Transcript Bridges - skillbank 2014: Website design and IT support

Bridges:
BaDI 1: John Errington MSc
King Edward VII bridge
and Redheugh bridge
Early bridges
Early beam bridges were made from
felled trees, used to span streams.
An alternative was to culvert the
stream and fill in to make the
roadway. Both of these were very
temporary and liable to be washed
away when the river flooded.
In the thirteenth century the first
mediaeval bridge was built at
Corbridge to span the Tyne river.
Unfortunately it became derelict by
the sixteenth century and was finally
replaced in 1674 by the bridge you
can see today.
Modern Bridge Designs
• There are six basic modern bridge forms: the beam, the
truss, the arch, the cantilever, the cable-stay, and the
suspension.
• A beam bridge is made of long timber, metal, or concrete
beams anchored at each end. If the beams are arranged
in a lattice, such as a triangle, so that each shares only a
portion of the weight on any part of the structure, the
result is a truss bridge. An arch bridge has a bowed
shape causing the vertical force of the weight it carries to
produce a horizontal outward force at its ends. It may be
constructed of steel, concrete, or masonry.
Cantilever bridge
• A cantilever bridge is formed by self-supporting arms
anchored at and projecting toward one another from the
ends; they meet in the middle of the span where they are
connected together or support a third member. Singlepiece, rolled steel beams can support spans of 50 to 100
ft (15–30 m), depending on the load. Larger, built-up
beams are made for longer spans; a steel box-beam
bridge with an 850-ft (260-m) span crosses the Rhine at
Cologne.
• The cantilevered Forth Bridge (1890) in Scotland was the
first major structure built entirely of steel, the material that
made possible its two record-setting spans of 1,710 ft
(521 m) each.
Forth Rail bridge
Located 9 miles (14 km) west of Edinburgh, the Forth Railway Bridge is a
remarkable cantilever structure which is still regarded as an engineering
marvel. The bridge was built to carry the two tracks of the North British
Railway the 1½ miles (2½ km) over the Firth of Forth between South
Queensferry and North Queensferry, at a height of 46m (150 feet) above the
high tide. The structure has three massive cantilever towers each 104m
(340 feet) high. During its construction each tower was built in balance to
prevent excess tension loading on the supports.
Truss Bridges
• The truss can span even greater distances and carry
heavy loads; it is therefore commonly used for railroad
bridges. A large truss span like that over the Columbia
River can extend to 1,232 ft (376 m).
• If the truss is shaped into an arch, even longer bridges
are possible; the Bayonne Bridge between New York
and New Jersey, and the Sydney Harbor Bridge in
Australia, are the longest steel arch bridges, at 1,675 ft
(510 m), and 1,670 ft (509 m) respectively.
QE2 bridge Newcastle
Sydney Harbour Bridge
Concrete arch bridges
• Concrete arch bridges tend to be somewhat
smaller than truss bridges, the largest being the
Krk Bridge in Croatia and the Gladesville Bridge
across the Parramatta River at Sidney, Australia,
at 1,280 ft (390 m) and 1,000 ft (305 m),
respectively.
• Usually arch bridges employ vertical supports
called "spandrels" to distribute the weight of the
roadway to the arch below
Krk bridge, Croatia
Natchez Trace Bridge
The Natchez Trace Parkway Bridge is the nation's first segmentally constructed
concrete arch bridge. Spanning 502 m (1,648 feet), the double arch structure
offers motorists a view from 47m (155 feet) above the valley floor and is one of
the final links in the Natchez Trace Parkway project. The bridge's arches are
designed to support the deck without evenly spaced spandrel columns, resulting
in a picturesque, unencumbered appearance.
Cable-Stayed Bridges
• The cable-stayed bridge is the most modern type,
coming into prominence during the 1950s. The longest is
the Tatara Bridge in Ehime, Japan.
• In a cable-stayed bridge, the roadway is supported by
cables attached directly to the supporting tower or
towers. This differs from a suspension bridge, where the
roadway is suspended from vertical cables that are in
turn attached to two or more main cables. These main
cables hang from two towers and have their ends
anchored in bedrock or concrete.
Tatara Bridge
The Tatara Bridge in Japan is a 3-span continuous cable-stayed bridge with a
steel box girder deck. With a centre span of 890 m, and a total length of 1,480 m it
is the longest cable-stayed bridge in the world.
Suspension Bridges
• The suspension bridge is used for the longest spans.
