P.2-i 

Table of Contents

Basic Concepts 

Primer ..................................................................................................................................................

 

 P.2 Bridge Mechanics ........................................................................P.2.1 

 P.2.1 Introduction ........................................................................P.2.1 

 P.2.2 Bridge Design Loadings.....................................................P.2.1 

 Dead Loads ..................................................................P.2.2 

 Primary Live Loads......................................................P.2.2 

 AASHTO Truck Loadings ....................................P.2.3 

 AASHTO Lane Loadings......................................P.2.5 

 LRFD Live Loads..................................................P.2.5 

 Alternate Military Loading....................................P.2.7 

 Permit Vehicles .....................................................P.2.8 

 Secondary Loads..........................................................P.2.8 

 P.2.3 Bridge Response to Loadings.............................................P.2.9 

 Equilibrium ..................................................................P.2.9 

 Axial Forces...............................................................P.2.10 

 Bending Forces ..........................................................P.2.11 

 Shear Forces...............................................................P.2.13 

 Torsional Forces.........................................................P.2.14 

 Reactions....................................................................P.2.15 

 

 P.2.4 Material Response to Loadings ........................................P.2.16 

 Force ..........................................................................P.2.16 

 Stress..........................................................................P.2.16 

 Deformation ...............................................................P.2.17 

 Strain ...................................................................P.2.17 

 Elastic Deformation.............................................P.2.17 

 Plastic Deformation.............................................P.2.17 

 Creep ...................................................................P.2.18 

 Thermal Effects ...................................................P.2.18 

 Stress-Strain Relationship..........................................P.2.18 

 Modulus of Elasticity ..........................................P.2.18 

 Overloads...................................................................P.2.19 

 Buckling ..............................................................P.2.19 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2-ii

 Elongation ...........................................................P.2.20 

 Ductility and Brittleness ............................................P.2.20 

 Fatigue ......................................................................P.2.20 

 Isotropy ......................................................................P.2.21 

 P.2.5 Mechanics of Materials ....................................................P.2.21 

 Yield Strength ............................................................P.2.21 

 Tensile Strength .........................................................P.2.21 

 Toughness ..................................................................P.2.21 

 P.2.6 Bridge Movements ...........................................................P.2.21 

 Live Load Deflections................................................P.2.21 

 Thermal Movements ..................................................P.2.22 

 Rotational Movements...............................................P.2.22 

 P.2.7 Design Methods................................................................P.2.22 

 Allowable Stress Design ...........................................P.2.22 

 Load Factor Design ...................................................P.2.22 

 Load and Resistance Factor Design...........................P.2.22 

 P.2.8 Bridge Ratings..................................................................P.2.22 

 Inventory Rating .......................................................P.2.23 

 Operating Rating........................................................P.2.24 

 Permit Loading...........................................................P.2.24 

 Rating Vehicles .........................................................P.2.24 

 Bridge Posting............................................................P.2.26 

 P.2.9 Span Classifications..........................................................P.2.27 

 Simple ......................................................................P.2.28 

 Continuous.................................................................P.2.29 

 Cantilever...................................................................P.2.30 

 P.2.10 Bridge Roadway Interaction.............................................P.2.31 

 Non-composite...........................................................P.2.31 

 Composite ..................................................................P.2.32 

 Integral ......................................................................P.2.33 

 Orthotropic.................................................................P.2.33 

 P.2.11 Redundancy......................................................................P.2.34 

 Load Path Redundancy ..............................................P.2.34 

 Structural Redundancy...............................................P.2.34 

 Internal Redundancy ..................................................P.2.34 

 P.2.12 Foundations ......................................................................P.2.35 

 Spread Footings .........................................................P.2.35 

 Deep Foundations .....................................................P.2.35 
P.2.iii 

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Basic Concepts Primer 

 TOPIC P.2: Bridge Mechanics 

P.2.iv 

Basic Equations of Bridge Mechanics 

where: A = area; cross-sectional area 

Aw = area of web 

c = distance from neutral axis 

to extreme fiber (or 

surface) of beam 

E = modulus of elasticity 

F = force; axial force 

fa = axial stress 

fb = bending stress 

fv = shear stress 

I = moment of inertia 

L = original length 

M = applied moment 

S = stress 

V = vertical shear force due to 

external loads 

ΔL = change in length 

ε = strain

A

P

f a = (Page P.2.9) 

L

L = Δ

ε (Page P.2.17) 

ε

S E = (Page P.2.18) 

A

V

f = w

v (Page P.2.13) 

I

Mc

f b = (Page P.2.11) 

 x Vehicles Weight (Tons) Rating Vehicle Live Load Plus Impact

Allowable Load- Dead Load Bridge Load Capacity Rating=

A

F S = (Page P.2.16) 
P.2.1

Basic Concepts Primer 

Topic P.2 Bridge Mechanics 

P.2.1 

Introduction Mechanics is the branch of physical science that deals with energy and forces and 

their relation to the equilibrium, deformation, or motion of bodies. The bridge 

inspector will primarily be concerned with statics, or the branch of mechanics 

dealing with solid bodies at rest and with forces in equilibrium. 

The two most important reasons for a bridge inspector to study bridge mechanics 

are: 

3⁄4 To understand how bridge members function 

3⁄4 To recognize the impact a defect may have on the load-carrying capacity 

of a bridge component or element 

While this topic presents the basic principles of bridge mechanics, the references 

listed in the bibliography should be referred to for a more complete presentation of 

this subject. 

P.2.2 

Bridge Design 

Loadings 

A bridge is designed to carry or resist design loadings in a safe and economical 

manner. Loads may be concentrated or distributed depending on the way in which 

they are applied to the structure. 

A concentrated load, or point load, is applied at a single location or over a very 

small area. Vehicle loads are considered concentrated loads. 

A distributed load is applied to all or part of the member, and the amount of load 

per unit of length is generally constant. The weight of superstructures, bridge 

decks, wearing surfaces, and bridge parapets produce distributed loads. Secondary 

loads, such as wind, stream flow, earth cover and ice, are also usually distributed 

loads. 

Highway bridge design loads are established by the American Association of State 

Highway and Transportation Officials (AASHTO). For many decades, the primary 

bridge design code in the United States was the AASHTO Standard Specifications 

for Highway Bridges (Specifications), as supplemented by agency criteria as 

applicable. 

During the 1990’s AASHTO developed and approved a new bridge design code, 

entitled AASHTO LRFD Bridge Design Specifications. It is based upon the 

principles of Load and Resistance Factor Design (LRFD), as described in Topic 

P.2.7. 

Load and Resistance Factor Rating (LRFR) consists of three methods: design load 

rating, legal load rating, and permit load rating. Each serves a specific purpose in 

the evaluation of bridge safety or serviceability. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.2 

Bridge design loadings can be divided into three principal categories: 

3⁄4 Dead loads 

3⁄4 Primary live loads 

3⁄4 Secondary loads 

Dead Loads Dead loads do not change as a function of time and are considered full-time, 

permanent loads acting on the structure. They consist of the weight of the 

materials used to build the bridge (see Figure P.2.1). Dead load includes both the 

self-weight of structural members and other permanent external loads. They can 

be broken down into two groups, initial and superimposed. 

