Transcript POPSICLE BRIDGES How Bridges Are Engineered To Withstand

POPSICLE BRIDGES
How Bridges Are Engineered To Withstand
Weight, While Being Durable,
And In Some Cases Aesthetically Pleasing
Institute Of Electrical And Electronics Engineers, Phoenix Section
ARIZONA SCIENCE LAB®
“Helping Students Transfer What Is Learned In The Classroom To The World Beyond”
Copyright Notice
This presentation includes material copied from these web sites:
HowStuffWorks — “How Bridges Work,”
http://science.howstuffworks.com/engineering/civil/bridge.htm
PBS “Building Big — The Labs,”
http://www.pbs.org/wgbh/buildingbig/lab/index.html
PBS “Building Big — Bridge Basics,” http://www.pbs.org/wgbh/buildingbig/bridge/basics.html
Oracle Education Foundation, ThinkQuest, http://library.thinkquest.org/J002223/types/types.html
YouTube — “Tacoma Bridge,”
http://www.youtube.com/watch?v=3mclp9QmCGs
Bridge Types — Beam Structure Bridges,
http://www.pennridge.org/works/brbeam.html
National Grid for Learning — The Bridges Project: Bridge Types,
http://www.bardaglea.org.uk/bridges/bridge-types/bridge-types-intro.html
Bridge Basics — A Spotter's Guide to Bridge Design,
http://www.pghbridges.com/basics.htm
This presentation may only be used free of charge and only for
educational purposes, and may not be sold or otherwise used
for commercial purposes
What Is A Bridge?
• A bridge is a structure built to span a valley, road, body
of water, or other physical obstacle, for the purpose of
providing passage over the obstacle
• There are more than half a million bridges in the
United States
• But do you know how they work?
• Or why some bridges are curved while others are
straight?
• Engineers must consider many things -- like the
distance to be spanned and the types of materials
available -- before determining the size, shape, and
overall look of a bridge
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What Is The Problem In Building A Bridge?
• The bridge will only be supported at each end
where it sits on the surrounding terrain
– There will not be any support in the middle of
the bridge unless we build a vertical pillar there,
and that may not be possible
• So the weight of the people, cars, trains, etc. on the
middle of the bridge has to be supported by the
two ends where the bridge sits on the surrounding
terrain
• Somehow the weight in the middle of the bridge
has to be transferred to the two ends
• How can this be accomplished?
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What Is A Force?
In physics, a force is any external agent that
causes a change in the motion of a free body,
or that causes stress in a fixed body
Or
In Simpler Terms . . .
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What Is A Force?
It can also be described as a push or pull that
can cause an object with mass to change its
speed or direction ( to accelerate ) or which can
cause a flexible object to deform.
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Compression, Tension & Shear Forces
•
•
•
•
•
Compression = squeezing
Tension = stretching
Shear = sliding
Torsion = twisting
All materials are stronger in compression and
tension and shear than in twisting (torsion) or
bending
• The various bridge structure designs endeavor to
maximize compression, tension and shear forces
while minimizing torsion and bending forces
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Stress And Strain
• Stress is a measurement of the strength of a material
• Strain is a measure of the change in the shape of the
object that is undergoing stress
• There are three main types of stress:
– If we stretch or compress an object, we are
subjecting it to a tensile stress
– If an object is subjected to a force along an entire
surface, changing its volume, then it is said to be
experiencing a bulk stress
– Finally, if the force is acting tangentially to the
surface, causing it to twist, then we are subjecting it
to a shear stress
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Stress And Strain (cont’d)
• Consider a bar of cross sectional area A being subjected to equal
and opposite forces F pulling at the ends
– If this were a rope, we would say that it is experiencing a
tension force
• Taking this concept over, we say that the bar is under tension,
and is experiencing a stress that we define to be the ratio of the
force to the cross sectional area
Stress = F/A
– This stress is called the tensile stress because every part of the
object is subjected to a tension
– The SI unit of stress is the Newton per square meter, which is
called the Pascal
– 1 Pascal = 1 Pa = 1 N/m2
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Stress And Strain (cont’d)
• The fractional amount that an object stretches when it is
subjected to a tensile stress is called the tensile strain
• Mathematically, we write this as
where l0 is the original unstressed length of the bar
• Robert Hooke found that, when the forces are not too large, the
amount of strain experience by an object was directly
proportional to the stress
• Define the elastic modulus to be
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Beam Bridge
• The beam bridge consists of a
horizontal beam supported at each
end by piers in the banks
– A log bridge thrown across a
stream or river is the oldest and
simplest beam bridge
• The weight of the beam pushes
straight down on the piers / banks
• The farther apart its piers / banks,
the weaker the beam becomes
• This is why beam bridges rarely
span more than 76 meters / 250
feet
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Beam Bridge: Forces
• When something pushes down on
the beam, the beam bends
• Its top edge is pushed together
(compression), and its bottom
edge is pulled apart (tension)
• So any weight sitting on the
center of the beam will be
transferred to the two ends of the
beam sitting on the river banks
(for example)
• If the supported weight becomes
very large a point will be reached
when the beam bends and breaks
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W
LOG
W/2
RIVER BED
W/2
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Why Are
Support
Beams Always
Oriented With
The Depth
Greater Than
The
Thickness?
