluminum
-18 to 50
-1 2 to 27
- 18 to 27
-12 to 24
- 18 to 2 4
- 35 to 50
Source: AASHTO LRFD Bridge Design Specifications,
2nd. ed., American Association of State Highway and
Transportation Officials. Washington, D.C., 1998. With
(v;.o Jln(Zo J
7. Channel Forces (SF and ICE).
Channel forces come from the stream flow, floating ice and bouyancy. These forces affect primarily the
The force Pavg of the stream flow upon the pier, is half the maximum stream flow pressure Pmax
measured by a hydrologic study.
For floating ice,
126.96.36.199.2 ICE STRENGTH
188.8.131.52.1 INCLINATION OF NOSE
The effective ice strength ranges from
100 lb/in2 to 400 lb/in2 and is dependent
on a variety of factors including the temperature of the ice mass at the time of
movement and the size of moving ice
pieces. Listed below are AASHTO's general guidel ines on selecting the effective
ice strength. In general, the lower the
temperature the ice moves at, the more
damage it can do to apier or other bridge
component it comes in contact with.
PIER SHAPE CONSTANT
The equation for the pressure due to
stream flows uses a constant to describe the geometry of the pier in a
water channel. The three possible values are listed below:
PIERS SUBJECTED TO
DRIFT BUILD-UP AND
SQUARE ENDED PIERS:
Where the pier ends are angled at 30
degrees or less.
The coefficient C varies depending on
the inclination of the nose to vertical (i.e.,
the pier nose angle inthe vertical plane).
Pier noses are often equipped with a
steel angle or similar device raked at an
angle to act as an ice breaker.
0 to 15 degrees:
15 to 30 degrees:
30 to 45 degrees:
p =100 lb/in2 (690 kPa)
Ice breaks apart at the melting temperature. Ice pieces are disintegrated and
move as small cakes.
p = 200 lb/in2 (1379 kPa)
Ice breaks apart at the m
elting temperature. Ice pieces are solid and move as
p =300 lb/in2 (2069 kPa)
When breaking apart, the ice m
large, solid sheets which may impact
with the pier.
p =400 lb/in2 (2758 kPa)
Ice breaks apart or moves at a temperaturewell below the melting temperature.
8. Longitudinal Forces (LF).
Longitudinal forces result from the transfer of momentum from the truck braking or accelerating on a
bridge. AASHTO 3.9 specifies that 5% of the appropriate lane load along with the concentrated force
for moment be used as the resulting longitudinal force. This force is applied 6 feet above the top of the
deck surface. The stiffer or rigid the structure, the greater the effect of the longitudinal force.
9. Centrifugal Forces (CF).
A truck turning on a bridge, because of a horizontal curve exerts a centrifugal force, as calculated
below, and located 6 feet above the top of the deck surface, using truck loading.
10. Live Load Impact (I).
Trucks at high speeds may hit the deck with a large vertical force (impact) because of several causes,
such as a pot hole, or a large vertical step between the approach slab and the rigid deck, etc. AASHTO
3.8.2 defines the impact factor as follows:
11. Construction Loads (I).
During the erection of the bridge, some members may be subjected to larger loads than those
calculated for normal use. The experienced designer usually consults with the (likely) contractors to
obtain information on the method of construction, the heavy equipment that may mount the bridge,
staging materials, and other problems in order to add these loads to the bridge analysis.
Creep is the deformation of a concrete mass caused by carrying a load over a period of time. When the
load is applied, the concrete experiences an instant strain (linearly related to the stress), and an instant
deformation. Over time however, an additional strain (creep strain) occurs, which may be from 150% to
300% larger than the instant linear strain. Creep strain is a function of its moisture during curing. If the
concrete is left to dry out, creep will be very large. On the other hand, a protected fresh concrete surface
that is kept moist, will experience minimal creep strain. Excessive concrete in the deck may deform the
length of the members and lead to warping or misalignments.