Initial dead loads are loads which are applied before the concrete deck is hardened, 

including the beam itself and the concrete deck. Initial deck loads must be resisted 

by the non-composite action of the beam alone. Superimposed dead loads are 

loads which are applied after the concrete deck has hardened (on a composite 

bridge), including parapets and any anticipated future deck pavement. 

Superimposed dead loads are resisted by the beam and the concrete deck acting 

compositely. Non-composite and composite action are described in Topic P.2.10. 

Dead load includes both the self-weight of the structural members and other 

permanent external loads. 

Example of self-weight: A 6.1 m (20-foot) long beam weighs 0.73 kN per m (50 

pounds per linear foot). The total weight of the beam is 4.45 kN (1000 pounds). 

This weight is called the self-weight of the beam. 

Example of an external dead load: If a utility such as a water line is 

permanently attached to the beam in the previous example, then the weight of the 

water line is an external dead load. The weight of the water line plus the self 

weight of the beam comprises the total dead load. 

Total dead load on a structure may change during the life of the bridge due to 

additions such as deck overlays, parapets, utility lines, and inspection catwalks. 

Figure P.2.1 Dead Load on a Bridge 

Primary Live Loads A live load is a temporary dynamic load applied to a structure. In bridge 

applications, the primary live loads are moving vehicular loads (see Figure P.2.2). 

To account for the affects of speed, vibration, and momentum, highway live loads 

are typically increased for impact. Impact is expressed as a fraction of the live 

load, and its value is a function of the span length. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.3 

Figure P.2.2 Vehicle Live Load on a Bridge 

AASHTO Truck Loadings

Standard vehicle live loads have been established by AASHTO for use in bridge 

design and rating. There are two basic types of standard truck loadings described 

in the current AASHTO Specifications. A third type of loading is used for 

AASHTO Load and Resistance Factor Design and Rating. 

The first type is a single unit vehicle with two axles spaced at 14 feet (4.3 m) and 

designated as a highway truck or “H” truck (see Figure P.2.3). The weight of the 

front axle is 20% of the gross vehicle weight, while the weight of the rear axle is 

80% of the gross vehicle weight. The “H” designation is followed by the gross 

tonnage of the particular design vehicle. The AASHTO LRFD design vehicular 

live load, designated HL-93, is a modified version of the HS-20 highway loadings 

from the AASHTO Standard Specifications. 

Example of an H truck loading: H20-35 indicates a 20 ton vehicle with a front 

axle weighing 4 tons, a rear axle weighing 16 tons, and the two axles spaced 14 

feet apart. This standard truck loading was first published in 1935. The 1935 

truck loading used a train of trucks that imitated the railroad industry’s standards. 

As trucks grew heavier during World War II, AASHTO developed the new 

concept of hypothetical trucks. These fictitious trucks are used only for design and 

do not resemble any real truck on the road. The loading is now performed by 

placing one truck, per lane, per span. The truck is moved along the span to 

determine the point where it produces the maximum moment. The current 

designation is H20-44 published in 1944. 

The second type of standard truck loading is a two unit, three axle vehicle 

comprised of a highway tractor with a semi-trailer. It is designated as a highway 

semi-trailer truck or “HS” truck (see Figure P.2.4). 

The tractor weight and wheel spacing is identical to the H truck loading. The 

semi-trailer axle weight is equal to the weight of the rear tractor axle, and its 

spacing from the rear tractor axle can vary from 4.3 to 9.1 m (14 to 30 feet). The 

“HS” designation is followed by a number indicating the gross weight in tons of 

the tractor only. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.4 

14’-0”

(4.3 m) 

8,000 lbs 

(35 kN) 

32,000 lbs 

(145 kN) 

(3.0 m) 

10’-0” 

CLEARANCE AND 

LOAD LANE WIDTH 

6’-0” 

(1.8 m) 

2’-0” 

(0.6 m) 

Figure P.2.3 AASHTO H20 Truck 

14’-0”

(4.3 m) 

8,000 lbs 

(35 kN)

32,000 lbs

(145 kN)

(3.0 m)

10’-0” 

CLEARANCE AND 

LOAD LANE WIDTH 

6’-0”

(1.8 m) 

2’-0” 

(0.6 m) 32,000 lbs

(145 kN)

V

Figure P.2.4 AASHTO HS20 Truck 

Example of an HS truck loading: HS20-44 indicates a vehicle with a front 

tractor axle weighing 4 tons, a rear tractor axle weighing 16 tons, and a semitrailer axle weighing 16 tons. The tractor portion alone weighs 20 tons, but the 

gross vehicle weight is 36 tons. This standard truck loading was first published in 

1944. 

In specifications prior to 1944, a standard loading of H15 was used. In 1944, the 

policy of affixing the publication year of design loadings was adopted. In 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.5 

Uniform Load of 9.3 N/mm (640 lbs. per linear foot) 

Concentrated Load - 80 kN (18,000 lbs.) for Moment

115 kN (26,000 lbs.) for Shear 

H20-44 Loading

HS20-44 Loading

specifications prior to 1965, the HS20-44 loading was designated as H20-S16-44, 

with the S16 identifying the gross axle weight of the semi-trailer in tons. 

The H and HS vehicles do not represent actual vehicles, but can be considered as 

“umbrella” loads. The wheel spacings, weight distributions, and clearance of the 

Standard Design Vehicles were developed to give a simpler method of analysis, 

based on a good approximation of actual live loads. These loads are used for the 

design of bridge members. Depending on such items as highway classification, 

truck usage and span classification, for example, an appropriate design load is 

chosen to determine the most economical member. Bridge posting is determined 

by performing a rating analysis using the current member condition of an inservice bridge. Various rating methods will be discussed further in Topic P.2.8. 

AASHTO Lane Loadings

In addition to the standard truck loadings, a system of equivalent lane loadings 

was developed in order to provide a simple method of calculating bridge response 

to a series, or “train” of trucks. Lane loading consists of a uniform load per linear 

foot of traffic lane combined with a concentrated load located on the span to 

produce the most critical situation in the structure (see Figure P.2.5). 

For design and load capacity rating analysis, an investigation of both a truck 

loading and a lane loading must be made to determine which produces the 

greatest stress for each particular member. Lane loading will generally govern 

over truck loading for longer spans. Both the H and HS loadings have 

corresponding lane loads. 

 * 

* Use two concentrated loads for negative moment in continuous spans (Refer to 

AASHTO Bridge Design Specifications, 2005 Interim; Article 3.6.1.3) 

Figure P.2.5 AASHTO Lane Loadings.

 LRFD Live Loads 

Under HS-20 loading as described earlier, the truck or lane load is applied to each 

loaded lane. Under HL-93 loading, the design truck or tandem is combined with 

the lane load and applied to each loaded lane. 

The LRFD design truck is exactly the same as the AASHTO HS-20 design truck. 

The LRFD design tandem, on the other hand, consists of a pair of 110 kN axels 

spread at 1.2 m (25 kip axles spaced 4 feet) apart. The transverse wheel spacing 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.6 

of all of the trucks is 6 feet. 

The magnitude of the HL-93 lane load is equal to that of the HS-20 lane load. 