• Because of the
force moments in
the beam
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What’s A “Moment”?
DEFINITION
A Force Acting Over a Distance
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What’s A “Moment”?
Balance happens when the moments
are EQUAL
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Where Do You Find “Moments”?
• Some Places Where Moments are at work:
o Boats
o See – Saw
o Swing Set
o Lever
o Airplanes
o You and Me
Beams in this Building
Bridges
Almost anywhere a force is at work!
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Calculating A “Moment”
MOMENT = FORCE X DISTANCE
Force2
Force1
distance1
Moment2 = ?
Moment1 = Force1 x distance1
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distance2
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Equal Forces
MOMENT = FORCE X DISTANCE
60 kg*
60 kg*
1 meter
1 meter
What are the moments?
*
The actual FORCE due to gravity is 600 Newtons
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Equal Moments
MOMENT = FORCE X DISTANCE
60 kg*
30 kg*
1 meter
2 meters
What are the moments?
*
The actual FORCES due to gravity are 600 Newtons and 300 Newtons
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Unequal Moments
60 kg*
30 kg*
1 meter
1 meter
WhatIthappens
Rotates!now?
*
The actual FORCES due to gravity are 600 Newtons and 300 Newtons
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Flexible Body
Force = 600 Nt
1 meter
Force = 300 Nt
2 meters
60 kg
30 kg
What are the moments?
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The Compression & Tension Forces Exert
A Moment About The Beam Center Point
LOAD ON BEAM ACTING
VERTICALLY DOWNWARDS
“CENTRAL AXIS” FOR
COMPRESSION FORCE
MOMENT (= “NEUTRAL
AXIS”)
BEAM
TENSION FORCE
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• THE COMPRESSION / TENSION
MOMENT IS LARGE FOR A THICK
BEAM AND SMALL FOR A THIN
BEAM
• FOR THE SAME VERTICAL
LOAD, THE COMPRESSION AND
TENSION FORCES ARE THE
SAME FOR A THICK OR THIN
BEAM
• A RIGID BEAM NEEDS A LARGE
MOMENT
• HENCE WHY THE BEAM DEPTH
IS SO IMPORTANT!