Shrinkage is also, like creep, a deformation due to material properties. It is a consequence of the natural
change in volume of concrete, and not related to load. The shrinking is due to the los of moisture during
its drying. Steel reinforcing is usually added to absorb some of the tensile stresses induced by the
shrinking. The best way to diminish shrinkage is to keep the concrete moist during curing, and using
plasticizer to provide workability in lieu of extra water which increase shrinkage (and creep).
Settlement of the foundations will produce sizable moments in the superstructure, especially differential
settlement. Settlement can have one or several causes, including (1) exceeding the bearing capacity of the
soils, (2) lowering of the phreatic surface, (3) vibrations, (4) loading the embankments, and (5) changes
in the soil properties (for example, shrinkage and swelling).
Some bridge configurations may produce the lifting of a span with respect to its adjacent elements. For
example, high loading a long span, next to a short span. This is called uplift, and its discussed in
16. Thermal Forces.
The fluctuations in temperature in a bridge may be very high, and produce sizable thermal forces. This
force is similar in nature to differential settlement. For example, a bridge in a northern climate, oriented
East-West, will always have its southern face heated, and the northern perennially in the shade. This
bridge will have a tendency towards thermal forces. Please refer to AASHTO 3.16 on this issue. One
common problem of extreme cold weather is brittle fracture of steel, which occurs instantaneously,
leading to fatal failure.
3.8.1 WHERE IMPACT APPLIES
The impact factor is applied only to
certain elements and components.
Group A elements include the impact
factor. Group B elements do not.
Also includes the legs of a rigid frame.
All features above the ground level.
Any concrete or steel piles supporting
the superstructure and above the ground
IMPACT NOT INCLUDED
Including any retaining walls or piles
(not falling into the Group A category)
Pressures and footings.
In addition to any structures with 3 ft
(0.9 m) or greater of cover.
184.108.40.206 THE LOADED LENGTH
The loaded length L varies depending
on the element being analyzed. The
following lists AASHTO's specification
for certain members and calculations.
Design span length.
Span length of member from center to
center of supports (e.g., afloor beam).
1Rt£K LOAD MOMENT CALCIIAnllt
Design span length. For cantilever
arms use length from moment center to
TRUCK LOAD SHEAR CALCULATION
Length of loaded portion of span from
point of analysis to farthest reaction.
For cantilever arms use I = 0.30.
Length of span being analyzed for positive moment plus the average of two
adjacent spans loaded for negative moment.
3.16 TEMPERATURE RANGES
AASHTO provides acceptable temperature variations depending on whether
the structure is in amoderate or cold
climate region. For metal structures,
the values are given in the form of
extreme hot and cold temperatures.
Concrete structures are given temperature rise and fall changes.
Moderate Climate: 0°F
Moderate Climate: 30°F
Group Loading Combinations.
Bridges experience a combination of the previously discussed forces. Experience has generated ten load
groups. These are described by the equation below.
1.0 and 0.5
Vertical and lateral loads on all
Lateral loads on rigid frames
(check both and use the one that
Lateral earth pressure for retaining walls and rigid frames
exclud ing rigid culverts.
3.22.1 NOTES ON TABLE OF
Live load plus impact for
AASHTO H or HS loading.
Live load plus impact consistentwith owner's overload
Pertains to culverts.
If member or connection carries only
wind load, then no increase in allowable
stress is allowed.
Lateral earth pressure when
checking positive moments in
For outside roadway girders, if the
governing load combination is
Sidewalk Live Load +
Traffi c Live Load with Impact
p = 1.25
Columns, when checking member for minimum axial load and
maximum moment or maximum
Columns, when checking member for maximum axial load and
The capacity of the section should not be
Traffic Live Load with Impact
p = 1.67
Compute the increase in the normal
allowable stress to be
Maximum Unit Stress
% = _....:.....:_--=-- - = - 100
Allowable Basic Unit Stress
Flexural and tension members.
Earth Pressure and Dead Load Coefficients
For working stress design method is the
percent increase of the basic unit stress.