The lane load is 9.3 N/mm (0.64 kips per linear foot) longitudinally and it is 

distributed uniformly over a 3 m (10 foot) width in the transverse direction. The

difference between the HL-93 lane load and the HS-20 lane load is that the HL-93 

lane load does not include a point load. The HL-93 design load consists of a 

combination of the design truck or design tandem, and design lane load (see 

Figure P.2.6). 

Finally, for LRFD live loading, the dynamic load allowance, or impact, is applied 

to the design truck or tandem but is not applied to the design lane load. It is 

typically 33 percent of the design vehicle. 

 

Figure P.2.6 AASHTO LRFD Loading

35 kN

(8k

)

110 kN

(24k)

145 kN

(32k

)

145 kN

(32k

)

110 kN

(24k

)

9.3 kN/m (0.64 kLF)

Truck (HS20)

Tandem

Uniform (HS20 w/o

point load)

or

plus

or

plus

4.3 m

(14')

V

1.2 m

(4')

35 kN

(8k

)

110 kN

(24k)

145 kN

(32k

)

145 kN

(32k

)

110 kN

(24k

)

kN/m (0.64 kLF)

Truck (HS20)

Tandem

Uniform (HS20 w/o

point load)

or

plus

or

plus

4.3 m

(14')

V

1.2 m

(4')
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.7 

Alternate Military Loading

The Alternate Military Loading is a single unit vehicle with two axles spaced at 

1.2 m (4 feet) and weighing 110 kN (12 tons) each. It has been part of the 

AASHTO Specifications since 1977. Bridges on interstate highways or other 

highways which are potential defense routes are designed for either an HS20 

loading or an Alternate Military Loading (see Figure P.2.7). 

1.2 m

(4')

110 kN

(24 k)

110 kN

(24 k)

Figure P.2.7 Alternate Military Loading 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.8 

 Permit Vehicles 

Permit vehicles are overweight vehicles which, in order to travel a state’s 

highways, must apply for a permit from that state. They are usually heavy trucks 

(e.g., combination trucks, construction vehicles, or cranes) that have varying axle 

spacings depending upon the design of the individual truck. To ensure that these 

vehicles can safely operate on existing highways and bridges, most states require 

that bridges be designed for a permit vehicle or that the bridge be checked to 

determine if it can carry a specific type of vehicle. For safe and legal operation, 

agencies issue permits upon request that identify the required gross weight, 

number of axles, axle spacing, and maximum axle weights for a designated route 

(see Figure P.2.8). 

Figure P.2.8 Permit Vehicle 

Secondary Loads In bridge applications, the secondary loads are temporary dynamic loads and 

consist of the following: 

3⁄4 Buoyancy - the force created due to the tendency of an object to rise when

submerged in water 

3⁄4 Centrifugal force - an outward force that a live load vehicle exerts on a 

curved bridge

3⁄4 Curb loading - curbs are designed to resist a lateral force of not less than 

7.3 kN per linear meter (500 pounds per linear foot) 

3⁄4 Earth pressure - a horizontal force acting on earth-retaining substructure 

units, such as abutments and retaining walls 

3⁄4 Earthquake - bridge structures must be built so that motion during an 

earthquake will not cause a collapse 

3⁄4 Ice pressure - a horizontal force created by static or floating ice jammed 

against bridge components 

3⁄4 Longitudinal force - a force in the direction of the bridge caused by 

braking and accelerating of live load vehicles 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.9 

3⁄4 Railing loading - railings are provided along the edges of structures for 

protection of traffic and pedestrians; the maximum transverse load applied 

to any one element need not exceed 44.5 kN (10 kips) 

3⁄4 Rib shortening - a force in arches and frames created by a change in the 

geometrical configuration due to dead load 

3⁄4 Shrinkage - applied primarily to concrete structures, this is a multidirectional force due to dimensional changes resulting from the curing 

process

3⁄4 Sidewalk loading - sidewalk floors and their immediate supports are 

designed for a pedestrian live load not exceeding 4.1 kN per square meter 

(85 pounds per square foot) 

3⁄4 Stream flow pressure - a horizontal force acting on bridge components 

constructed in flowing water 

3⁄4 Temperature - since materials expand as temperature increases and 

contract as temperature decreases, the force caused by these dimensional 

changes must be considered 

3⁄4 Wind load on live load - wind effects transferred through the live load 

vehicles crossing the bridge 

3⁄4 Wind load on structure - wind pressure on the exposed area of a bridge 

 

A bridge may be subjected to several of these loads simultaneously. The 

AASHTO Specifications have established a table of loading groups. For each 

group, a set of loads is considered with a coefficient to be applied for each 

particular load. The coefficients used were developed based on the probability of 

various loads acting simultaneously. 

P.2.3 

Bridge Response to 

Loadings 

Each member of a bridge is intended to respond to loads in a particular way. The 

bridge inspector must understand the manner in which loads are applied to each 

member in order to evaluate if it functions as intended. Once the inspector 

understands a bridge member’s response to loadings, he will be able to determine 

if a member defect has an adverse effect on the load-carrying capacity of that 

member. 

Bridge members respond to various loadings by resisting four basic types of 

forces. These are: 

3⁄4 Axial forces (compression and tension) 

3⁄4 Bending forces (flexure) 

3⁄4 Shear forces 

3⁄4 Torsional forces 

Equilibrium In calculating these forces, the analysis is governed by equations of equilibrium. 

Equilibrium equations represent a balanced force system and may be expressed as:

∑V =0 

∑H =0 

∑M =0 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.10 

where: ∑ = summation of 

V = vertical forces 

H = horizontal forces 

M = moments (bending forces) 

Axial Forces An axial force is a push or pull type of force which acts parallel to the longitudinal 

axis of a member. An axial force causes compression if it is pushing and tension if 

it is pulling (see Figure P.2.9). Axial forces are generally expressed in English 

units of pounds or kips, and metric units of Newtons or kilonewtons. 

Axial Compression

Axial Tension

Longitudinal Axis

Figure P.2.9 Axial Forces 

Examples of axial forces: A man sitting on top of a fence post is exerting an 

axial force that causes compression in the fence post. A group of people playing 

tug-of-war exerts an axial force that causes tension in the rope. 

Truss members are common bridge elements which carry axial loads. They are 

designed for either compression and tension forces. Cables are designed for axial 

forces in tension. 

True axial forces act uniformly over a cross-sectional area. Therefore, axial stress 

can be calculated by dividing the force by the area on which it acts. 

where: fa = axial stress 

P = axial force 

A = cross-sectional area 

When bridge members are designed to resist axial forces, the cross-sectional area 

will vary depending on the magnitude of the force, whether the force is tensile or 

compressive, and the type of material used. 

A

P

af =
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.11 

For tension and compression members, the cross-sectional area must satisfy the 

previous equation for an acceptable axial stress. However, the acceptable axial 

compressive stress is generally lower than that for tension because of a 

phenomenon called buckling. 

Bending Forces Bending forces in bridge members are caused when a load is applied 

perpendicular to the longitudinal or neutral axis. A moment is commonly 

developed by the perpendicular loading which causes a member to bend. The 

greatest bending moment that a beam can resist is generally the governing factor 

which determines the size and material of the member. Bending moments can be 

positive or negative and produce both compression and tension forces at different 

locations in the member (see Figure P.2.10). Moments are generally expressed in 

English units of pound-feet or kip-feet, and metric units of Newton-meters or 

kilonewton-meters. 