• The design of suspension bridges advanced when J. A.
Roebling, a German-born engineer designed the
Brooklyn Bridge across the East River (completed 1883),
which was the world's longest suspension bridge at the
time of its construction, having a main span of 1,595.5 ft
(487 m).
• Today the longest spans in the world are suspended.
The longest main spans are the Akashi Kaikyo Bridge,
Hyogo, Japan, 6,529 ft (1,990 m); Humber River Bridge,
Hull, England, 4,626 ft (1410 m); Golden Gate Bridge,
San Francisco, 4,200 ft (1,280 m);
Suspension bridges
The Clifton Suspension Bridge, spanning
the beautiful Avon Gorge, designed by
Isambard Kingdom Brunel who was
appointed project engineer. The chains and
suspension rods are made of wrought iron.
The total length is 1,352 ft (414 m), with a
centre span of 702 ft (214 m)
Akashi-Kaikyō Ōhashi) is a suspension bridge
in Japan that crosses the Akashi Strait as part
of the Honshu-Shikoku Highway. The central
section is the longest bridge span in the world
at 1991 m. The central span was originally only
1990 meters but was stretched by a further
meter in the Kobe earthquake on January 17,
1995. You will see the roadway is built on a
truss for rigidity.
Combination spans
• Combination spans are often used to bridge
even longer stretches of water.
• The San Francisco–Oakland Bay Bridge, noted
for its three long spans, of which two are
suspension spans and the third a cantilever, has
a total length of 8.25 mi (13.2 km).
• The longest combination spans are the twin
Lake Ponchartrain Causeways near New
Orleans, Louisiana, whose parallel roadways
stretch nearly 24 mi (38 km).
San Francisco-Oakland Bay Bridge
Eastern Cantilever Bridge,
and truss bridges viewed
from Yerba Buena Island at
the entrance to the Coast
Guard station
Western portion viewed
from San Francisco
showing the four towers
of two suspension
bridges and their central
anchorage
Bridge Design: beams
Examples of the three common travel
surface configurations
• In a Deck configuration, traffic
travels on top of the main
structure;
• in a Pony configuration, traffic
travels between parallel
superstructures which are not
cross-braced at the top;
• in a Through configuration,
traffic travels through the
superstructure (usually a truss)
which is cross-braced above
and below the traffic.
Truss - simple types
•
A truss is a structure made of many
smaller parts. Once constructed of
wooden timbers, and later including iron
tension members, most truss bridges are
built of metal.
•
The king post truss is the simplest type;
when loaded the angled sections are in
compression, with the vertical member
and deck in tension.
•
the queen post truss adds a horizontal
top chord to achieve a longer span, but
the centre panel tends to be less rigid
due to its lack of diagonal bracing.
Pratt truss variations
•
The basic identifying features of a Pratt truss are
the diagonal web members which form a V-shape.
The center section commonly has crossing
diagonal members. Additional counter braces may
be used and can make identification more difficult,
however the Pratt and its variations are the most
common type of all trusses.
•
Charles H. Parker modified the Pratt truss to
create a "camelback" truss having a top chord
which does not stay parallel with the bottom
chord. This creates a lighter structure without
losing strength; there is less dead load at the
ends and more strength concentrated in the
center. It is somewhat more complicated to build
since the web members vary in length from one
panel to the next.
Warren Truss
• The Warren truss is perhaps the
most common truss for both
simple and continuous trusses.
• For smaller spans, no vertical
members are used lending the
structure a simple look.
• For longer spans vertical
members are added providing
extra strength
• Warren trusses are typically
used in spans of between 50 100m.
Howe truss
The Howe truss is the opposite of the Pratt truss.
The diagonal members face in the opposite
direction and handle compressive forces. This
makes it very uneconomic design for steel bridges
and its use is rarely seen.
Patented in 1840 by William Howe, this design was
common on early railroads. The three drawings
show various levels of detail. The thicker lines
represent wood braces; the thinner lines are iron
tension rods.
Arch bridges may be constructed using a shaped
truss as shown here. A tied arch resists spreading
(drift) at its bearings by using the deck as a tie
piece.
About space frames
A
B
D
C
A
D
B
C
A
B
D
C
• In analysing stresses on a rigid structure
we assume that each joint is ‘pinned’ or in
other words hinged so that the members
are free to rotate but cannot come apart.
• Any shape with more than three members
is able to deform, as shown here.
