1. BRIDGES Christopher Rego October 28, 2006 FIU Revised June 2003
SECME – M-DCPS Division of Mathematics and Science Education
FIU

2. Work Plan History of Bridge Development How Bridges Work
Basic Concepts
Types of Bridges
Concepts Associated with Bridge Engineering
Truss Analysis
Tips for Building Bridges
Bridge Construction

3. Great Stone Bridge in China
History of Bridge Development
Natural Bridges
700 A.D. Asia
Great Stone Bridge in China
Clapper Bridge
Tree trunk
Stone
Low Bridge
Shallow Arch
Roman Arch Bridge
Strength of Materials
Mathematical Theories
Development of Metal
The Arch
Natural Cement
1300 A.D. Renaissance
100 B.C. Romans

4. History of Bridge Development
1800 A.D.
1900 A.D.
2000 A.D.
Truss Bridges
Prestressed Concrete
Steel
First Cast-Iron Bridge
Coalbrookdale, England
Mechanics of Design
Suspension Bridges
Britannia Tubular Bridge
Use of Steel for the suspending cables
Wrought Iron
1850 A.D.
1920 A.D.

5. How Bridges Work?
Every passing vehicle shakes the bridge up and down, making waves that can travel at hundreds of kilometers per hour.  Luckily the bridge is designed to damp them out, just as it is designed to ignore the efforts of the wind to turn it into a giant harp.  A bridge is not a dead mass of metal and concrete: it has a life of its own, and understanding its movements is as important as understanding the static forces.

6. Basic Concepts
Span - the distance between two bridge supports, whether they are columns, towers or the wall of a canyon.
Force - any action that tends to maintain or alter the position of a structure
Compression - a force which acts to compress or shorten the thing it is acting on.
Tension - a force which acts to expand or lengthen the thing it is acting on.
Compression
Tension

7. Basic Concepts Beam - a rigid, usually horizontal, structural element
Pier
Pier - a vertical supporting structure, such as a pillar
Cantilever - a projecting structure supported only at one end, like a shelf bracket or a diving board
Load - weight distribution throughout a structure

8. Basic Concepts
Truss - a rigid frame composed of short, straight pieces joined to form a series of triangles or other stable shapes
Stable - (adj.) ability to resist collapse and deformation; stability (n.) characteristic of a structure that is able to carry a realistic load without collapsing or deforming significantly
Deform - to change shape

9. Basic Concepts
Buckling is what happens when the force of compression overcomes an object's ability to handle compression. A mode of failure characterized generally by an unstable lateral deflection due to compressive action on the structural element involved.
Snapping is what happens when tension overcomes an object's ability to handle tension.
To dissipate forces is to spread them out over a greater area, so that no one spot has to bear the brunt of the concentrated force.
To transfer forces is to move the forces from an area of weakness to an area of strength, an area designed to handle the forces.

10. Types of Bridges Basic Types: Beam Bridge Arch Bridge
Suspension Bridge
The type of bridge used depends on various features of the obstacle. The main feature that controls the bridge type is the size of the obstacle. How far is it from one side to the other? This is a major factor in determining what type of bridge to use.
The biggest difference between the three is the distances they can each cross in a single span.

11. Types of Bridges Beam Bridge
Consists of a horizontal beam supported at each end by piers. The weight of the beam pushes straight down on the piers. The farther apart its piers, the weaker the beam becomes. This is why beam bridges rarely span more than 250 feet.

12. Types of Bridges Beam Bridge Forces
When something pushes down on the beam, the beam bends. Its top edge is pushed together, and its bottom edge is pulled apart.

13. Types of Bridges Truss Bridge Forces
Every bar in this cantilever bridge experiences either a pushing or pulling force. The bars rarely bend. This is why cantilever bridges can span farther than beam bridges

14. Types of Bridges Arch Bridges
The arch 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.

15. Types of Bridges Arch Bridges Forces
The arch is squeezed together, and this squeezing force is carried outward along the curve to the supports at each end. The supports, called abutments, push back on the arch and prevent the ends of the arch from spreading apart.

16. Types of Bridges Suspension Bridges
This kind of bridges can span 2,000 to 7,000 feet -- way farther than any other type of bridge! Most suspension bridges have a truss system beneath the roadway to resist bending and twisting.

17. Types of Bridges Suspension Bridges Forces
In all suspension bridges, the roadway hangs from massive steel cables, which are draped over two towers and secured into solid concrete blocks, called anchorages, on both ends of the bridge. The cars push down on the roadway, but because the roadway is suspended, the cables transfer the load into compression in the two towers. The two towers support most of the bridge's weight.

18. Types of Bridges Cable-Stayed Bridge
The cable-stayed bridge, like the suspension bridge, 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 are becoming the most popular bridges for medium-length spans (between 500 and 3,000 feet).