Example of bending moment: When a rectangular rubber eraser is bent, a 

moment is produced in the eraser. If the ends are bent upwards, the top half of the 

eraser can be seen to shorten, while the bottom half can be seen to lengthen. 

Therefore, the moment produces compression forces in the top layers of the eraser 

and tension forces in the bottom layers. 

Compression (C)

Neutral Axis (NA)

Tension (T)

Positive Moment

T

C

N.A.

Compression (C)

Neutral Axis (N.A.)

Tension (T)

Negative Moment

C

T

N.A.

Figure P.2.10 Positive and Negative Moment 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.12 

Beams and girders are the most common bridge elements used to resist bending 

moments. The flanges are most critical because they provide the greatest 

resistance to the compressive and tensile forces developed by the moment (see 

Figure P.2.11). 

Figure P.2.11 Girder Cross Section 

Bending stress is normally considered zero at the neutral axis. On a cross section 

of a member, bending stresses vary linearly with respect to the distance from the 

neutral axis (see Figures P.2.10 and P.2.12). 

The formula for maximum bending stress is (see Figure P.2.12): 

 

where: fb = bending stress on extreme fiber (or surface) of beam 

M = applied moment 

c = distance from neutral axis to extreme fiber (or surface) of 

beam 

I = moment of inertia (a property of the beam cross-sectional 

area and shape) 

N/A 

I

Mc

b

f =
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.13 

Figure P.2.12 Bending Stresses 

Shear Forces Shear is a force, which results from equal but opposite transverse forces, which 

tend to slide one section of a member past an adjacent section (see Figure P.2.13). 

Shear forces are generally expressed in English units of pounds or kips, and 

metric units of Newtons or kilonewtons. 

Example of shear: When scissors are used to cut a piece of paper, a shear force 

has caused one side of the paper to separate from the other. Scissors are often 

referred to as shears since they exert a shear force. 

Figure P.2.13 Shear Forces in a Member Element 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.14 

Beams and girders are common shear resisting members. In an I- or T-beam, 

most of the shear is resisted by the web (see Figure P.2.11). The shear stress 

produced by the transverse forces is manifested in a horizontal shear stress which 

is accompanied by a vertical shear stress of equal magnitude. The horizontal 

shear forces are required to keep the member in equilibrium (not moving). 

Vertical shear strength is generally considered in most design criteria. The 

formula for vertical shear stress in I- or T-beams is: 

where: fv = shear stress 

V = vertical shear due to external loads 

Aw = area of web 

Torsional Forces Torsion is a force resulting from externally applied moments which tend to rotate 

or twist a member about its longitudinal axis. Torsional force is commonly 

referred to as torque and is generally expressed in English units of pound-feet or 

kip-feet, and metric units of Newton-meters or Kilonewtons-meters. 

Example of torsion: One end of a long rectangular steel bar is clamped 

horizontally in a vise so that the long side is up and down. Using a large wrench, 

a moment is applied to the other end, which causes it to rotate so that the long side 

is now left to right. The steel bar is resisting a torsional force or torque which has 

twisted it 90 ̊ with respect to its original orientation (see Figure P.2.14). 

Torsional forces develop in bridge members, which are interconnected and 

experience unbalanced loadings. Bridge elements are generally not designed as 

torsional members. However, in some bridge superstructures where elements are 

framed together, torsional forces can occur in longitudinal members. When these 

members experience differential deflection, adjoining transverse members apply 

twisting moments resulting in torsion. In addition, curved bridges are generally 

subject to torsion (see Figure P.2.15). 

Figure P.2.14 Torsion 

W

v A

V f =
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.15 

Figure P.2.15 Torsional Distortion 

Reactions A reaction is a force provided by a support that is equal but opposite to the force 

transmitted from a member to its support (see Figure P.2.16). Reactions are most 

commonly vertical forces, but a reaction can also be a horizontal force. The 

reaction at a support is the measure of force that it must transmit to the ground. A 

vertical reaction increases as the loads on the member are increased or as the 

loads are moved closer to that particular support. Reactions are generally 

expressed in English units of pounds or kips, and metric units of Newtons or 

kilonewtons. 

Example of reactions: Consider a bookshelf consisting of a piece of wood 

supported at its two ends by bricks. The bricks serve as supports, and the reaction 

is based on the weight of the shelf and the weight of the books on the shelf. As 

more books are added, the reaction provided by the bricks will increase. As the 

books are shifted to one side, the reaction provided by the bricks at that side will 

increase, while the reaction at the other side will decrease. 

Figure P.2.16 Types of Supports 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.16 

The loads of the entire bridge always equal the reactions provided by the 

abutments and the piers. However, on a smaller scale, each individual beam and 

girder also exerts forces, which create reactions provided by its supporting 

members. 

P.2.4 

Material Response 

to Loadings 

Each member of a bridge has a unique purpose and function, which directly affects 

the selection of material, shape, and size for that member. Certain terms are used 

to describe the response of a bridge material to loads. A working knowledge of 

these terms is essential for the bridge inspector. 

Force A force is the action that one body exerts on another body. Force has two 

components: magnitude and direction (see Figure P.2.17). The basic English unit 

of force is called pound (abbreviated as lb.). The basic metric unit of force is 

called Newton (N). A common unit of force used among engineers is a kip (K), 

which is 1000 pounds. In the metric system, the kilonewton (kN), which is 1000 

Newtons, is used. Note: 1 kip = 4.4 kilonewton. 

Fy

Fz

Fx

F (Force)

Figure P.2.17 Basic Force Components 

Stress Stress is a basic unit of measure used to denote the intensity of an internal force. 

When a force is applied to a material, an internal stress is developed. Stress is 

defined as a force per unit of cross-sectional area. 

The basic English unit of stress is pounds per square inch (abbreviated as psi). 

However, stress can also be expressed in kips per square inch (ksi) or in any other 

units of force per unit area. The basic metric unit of stress is Newton per square 

meter, or Pascal (Pa). An allowable unit stress is generally established for a given 

material. Note: 1 ksi = 6.9 Pa. 

Area (A)

Force (F) Stress(S) =
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.17 

Example of a stress: If a 30,000 lb. force acts uniformly over an area of 10 

square inches, then the stress caused by this force is 3000 psi (or 3 ksi). 

Similarly, if a 40,000 Newton force acts uniformly over an area of 20 square 

meters, then the stress caused by this force is 2000 Pa. 

Deformation Deformation is the local distortion or change in shape of a material due to stress. 

Strain 

Strain is a basic unit of measure used to describe an amount of deformation. It 

denotes the ratio of a material’s deformed dimension to a material’s original 

dimensions. For example, strain in a longitudinal direction is computed by 

dividing the change in length by the original length. 

Original Length (L)

Change in Length ( L) Strain ( ) Δ

ε =

Strain is a dimensionless quantity. However, it can also be expressed as a 

percentage or in units of length per length (e.g., inch/inch). 

Example of strain: If a force acting on a 20 foot long column causes an axial 

deformation of 0.002 feet, then the resulting axial strain is 0.002 feet divided by 20 

feet, or 0.0001 foot/foot. This strain can also be expressed simply as 0.0001 (with 

no units) or as 0.0l%. 