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Making The Beam Stronger
• A single beam spanning any distance
experiences compression and tension
• The very top of the beam experiences
the most compression, and the very
bottom of the beam experiences the
most tension
• The middle of the beam experiences
very little compression or tension
• If the beam were designed so that
there was more material on the top
and bottom, and less in the middle, it
would be better able to handle the
forces of compression and tension
– For this reason, I-beams are more
rigid than simple rectangular beams
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Wooden I-beams (“Engineered Wood Beams”) Are
Now Used In House Construction
• Engineered wood I-beam is a structural
component of top and bottom flanges,
which could be solid or laminated wood,
united with a plywood or oriented strand
board web of various depths separating
them
• Engineered wood I-beams are primarily
used for floor systems but can also be
found in some roof applications
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The Shape Of A Structure Affects How Strong It Is
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Triangulation
• As you saw, a triangle is a very strong
structural form
• The triangle is used in structural
designs to reinforce and support
weight
• All structures on this page rely on
the strength of the triangle
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Triangles Can Be Assembled Into A Beam Structure
• This wooden beam has been made from lengths of 2x4 stud
joined together in triangular shapes
• Because of the triangles, the beam is very strong
• A truss system takes the concept of the I-beam one step
further
• The center of the beam is made up of the diagonal
members of the truss, while the top and bottom of the
truss represent the top and bottom of the beam
• Looking at a truss in this way, we can see that the top and
bottom of the beam contain more material than its center
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These Structures Are Known As “Trusses”
• The truss is structure made up from triangular
designs and used for support to hold up more
weight and span more distance
• A truss structure is much lighter than a
corresponding solid beam of the same strength
• For this reason they are used both in house
construction and bridge construction
• A truss is always under compression and tension
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House Construction Uses The Strength Of
Triangles To Make Strong, Light Roof Supports
Over Wide Spans From 2x4 Wooden Studs
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Wooden Roof Trusses For Houses Come In
A Variety Of Shapes
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Truss Bridge
• The truss bridge consists of
an assembly of triangles
• A truss bridge is basically a
fancy beam bridge
• The triangular supports span
across the top sides of the
bridge, and sometimes
trusses are part of the under
structure of a truss bridge
• There are also trusses across
the bridge at top and bottom
to give it side-to-side
torsional (twisting) strength!
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There Are A Large Number Of Truss
Designs Used For Bridges
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Let’s Build A Bridge!
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Let’s Build A Truss Bridge!
• You will be in teams of two
• You will be given
– 200 Popsicle sticks
– A hot glue gun
• Your challenge is to design and build a truss structure bridge that will
– Span a gap of 61 cms / 24 inches between two work tables
– Support a weight of 23 kg / 50 pounds at the center point of the
bridge
– (a really well designed bridge should also support one of your
colleagues!)
– Use no more than 200 popsicle sticks
• The load weight will be placed on the upper surface of your bridge so
do not worry about building road surfaces through the bridge!
• Don’t forget to include side-to-side torsional (twisting) strength!
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OTHER TYPES OF BRIDGES
• There are other ways to design a bridge
• They all involve the same compression, tension
and shear forces as the beam and truss bridges
we have been discussing
• But these other designs accommodate those
forces in different ways from the beam and truss
and from each other
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Arch Bridge
• The arch bridge has great natural
strength
• Thousands of years ago, Romans
built arches out of stone
• Today, most arch bridges are made
of steel or concrete, and they can
span up to 800 feet
• Arches can also be set above the
deck as on the Sydney harbor bridge
in Australia
• This allows much more space
beneath for ships to pass under
• In this case the arch is combined
with the truss structure
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Arch Bridge: Forces
• The design of the arch, the semicircle,
naturally diverts the weight from the
bridge deck to the abutments
• Arch bridges are always under
compression
• The force of compression is pushed
outward along the curve of the arch
toward the abutments
• The shape of the arch itself is all that is
needed to effectively dissipate
the weight from the center of the deck
to the abutments
• As with the beam bridge, the limits of
size will eventually overtake the
natural strength of the arch
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Starrucca
Viaduct
• A stone arch bridge that
spans Starrucca
Creek near Lanesboro,
Pennsylvania
• At the time of its
construction, the bridge
was thought to be the most
expensive railway bridge in
the world, at a cost of
$320,000 (equal to
$8,595,692 today)
• It was the largest stone rail
viaduct in the mid-19th
century.
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Red River Gorge Bridge, Taos, New
Mexico
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Hoover Dam Bridge
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Conversion Of The Roman Arch To The
Gothic Arch
• The medieval stone masons belonged to “guilds”
– These were professional organizations like the IEEE!
• They did not know math and physics but they were engineers
– They observed, experimented and applied what they learnt to
the design of church structures
• Thus they realized by trial and error that the Roman arch would
be stronger if it was pointed instead of curved
– The sides of the arch would not bow outwards to the same
extent as the Roman arch
• This new design was the Gothic arch
– It allowed churches to be built with vaulting, wide ceiling
spans and reduced the number of supporting pillars
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Roman Arch
Church
• The facade of Notre Dame
du Puy, le Puy en Velay,
France
• It has a more complex
arrangement of diversified
arches:
– Doors of varying widths
– Blind arcading,
windows and open
arcades
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Gothic Arch Church (Notre Dame de
Paris)
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Interior Of Notre Dame de Paris: Gothic
Vaulted Ceiling
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Flying Buttresses: Transfer The Thrust Of The Roof
On The Arch Outwards And Down To A Pier
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Suspension Bridge
• The suspension bridge can span 610
to 2134 meters / 2,000 to 7,000 feet,
much farther than any other type of
bridge!