19. Interactive Page Let’s try it:
How do the following affect your structure?
Forces
Loads
Materials
Shapes
Let’s try it:
The bridge challenge at Croggy Rock:

21. Congratulations!

22. Basic math and science concepts
Bridge Engineering
Basic math and science concepts
Pythagorean Theorem a g b c
c2=b2+a2
a+b+g=180

23. Basic math and science concepts
Bridge Engineering
Basic math and science concepts
Fundamentals of Statics F R1 R2 x y
SFx = 0
SFy = R1+R2-P = 0

24. Basic math and science concepts
Bridge Engineering
Basic math and science concepts
Fundamentals of Mechanics of Materials
Modulus of Elasticity (E): E=
Stress
Strain
F/A
DL/Lo = F E e s Lo
Where:
F = Longitudinal Force
A = Cross-sectional Area
DL = Elongation
Lo = Original Length F

25. Basic math and science concepts
Bridge Engineering
Basic math and science concepts
To design a bridge like you need to take into account the many forces acting on it :
The pull of the earth on every part
The ground pushing up the supports
The resistance of the ground to the pull of the cables
The weight of every vehicle
Then there is the drag and lift produced by the wind
The turbulence as the air rushes past the towers

26. Basic math and science concepts
Bridge Engineering
Basic math and science concepts
Balsa Wood Information

27. Bridge Engineering Truss Analysis Structural Stability Formula
Where:
K = The unknown to be solved
J = Number of Joints
M = Number of Members
R = 3 (number of sides of a triangle)
K = 2J - R
K Results Analysis:
If M = K Stable Design
If M < K Unstable Design
If M > K Indeterminate Design

28. Bridge Engineering Truss Analysis
Structural Stability Formula (Example)
Joints
J=9
Members
M=15
K = 2 (9) – 3 = 15
15 = M = K then The design is stable

29. Bridge Engineering Truss Analysis
West Point Bridge Software:

30. Tips for building a bridge
1. Commitment - Dedication and attention to details. Be sure you understand the event rules before designing your prototype.
Draw your preliminary design
ALL joints should have absolutely flush surfaces before applying glue.
Glue is not a "gap filler", it dooms the structure!
Structures are symmetric.
Most competitions require these structures to be weighed. Up to 20% of the structure's mass may be from over gluing.

31. The Importance of Connections
Stresses flow like water.
Where members come together there are stress concentrations that can destroy your structure.
Here is a connection detail of one of the spaghetti bridges.

32. Tacoma Narrows Failure

33. Basswood Bridge Assignment
Brainstorm & decide on a truss configuration.
Use Appendix A for help
Create the structural model.
Check static determinacy and stability.
Draw plans.
Create a schedule of truss members.
Build the bridge.

34. Decide on Truss Configuration
Are you going for aesthetics or strength or ease of construction?
Only basswood sized at 3/32 inch square cross-section is allowed.
Any commonly available adhesive is allowed.
Basswood may be notched, cut, sanded or laminated.
Bridge may not be stained, painted or coated in any fashion with any foreign substance.

35. Truss Configuration Mass shall be no greater than 25grams
Bridge must span a gap (S) of 300 mm
Maximum length (L) of 400 mm
Maximum width (W) of 80 mm
Maximum height (H) of 200 mm above the support surfaces
No portion of the bridge may extend below the top of the support surfaces.
The loading plane (P) shall be horizontal and shall lie on the physical top of the bridge between
100 mm -200 mm above the support surfaces.
Bridge must support loading plate
without rod attached
Clearance allowed for loading eyebolt to be attached to the plate and hang down vertically through the bridge below the loading point.

36. Truss Configuration
The load will be applied downward, from below, by means of a 50.0 mm square plate
The plate will be 6.35 mm (1/4 inch) thick
The eyebolt will have a 9.53 mm (3/8 inch) diameter
Loading points are 50 mm on either side of the center of the 300 mm span.

37. Structural Model A pair of identical two-dimensional trusses.
Draw the geometry of one main truss
Indicate the dimensions of the member centerlines.
Identify joints with the letters A -Z.

38. Check Static Determinacy and Stability
We must first verify that it is statically determinate and stable (slide #27)
j is the number of joints
m is the number of members
K=2J-R
K Results Analysis:
If M = K Stable Design
If M < K Unstable Design
If M > K Indeterminate Design

39. Draw Plans FULL SCALE LAYOUT ACCURACY COUNTS!!!
Now you are smart enough to do the drawing yourself!
Big sheet of paper
Metric Ruler
Pencil
Good Eraser
T-Square
Triangles
Tape
Graph paper works well
Parallel and Perpendicular lines should be just that!!!

40. Draw Plans Lay Out Centerlines Draw one main truss
Drawing must be exactly full size
Use the dimensions decided on your structural model to ensure that all joints and members are at their correct positions.
Label the joints with letters
Use only a single line for each member.
These lines are the centerlines of the members.

41. Draw Plans
All member centerlines must intersect precisely at the joints.
If centerlines do not all intersect at a common point, the members will bend when the truss is loaded.
Bending may cause some members to fail at a lower load than they were designed for.
Performance depends heavily on the accuracy of the member centerlines!
Draw with Care!!!!