Similarly, if a force acting on a 50 m long column causes an axial deformation of 

0.05 m, then the resulting axial strain is 0.001 m/m. This strain can also be 

compressed simply as 0.001 (with no units) or as 0.1%. 

Elastic Deformation

Elastic deformation is the reversible distortion of a material. A member is 

elastically deformed if it returns to its original shape upon removal of a force. 

Elastic strain is sometimes termed reversible strain because it disappears after the 

stress is removed. Bridges are designed to deform elastically and return to their 

original shape after the live loads are removed. 

Example of elastic deformation: A stretched rubber band will return to its 

original shape after being released from a taut position. Generally, if the strain is 

elastic, there is a direct proportion between the amount of strain and the applied 

stress. 

Plastic Deformation

Plastic deformation is the irreversible or permanent distortion of a material. A 

material is plastically deformed if it retains a deformed shape upon removal of a 

stress. Plastic strain is sometimes termed irreversible or permanent strain because 

it remains after the stress is removed. Plastic strain is not directly proportional to 

the given applied stress as is the case with the elastic strain. 

Example of plastic deformation: If a car crashed into a brick wall, the fenders 

and bumpers would deform. This deformation would remain even after the car is 

backed away from the wall. Therefore, the fenders and bumpers have undergone 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.18 

plastic deformation. 

Creep

Creep is a form of plastic deformation that occurs gradually at stress levels 

normally associated with elastic deformation. Creep is defined as the gradual, 

continuing irreversible change in the dimensions of a member due to the sustained 

application of load. It is caused by the molecular readjustments in a material under 

constant load. The creep rate is the change in strain (plastic deformation) over a 

certain period of time. 

Example of creep: If heavy paint cans remain left untouched on a thin wooden 

shelf for several months, the shelf will gradually deflect and change in shape. This 

deformation is due to the sustained application of a constant dead load and 

illustrates the effects of creep. 

Thermal Effects

In bridges, thermal effects are most commonly experienced in the longitudinal 

expansion and contraction of the superstructure. It is possible to disregard 

deformations caused by thermal effects when members are free to expand and 

contract. However, there may be members for which expansion and contraction is 

inhibited or prevented in certain directions. Thermal changes in these members can 

cause significant frictional stresses and must be considered by the inspector. 

Materials expand as temperature increases and contract as temperature decreases. 

The amount of thermal deformation in a member depends on: 

3⁄4 A coefficient of thermal expansion, unique for each material 

3⁄4 The temperature change 

3⁄4 The member length 

Example of thermal effects: Most thermometers operate on the principle that the 

material within the glass bulb expands as the temperature increases and contracts 

as the temperature decreases. 

Stress-Strain 

Relationship 

For most structural materials, values of stress and strain are directly proportional 

(see Figure P.2.18). However, this proportionality exists only up to a particular 

value of stress called the elastic limit. Two other frequently used terms, which 

closely correspond with the elastic limit, are the proportional limit and the yield 

point. 

When applying stress up to the elastic limit, a material deforms elastically. 

Beyond the elastic limit, deformation is plastic and strain is not directly 

proportional to a given applied stress. The material property, which defines its 

stress-strain relationship, is called the modulus of elasticity, or Young’s modulus. 

Modulus of Elasticity

Each material has a unique modulus of elasticity, which defines the ratio of a given 

stress to its corresponding strain. It is the slope of the elastic portion of the stressstrain curve. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.19 

Strain ( )

Stress(S) Modulus of Elasticity (E)

ε =

The modulus of elasticity applies only as long as the elastic limit of the material 

has not been reached. The units for modulus of elasticity are the same as those for 

stress (i.e., psi or ksi for English, and Pa or kPa for metric). 

Figure P.2.18 Stress-Strain Diagram 

Example of modulus of elasticity: If a stress of 20 MPa (2900 psi) is below the 

elastic limit and causes a strain of 0.0001, then the modulus of elasticity can be 

computed based on these values of stress and strain. 

29,000,000 psi 29,000 ksi(200,000 MPa) 0.0001

2,900 psi E = = =

This is approximately equal to the modulus of elasticity for steel. The modulus of 

elasticity for concrete is approximately 20,700 to 31,000 MPa (3000 to 4500 ksi), 

and for commonly used grades of timber it is approximately 11,000 MPa (1600 

ksi). 

Overloads Overload damage may occur when members are overstressed. Overload occurs 

when the stresses applied are greater than the elastic limit for the material. 

Buckling 

Buckling is the tendency of a member to crush or bend out of plane when 

subjected to a compressive force. As the length and slenderness of a compression 

member increases, the likelihood of buckling also increases. 

Compression members require additional cross-sectional area or bracing to resist 

buckling. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.20 

Example of buckling: A paper or plastic straw compressed axially at both ends 

with an increasing force will eventually buckle. 

Elongation 

Elongation is the tendency of a member to extend, stretch or crack when 

subjected to a tensile force. Elongation can be either elastic or plastic. 

Example of elongation: A piece of taffy pulled will stretch in a plastic manner. 

Ductility is the measure of plastic (permanent) strain that a material can endure. 

A ductile material will undergo a large amount of plastic deformation before 

breaking. It will also have a greatly reduced cross-sectional area before breaking.

Example of ductility: A baker working with pizza dough will find that the 

dough can be stretched a great deal before it will break into two sections. 

Therefore, pizza dough is a ductile material. When the dough finally does break, 

it will have a greatly reduced cross-sectional area. 

Structural materials for bridges that are generally ductile include: 

Ductility and Brittleness 

3⁄4 Steel 

3⁄4 Aluminum 

3⁄4 Copper 

3⁄4 Wood 

Brittle, or non-ductile, materials will not undergo significant plastic deformation 

before breaking. Failure of a brittle material occurs suddenly, with little or no 

warning. 

Example of brittleness: A glass table may be able to support several magazines 

and books. However, if more and more weight is piled onto the table, the glass 

will eventually break with little or no warning. Therefore, glass is a brittle 

material. 

Structural materials for bridges that are generally brittle include: 

3⁄4 Concrete 

3⁄4 Cast iron 

3⁄4 Stone 

3⁄4 Fiber Reinforced Polymer 

 

Fatigue Fatigue is a material response that describes the tendency of a material to break 

when subjected to repeated loading. Fatigue failure occurs within the elastic 

range of a material after a certain number and magnitude of stress cycles have 

been applied. 

Each material has a hypothetical maximum stress value to which it can be loaded 

and unloaded an infinite number of times. This stress value is referred to as the 

fatigue limit and is usually lower than the breaking strength for infrequently 

applied loads. 

Ductile materials such as steel and aluminum have high fatigue limits, while 

brittle materials such as concrete have low fatigue limits. Wood has a high 

fatigue limit even though it is more like a brittle material than a ductile one. 

Example of fatigue: If a rubber band is stretched and then allowed to return to 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.21 

its original position (elastic deformation), it is unlikely that the rubber band will 

break. However, if this action is repeated many times, the rubber band will 

eventually break. The rubber band failure is analogous to a fatigue failure. 

For a description of fatigue categories for various steel details, refer to Topic 8.1. 