• A suspension bridge is one
where cables (or ropes or chains)
are strung across the river (or
whatever the obstacle happens to
be) and the deck is suspended from
these cables
• Modern suspension bridges have
two tall towers through which the
cables are strung
• Thus, the towers are supporting the
majority of the roadway's weight
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Suspension Bridge: Forces
• The force of compression pushes down on the suspension bridge's
deck, but because it is a suspended roadway, the cables transfer the
compression to the towers, which dissipate the compression directly
into the earth where they are firmly entrenched
• The supporting cables, running between the two anchorages, are the
lucky recipients of the tension forces
• The cables are literally stretched from the weight of the bridge and its
traffic as they run from anchorage to anchorage
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Suspension Bridge: Forces (cont’d)
• The anchorages are also under tension, but since they, like the
towers, are held firmly to the earth, the tension they experience
is dissipated
• Almost all suspension bridges have, in addition to the cables, a
supporting truss system beneath the bridge deck (a deck truss)
• This helps to stiffen the deck and reduce the tendency of the
roadway to sway and ripple
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Cable-Stayed Bridge
• The cable-stayed bridge is a variant of
the suspension bridge
• Like the suspension bridge, it
supports the roadway with massive
steel cables, but in a different way
• The cables run directly from the
roadway up to a tower, forming a
unique "A" shape
• Cable-stayed bridges, like the
Sunshine Skyway in Florida, require
less cable and can be built much
faster than suspension bridges
• Cable-stayed bridges are becoming
the most popular bridges for mediumlength spans (between 152 and 914
meters / 500 and 3,000 feet).
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The Millau Viaduct Is Part Of The New E11
Expressway Connecting Paris And Barcelona
• It is a cable-stayed
bridge
• It features the highest
bridge piers ever
constructed
• The tallest is 240
meters / 787 feet high
• The overall height is
an impressive 336
meters / 1102 feet,
making this the
highest bridge in the
world
• It's taller than the
Eiffel Tower!
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The Millau Viaduct
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Reinforced Concrete: Rebars Of Sagrada
Familia’s Roof In Construction (2009)
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Additional Bridge Forces: Torsion
• There are dozens of forces other than compression, tension and shear that
also must be taken into consideration when designing a bridge
• These forces are usually specific to a particular location or bridge design
• Torsion, which is a rotational or twisting force, is one which has been
effectively eliminated in all but the largest suspension bridges
• The natural shape of the arch and the additional truss structure of the
beam bridge have eliminated the destructive effects of torsion on these
bridges
• Suspension bridges, however, because of the very fact that they are
suspended (hanging from a pair of cables), are somewhat more susceptible
to torsion, especially in high winds
• All suspension bridges have deck-stiffening trusses which, as in the case of
beam bridges, effectively eliminate the effects of torsion; but in
suspension bridges of extreme length, the deck truss alone is not enough
• Wind-tunnel tests are generally conducted on models to determine the
bridge's resistance to torsional movements
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Additional Bridge Forces: Resonance
•
•
•
Resonance (a vibration in something caused by an external force that is in harmony
with the natural vibration of the original thing) is a force which, unchecked, can be fatal
to a bridge
– Resonant vibrations will travel through a bridge in the form of waves
A very famous example of resonance waves destroying a bridge is the Tacoma Narrows
bridge, which fell apart in 1940 in a 40-mph / 64-kph wind
– Close examination of the situation suggested that the bridge's deck-stiffening truss
was insufficient for the span, but that alone was not the cause of the bridge's
demise
– The wind that day was at just the right speed, and hitting the bridge at just the
right angle, to start it vibrating
– Continued winds increased the vibrations until the waves grew so large and violent
that they broke the bridge apart
When an army marches across a bridge, the soldiers are often told to "break step“
– This is to avoid the possibility that their rhythmic marching will start resonating
throughout the bridge
– An army that is large enough and marching at the right cadence could start a bridge
swaying and undulating until it broke apart
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VIDEO: Tacoma Narrows
Suspension Bridge Failure
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