• A rectangle or square can be stabilized or
made rigid by adding a brace to make one
or more triangles.
• Depending on the forces acting on the
frame the brace may be under tension (a
tie) or compression (a strut)
A Simple Truss
Load
C
Truss members are pinned together:
this means they are free to rotate
B
A
d1
d2
Support points of the truss
Reaction Forces in a Simple Truss
F1
Force Equilibrium Equation
F1 = F2 + F3
Moment Equilibrium Equation
F2* d1 = F3* d2
F2
d1
d2
F3
Member Forces in a Simple Truss
Load
C
Truss members have tensile or
compressive internal forces
Blue arrows indicate the
action of the joints on the
members
B
A
Tension
d1
d2
Joint Forces in a Simple Truss
F1
C
Notice that for each
member the forces at
each end are shown
equal and opposite.
The forces in each joint must
be in equilibrium for the truss
to be in equilibrium
FCA
FCB
White arrows indicate the
action of the members on
the joints
B
A
FAB
F2
d1
d2
F3
Joint Forces in a Simple Truss
F1
C
FCB
FCA
FCA
A Free Body Diagram is
drawn for each joint in the
truss.
The joints can be isolated
and the equilibrium of
each joint determined
FCB
B
A
FAB
FAB
F2
F3
Joint Forces in a Simple Truss
FCB
Joint C
F1
FCA
A Force Triangle is drawn for
each joint in the truss.
Joint B
Solve the force triangles
for the member forces.
Joint A
FCB
F3
FCA
F2
FAB
FAB
How Do We Determine Tension and
Compression in the Members?
To find the force
magnitudes, measure the
forces in the triangle and
scale the values as before.
When you solve for the
forces in the joint, the
forces must add head-totail. This sets the
direction of the forces.
Joint A
FCA
F2
FAB
Lines of action of the two
unknown forces are in the
directions of the truss
members they represent.
F2 is a known force from
finding the truss reactions.
Draw F2 to scale as before.
How Do We Determine Tension and
Compression in the Members?
You have compression
when the member force
pushes on the joint.
Set the arrows from the
force triangle over the
members at the joint you
are analyzing.
A
F2
You have tension
when the member
force pulls away from
the joint.
FCA
F2
FAB
Joint A
Force analysis of a simple truss
All the triangles are equilateral triangles, the angle between the sides is 60o
Sum of moments at A = (1m)*(-400N) + (3m)*(-800N)+(4m)*E = 0 :
E=700N
Sum of forces = Ay + E - 400N - 800N:
Ay=500N
• Now that we know how the forces are laid out,
lets take a look at what is happening at point A.
• Remember that all forces are in equilibrium, so
they must add up to zero
Remember the system is in
equilibrium, so the forces
must all balance out. If
there was a net force in any
direction something would
have to move.
Sum of Fx= TAC + TAB cos 60o = 0
Sum of Fy= TAB sin 60o +500N = 0
Solving for the two above equations we get
TAB = -577N
TAC= 289N
Compression and Tension
TAB = -577N
TAC = 289N
negative force means that
there is a compression
force, and
positive force means that
there is a tension force
Forces and moments at point B
Sum of Fx = TBD + TBC cos 60o + 577 cos 60o= 0
Sum of Fy = -400N + 577sin60o -TBCsin60o=0
Once again, solving the two equations
TBC = 115N
TBD = -346N
Tension and Compression
TBC = 115N
TBD = -346N
BD (negative) is under
compression, while
BC (positive) is under
tension
Forces in a Truss
If we calculate the rest of the forces acting on the various
points of our truss, we will see that there is a mixture of
both compression and tension forces and that these forces
are spread out across the truss.
TBD= -346N
TAB = -577N
TBC=115N
TAC= 289N
Remember: negative force
means that there is a
compression force and a
positive force means that
there is a tension force
Limitations of a Truss
• As the unsupported span increases the weight of
the bridge increases, and so its load efficiency
falls.
• Truss bridges are very heavy due to the massive
amount of material involved in construction.
• Truss bridges can be built to take advantage of
materials that are good under tension (e.g. steel)
and under compression (e.g. timber)
• Computer packages are available to take the
hard work out of bridge calculations.
References
•
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•
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http://www.du.edu/~jcalvert/tech/machines/bridges.htm
http://pghbridges.com/basics.htm
http://www.matsuo-bridge.co.jp/
http://www.jhu.edu/~virtlab/bridge/truss.htm