Isotropy A material that has the same mechanical properties regardless of which direction 

it is loaded is said to be isotropic. 

Example of isotropy: Plain, unreinforced concrete, and steel. 

For a description of isotropic materials, refer to Topics 2.2 and 2.3. 

P.2.5 

Mechanics of 

Materials 

Materials respond to loadings in a manner dependent on their mechanical 

properties. In characterizing materials, certain mechanical properties must be 

defined. 

Yield Strength The ability of a material to resist plastic (permanent) deformation is called the 

yield strength. Yield strength corresponds to stress level defined by a material’s 

yield point. 

Tensile Strength The tensile strength of a material is the stress level defined by the maximum 

tensile load that it can resist without failure. Tensile strength corresponds to the 

highest ordinate on the stress-strain curve and is sometimes referred to as the 

ultimate strength. 

Toughness Toughness is a measure of the energy required to break a material. It is related to 

ductility. Toughness is not necessarily related to strength. A material might have 

high strength but little toughness. A ductile material with the same strength as a 

non-ductile material will require more energy to break and thus exhibit more 

toughness. For highway bridges, the CVN (Charpy V-notch) toughness is the 

toughness value usually used. It is an indicator of the ability of the steel to resist 

crack propagation in the presence of a notch or flaw. The unit for toughness N-m 

@ degrees C (ft-lbs @ degrees F). 

P.2.6 

Bridge Movements Bridges move because of many factors; some are anticipated, but others are not. 

Unanticipated movements generally result from settlement, sliding, and rotation 

of foundations. Anticipated movements include live load deflections, thermal 

expansions and contractions, shrinkage and creep, earthquakes, rotations, wind 

drifting, and vibrations. Of these movements, the three major anticipated 

movements are live load deflections, thermal movements. and rotational 

movements. 

Live Load Deflections Deflection produced by live loading should not be excessive because of 

aesthetics, user discomfort, and possible damage to the whole structure. 

Limitations are generally expressed as a deflection-to-span ratio. AASHTO 

generally limits live load bridge deflection for steel and concrete bridges to 1/800 

(i.e., 25-mm (1inch) vertical movement per 20.3 m (67 feet) of span length). For 

bridges that have sidewalks, AASHTO limits live load bridge deflection to 1/1000 

(i.e., 25-mm (1-inch) vertical movement per 25 m (83 feet) of span length). 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.22 

Thermal Movements The longitudinal expansion and contraction of a bridge is dependent on the range 

of temperature change, length of bridge, and most importantly, materials used in 

construction. Thermal movements are frequently accommodated using expansion 

joints and movable bearings. To accommodate thermal movements, AASHTO 

recommends the designer allow 32-mm (1-1/4 inches) of movement for each 30.5 

m (100 feet) of span length for steel bridges and 30-mm (1-3/16 inches) of 

movement for each 30.5 m (100 feet) of span length for concrete bridges. 

Rotational Movements Rotational movement in bridges is a direct result of live load deflection and 

occurs with the greatest magnitude at the bridge supports. This movement can be 

accommodated using bearing devices that permit rotation. 

P.2.7 

Design Methods Bridge engineers use various design methods that incorporate safety factors to 

account for uncertainties and random deviations in material strength, fabrication, 

construction, durability, and loadings. 

Allowable Stress Design The Allowable Stress Design (ASD) or Working Stress Design (WSD) is a 

method in which the maximum stress a particular member may carry is limited to 

an allowable or working stress. The allowable or working stress is determined by 

applying an appropriate factor of safety to the limiting stress of the material. For 

example, the allowable tensile stress for a steel tension member is 0.55 times the 

steel yield stress. This results in a safety factor of 1.8. The capacity of the 

member is based on either the inventory rating level or the operating rating level. 

AASHTO currently has ten possible WSD group loadings. 

Load Factor Design Load Factor Design (LFD) is a method in which the ultimate strength of a 

material is limited to the combined effect of the factored loads. The factored 

loads are determined from the applied loadings, which are increased by selected 

multipliers that provide a factor of safety. The load factors for AASHTO Group I 

are 1.3(DL+1.67(LL+I)). AASHTO currently has ten possible LFD group 

loadings. 

Load and Resistance 

Factor Design 

Load and Resistance Factor Design (LRFD) is a design procedure based on the 

actual strength, rather than on an arbitrary calculated stress. It is an ultimate 

strength concept where both working loads and resistance are multiplied by 

factors, and the design performed by assuming the strength exceeds the load. 

(The load multipliers used in LRFD are not the same multipliers that are used in 

LFD.) 

These design methods are conservative due to safety factors and limit the stress in 

bridge members to a level well within the material’s elastic range, provided that 

the structural members are in good condition. That is why it is important for 

inspectors to accurately report any deficiency found in the members. 

P.2.8 

Bridge Ratings One of the primary functions of a bridge inspection is to collect information 

necessary for a bridge load capacity rating. Therefore, the bridge inspector 

should understand the principles of bridge load ratings. Bridge load rating 

methods and guidelines are provided by AASHTO in the Manual for Condition 

Evaluation of Bridges, and Manual for Condition Evaluation and LRFR of

Highway Bridges. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.23 

A bridge load rating is used to determine the usable live load capacity of a bridge. 

Each member of a bridge has a unique load rating, and the bridge load rating 

represents the most critical one. Bridge load rating is generally expressed in units 

of tons, and it is computed based on the following basic formula: 

A L(1 I)

C A D Bridge Rating Factor (RF)

2

1

+

− =

where: RF= the rating factor for the live-load carrying capacity; the 

rating factor multiplied by the rating vehicle in tons gives 

the rating of the structure 

 C = the capacity of the member 

 D = the dead load effect on the member 

 L = the live load effect on the member 

 I = the impact factor to be used with the live load effect 

 A1 = factor for dead loads 

 A2 = factor for live loads 

Bridge load rating for LRFR is computed based on the following basic formula: 

( IM)

C ( Bridge Rating Factor (RF) )(LL

)(DC) ( )(DW) ( )(P)

L

DC DW P

γ +

− γ = − γ ± γ

where: RF= rating factor 

 C = capacity 

 DC = dead load effect due to structural components and 

attachments 

 DW= dead load effect due to wearing surface and utilities 

 P = permanent load other than dead loads 

 LL = live load effect 

 IM = dynamic load allowance 

 γDC = LRFD load factor for structural components and 

attachments 

 γDW = LRFD load factor for wearing surfaces and utilities 

 γP = LRFD load factor for permanent loads other than dead 

loads = 1.0 

 γL = evaluation live-load factor 

Both of the formulas above determine a rating factor for the controlling member 

of the bridge. For either case, the safe load capacity in tons can be calculated as 

follows: 

RT = RF× W

where: RT= rating in tons for truck used in computing live-load effect

 RF= rating factor 

 W = weight in tons of truck used in computing live-load effect 

Note that when LRFR lane loading controls the rating, the equivalent truck weight 

(W) to be used in calculating the safe load capacity in tons is 40 tons. 

Inventory Rating The inventory rating level generally corresponds to the customary design level of 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.24 

stresses but reflects the existing bridge and material conditions with regard to 

deterioration and loss of section. Load ratings based on the inventory level allow 

comparisons with the capacity for new structures and, therefore, results in a live 

load, which can safely utilize an existing structure for an indefinite period of time. 

For the allowable stress method, the inventory rating for steel used to be based on 

55% of the yield stress. Inventory ratings have been refined to reflect the various 

material and load types. See the AASHTO Manual for Condition Evaluation of

Bridges (Section 6.6.2 for Allowable Stress Inventory Ratings and Section 6.6.3 

for Load Factor Inventory Ratings). 

The LRFD design level is comparable to the traditional Inventory rating. Bridges 

that pass HL-93 screening at the Inventory level are capable of carrying 

AASHTO legal loads and state legal loads within the AASHTO exclusion limits 

described in the LRFD Bridge Design Specifications. 

Operating Rating Load ratings based on the operating rating level generally describe the maximum 

permissible live load to which the structure may be subjected. Allowing 

unlimited numbers of vehicles to use the bridge at operating level may shorten the 

life of the bridge. For steel, the allowable stress for operating rating used to be 

75% of the yield stress. Operating ratings have been refined to reflect the various 

material and load types. See the AASHTO Manual for Condition Evaluation of

Bridges (Section 6.6.2 for Allowable Stress Operating Ratings and Section 6.6.3 

for Load Factor Operating Ratings). 

 

Permit Loading Special permits for heavier than normal vehicles may occasionally be issued by a 

governing agency. The load produced by the permit vehicle must not exceed the 

structural capacity determined by the operating rating. 

The second level rating is a legal load rating providing a single safe load capacity 

for a specific truck configuration. The second level rating is comparable to the 

traditional Operating rating. Bridges that pass HL-93 screening at the Operating 

level are capable of carrying AASHTO legal loads, but may not rate for state legal 

loads especially those that are considerably heavier than AASHTO trucks. 

The third level rating is used to check the serviceability and safety of bridges in 

the review of permit applications. Permits are required for vehicles above the 

legal load. This third level rating should only be applied to bridges with sufficient 

capacity for AASHTO legal loads. Calibrated load factors by permit type and 

traffic conditions are specified for checking the effect of the overweight vehicle. 

Guidance on checking serviceability criteria are also given. 

Rating Vehicles Rating vehicles are truck loads applied to the bridge to establish the inventory and 

operating ratings. These rating vehicles (see Figure P.2.19) include: 

3⁄4 H loading 

3⁄4 HS loading 

3⁄4 HL-93 

3⁄4 Alternate Interstate Loading (Military Loading) 

3⁄4 Type 3 unit 

3⁄4 Type 3-S2 unit 

3⁄4 Type 3-3 unit 

3⁄4 The maximum legal load vehicles of the state 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.25 

Figure P.2.19 Rating Vehicles 

The axle spacing and weights of the Type 3 unit, Type 3-S2 unit, and Type 3-3 

unit are based on actual vehicles. However, as described previously, the H and 

HS loadings do not represent actual vehicles. 

These standard rating vehicles were chosen based on load regulations of most 

states and governing agencies. However, individual states and agencies may also 

establish their own unique rating vehicles. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.26 

Bridge Posting Bridge loads are posted to warn the public of the load capacity of a bridge, to 

avoid safety hazards, and to adhere to federal law. Federal regulation requires 

highway bridges on public roads to be inspected every twenty-four months for 

lengths greater than 6.1 m (20 feet). Federal regulation also requires bridges to be 

posted when the State's legal loads exceed the operating rating or equivalent 

rating factor for the bridge. It is the inspector’s responsibility to gather and 

provide information that the structural engineer can use to analyze and rate the 

bridge. 

The safe load-carrying capacity of a bridge considers the following criteria: 

3⁄4 Physical condition 

3⁄4 Potential for fatigue damage 

3⁄4 Type of structure/configuration 

3⁄4 Truck traffic data 

Bridge postings show the maximum allowable load by law for single vehicles and 

combinations while still maintaining an adequate safety margin (see Figure 

P.2.20). 

Figure P.2.20 Bridge Weight Limit Posting 

Failure to comply with bridge posting may result in fines, tort suits/financial 

liabilities, accidents, or even death. In addition, bridges may be damaged when 

postings are ignored (see Figure P.2.21). 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.27 

Figure P.2.21 Damaged Bridge due to Failure to Comply with Bridge Posting 

P.2.9 

Span Classifications Beams and bridges are classified into three span classifications that are based on 

the nature of the supports and the interrelationship between spans. These 

classifications are: 

3⁄4 Simple 

3⁄4 Continuous 

3⁄4 Cantilever 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.28 

Beam

Diagram

Deflection

Diagram

Shear Diagram

Moment

Diagram

 C - compression

 T - tension

N/A - neutral axis

Detail A

See Detail A

N/A T

C

Simple A simple span is a span with only two supports, each of which is at or near the end 

of the span (see Figure P.2.22). 

Figure P.2.22 Simple Span 

A simple span bridge can have a single span supported at the ends by two 

abutments or multiple spans with each span behaving independently of the others. 

Some characteristics of simple span bridges are: 

3⁄4 When loaded, the span deflects downward and rotates at the supports (i.e., 

the abutments) 

3⁄4 The sum of the reactions provided by the two supports equals the entire 

load 

3⁄4 Shear forces are maximum at the supports and zero at or near the middle 

of the spans 

3⁄4 Bending moment throughout the span is positive and maximum at or near 

the middle of the span (the same location at which shear is zero); bending 

moment is zero at the supports 

3⁄4 The part of the superstructure below the neutral axis is in tension while 

the portion above the neutral axis is in compression 

A simple span bridge is easily analyzed using equilibrium equations. However, it 

does not always provide the most economical design solution. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.29 

Beam Diagram

Deflection Diagram

Shear Diagram

Moment Diagram

See Detail A See Detail B

 C - compression

 T - tension

N/A - neutral axis

Detail A

N/A T

C

Detail B

N/A T

C

Continuous A continuous span is a configuration in which a beam has one or more 

intermediate supports and the behavior of each individual span is dependent on its 

adjacent spans (see Figure P.2.23). 

A continuous span bridge is one which is supported at the ends by two abutments 

and which spans uninterrupted over one or more piers. Some characteristics of 

continuous span bridges are: 

3⁄4 When loaded, the spans deflect downward and rotate at the supports (i.e., 

the abutments and the piers) 

3⁄4 The reactions provided by the supports depend on the span configuration 

and the distribution of the loads 

3⁄4 Shear forces are maximum at the supports and zero at or near the middle 

of the spans 

3⁄4 Positive bending moment is greatest at or near the middle of each span 

3⁄4 Negative bending moment is greatest at the intermediate supports (i.e., 

the piers); the bending moment is zero at the end supports (i.e., the 

abutments); there are also two locations per intermediate support at which 

bending moment is zero, known as inflection points 

3⁄4 For positive bending moments, compression occurs on the top portion of 

the beam and tension occurs on the bottom portion of the beam 

3⁄4 For negative bending moments, tension occurs on the top portion of the 

beam and compression occurs on the bottom portion of the beam 

Figure P.2.23 Continuous Span 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.30 

Beam Diagram

Deflection Diagram

Shear Diagram

Moment Diagram

See Detail A

N/A

T

C C - compression

 T - tension

N/A - neutral axis

Detail A

A continuous span bridge allows longer spans and is more economical than a 

bridge consisting of many simple spans. This is due to its efficient design with 

members that are shallower. However, a continuous bridge is more difficult to 

analyze than a simple span bridge and is more susceptible to overstress conditions 

if the abutments or piers settle. 

Cantilever A cantilever span is a span with one end restrained against rotation and deflection 

and the other end completely free (see Figure P.2.24). The restrained end is also 

known as a fixed support (see Figure P.2.18). 

While a cantilever generally does not form an entire bridge, portions of a bridge 

can behave as a cantilever (e.g., cantilever bridges and bascule bridges). Some 

characteristics of cantilevers are: 

3⁄4 When loaded, the span deflects downward, but there is no rotation or 

deflection at the support 

3⁄4 The fixed support reaction consists of a vertical force and a resisting 

moment 

3⁄4 The shear is maximum at the fixed support and is zero at the free end 

3⁄4 The bending moment throughout the span is negative and maximum at the 

fixed support; bending moment is zero at the free end 

Figure P.2.24 Cantilever Span 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.31 

When cantilever spans are incorporated into a bridge, they are generally extensions 

of a continuous span. Therefore, moment and rotation at the cantilever support 

will be dependent on the adjacent span (see Figure P.2.25). 

Beam Diagram

Deflection Diagram

Shear Diagram

Moment Diagram

See Detail A

 C - compression

 T - tension

N/A - neutral axis

Detail A

N/A

T

C

Anchor Span

Suspended

Span Anchor Span

Cantilever

Figure P.2.25 Cantilever Bridge 

P.2.10 

Bridge Roadway 

Interaction 

Bridges also have two classifications that are based on the relationship between the 

deck and the superstructure. These classifications are: 

3⁄4 Non-composite 

3⁄4 Composite 

Non-composite A non-composite structure is one in which the superstructure acts independently of 

the deck. Therefore, the beams or floor systems alone must resist all of the loads 

applied to them, including the dead load of the superstructure, deck, and railing, 

and all of the live loads. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.32 

Composite A composite structure is one in which the deck acts together with the 

superstructure to resist the loads (see Figure P.2.26). The deck material must be 

strong enough to contribute significantly to the overall strength of the section. The 

deck material is different than the superstructure material. The most common 

combinations are concrete deck on steel superstructure and concrete deck on 

prestressed concrete superstructure. Shear connectors such as studs, spirals, 

channels, or stirrups that are attached to the superstructure and are embedded in a 

deck provide composite action. This ensures that the superstructure and the deck 

will act as a unit by preventing slippage between the two when a load is applied. 

Figure P.2.26 Composite Concrete Deck on Steel Beams and Pretressed 

Concrete Beams 

Composite action is achieved only after the concrete deck has hardened. 

Therefore, some of the dead load (Dead Load 1) must be resisted by the noncomposite action of the superstructure alone. These dead loads include the weight 

of: 

3⁄4 The superstructure itself 

3⁄4 Any diaphragms and cross-bracing 

3⁄4 The concrete deck 

3⁄4 Any concrete haunch between the superstructure and the deck 

3⁄4 Any other loads which are applied before the concrete deck has hardened 

Other dead loads, known as superimposed dead loads (Dead Load 2), are resisted 

by the superstructure and the concrete deck acting compositely. Superimposed 

dead loads include the weight of: 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.33 

3⁄4 Any anticipated future deck pavement 

3⁄4 Parapets 

3⁄4 Railings 

3⁄4 Any other loads which are applied after the concrete deck has hardened 

Since live loads are applied to the bridge only after the deck has hardened, they 

are also resisted by the composite section. 

The bridge inspector can identify a simple span, a continuous span, and a 

cantilever span based on their configuration. However, the bridge inspector can 

not identify the relationship between the deck and the superstructure while at the 

bridge site. Therefore, bridge plans must be reviewed to determine whether a 

structure is non-composite or composite. 

Integral On an integral bridge deck, the deck portion of the beam is constructed to act 

integrally with the stem, providing greater stiffness and allowing increased span 

lengths (see Figure P.2.27). 

Figure P.2.27 Integral Bridge 

Orthotropic An orthotropic deck consists of a flat, thin steel plate stiffened by a series of 

closely spaced longitudinal ribs at right angles to the floor beams. The deck acts 

integrally with the steel superstructure. An orthotropic deck becomes the top 

flange of the entire floor system. Orthotropic decks are occasionally used on large 

bridges (see Figure P.2.28). 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.34 

Steel Plate Deck

Types of Closed

Ribs

Epoxy Asphalt

Wearing Surface 3⁄4"

to 2" Thick

Figure P.2.28 Orthotropic Bridge Deck 

P.2.11 

Redundancy Redundancy is the quality of a bridge that enables it to perform its design function 

in a damaged state. 

There are three types of redundancy in bridge design. 

Load Path Redundancy 

Bridge designs that are load path redundant have three or more main load-carrying 

members or load paths between supports. If one member were to fail, load would 

be redistributed to the other members and bridge failure would not be expected. 

Bridge designs that are non-redundant have two or fewer main load carrying 

members or load paths. 

Structural Redundancy

Most bridge designs, which provide continuity of load path from span to span are 

referred to as structurally redundant. Some continuous span two-girder bridge 

designs are structurally redundant. In the event of a member failure, loading from 

that span can be redistributed to the adjacent spans and total bridge failure may not 

occur. 

Internal Redundancy

Internal redundancy is when a bridge member contains several elements which are 

mechanically fastened together so that multiple load paths are formed. Failure of 

one member element would not cause total failure of the member. 

Redundancy is discussed in greater detail in Topic 8.1. 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.35 

P.2.12 

Foundations Foundations are critical to the stability of the bridge since the foundation 

ultimately supports the entire structure. There are two basic types of bridge 

foundations: 

3⁄4 Shallow foundations commonly referred to as spread footings 

3⁄4 Deep foundations 

Spread Footings

A spread footing is used when the bedrock layers are close to the ground surface or 

when the soil is capable of supporting the bridge. A spread footing is typically a 

rectangular slab made of reinforced concrete. This type of foundation "spreads 

out" the loads from the bridge to the underlying rock or well-compacted soil. 

While a spread footing is usually buried, it is generally covered with a minimal 

amount of soil. In cold regions, the bottom of a spread footing will be just below 

the recognized maximum frost line depth for that area (see Figure P.2.29). 

Deep Foundations

A deep foundation is used when the soil is not suited for supporting the bridge or 

when the bedrock is not close to the ground surface. A pile is a long, slender 

support that is typically driven into the ground but can be partially exposed. It is 

made from steel, concrete, or timber. Various numbers and configurations of piles 

can be used to support a bridge foundation. This type of foundation transfers load 

to sound material well below the surface or, in the case of friction piles, to the 

surrounding soil (see Figure P.2.30). “Caissons”, “drilled caissons”, and “drilled 

shafts” are frequently used to transmit loads to bedrock in a manner similar to 

piles. 

Soil

Soil

Rock

Figure P.2.29 Spread Footing 
SECTION P: Basic Concepts Primer 

Topic P.2: Bridge Mechanics 

P.2.36 

Soil

Rock

Soil

Figure P.2.30 Pile Foundation