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## The Waddell A-Truss Bridge

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**1. **The Waddell A-Truss Bridge Designing and Building File-Folder Bridges as an Introduction to Civil Engineering

**2. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**3. **Engineering Design Process A systematic design process precedes construction.
Engineers design; contractors build.
The design process is informed by math and science.
Design is iterative.
Structures are designed to carry code-specified loads safely and economically.
Designed to stand up, not to fail.

**4. **Engineering Design Process Design Requirements:
Length, width, loading, budget
Decide on bridge configuration.
Materials property testing
Perform a structural analysis.
Reactions
Internal member forces
Select member sizes based on required strength.
Draw plans.
Build the bridge.
Test

**5. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**6. **Basic Bridge Types

**7. **What is a Truss? A structure composed of members connected together to form a rigid framework.
Usually composed of interconnected triangles.
Members carry load in tension or compression.

**8. **Tension and Compression

**9. **Component Parts

**10. **Standard Configurations

**11. **Structural Members

**12. **Truss Connections

**13. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**14. **Beginning the Design Process

**15. **Lets build this bridge

**16. **Our A-Truss Bridge

**17. **Our Truss Configuration

**18. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**19. **Materials & Equipment File folders or legal size card stock paper
Yellow carpenters glue
Building board (Styrofoam or cork)
Pins
Scissors
Metal ruler
Plastic wrap or wax paper
Plans and Parts Template
Download from TECT website

**20. **File Folders or Card Stock? Inexpensive.
Easy to cut, bend, and glue.
Surprisingly predictable structural behavior.
Can be used to build:
Tubes and bars.
Connections that are stronger than the attached structural members.

**21. **Test Specimens Bars (tension members)
3 2 mm (1/16) x 15 cm (6)
3 4 mm (5/32) x 15 cm (6)
3 6 mm (1/4) x 15 cm (6)
Tubes (compression members)
3 10 mm2 (3/8) x 8 cm (3)
3 10 mm2 (3/8) x 12 cm (4.5)
3 10 mm2 (3/8) x 15 cm (6)

**22. **A Hydraulic Testing Machine

**23. **Our Testing Machine

**24. **Testing Tensile Strength

**25. **Testing Tensile Strength

**26. **Testing Tensile Strength

**27. **Testing Tensile Strength

**28. **The Principle of the Lever

**29. **Graph the Results

**30. **Results of Tension Testing Tensile strength depends on:
Type of material
Thickness of cross-section
Width of cross-section
Tensile strength does not depends on:
Length of member
Shape of cross-section

**31. **Testing Compressive Strength

**32. **Testing Compressive Strength

**33. **Graph the Results

**34. **Results of Compression Testing Compressive strength depends on:
Type of material
Length of member
Width and thickness of cross-section
Shape of cross-section

**35. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**36. **Prefabrication of Members Paste template to file folder or print to legal size card stock
Cut out bars
Cut out and assemble tubes
Cut out gusset plates

**37. **Template Parts Locations

**38. **Set up the Building Board

**39. **Set up the Building Board

**40. **Add Gusset Plates

**41. **Add Gusset Plates

**42. **Add Bars

**43. **Add Bars

**44. **Add Tubes

**45. **Add Tubes

**46. **Add Tubes

**47. **The Finished Half-Truss

**48. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**49. **Forces, Loads, & Reactions Force A push or pull.
Load A force applied to a structure.
Reaction A force developed at the support of a structure to keep that structure in equilibrium.

**50. **Equilibrium

**51. **Tension and Compression

**52. **Structural Analysis For a given load, find the internal forces (tension and compression) in all members.
Why?
Procedure:
Model the structure:
Define supports & loads.
Draw a free body diagram.
A sketch of the geometry, loads & supports
Calculate reactions.
Calculate internal forces.

**53. **Model the Structure

**54. **Draw a Free Body Diagram

**55. **Calculate Reactions Total downward force is 24.5 N.
Total upward force must be 24.5 N.
Loads, structure, and reactions are all symmetrical.

**56. **Calculate Reactions

**57. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**58. **Assemble the Two Halves

**59. **Assemble the Two Halves

**60. **Assemble the Two Halves

**61. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Truss
Select Member Sizes
Test Bridge

**62. **Structural Analysis Methods Graphical Method
Less Mathematical (but not less exact!)
Method of Joints
Analytical (trigonometry based)
Vector Components
Linear Algebra (more complex structures)
Preferred Engineering Methodology
Computer Modeling & Simulation

**63. **Some Basic Vector Concepts All forces are vectors that have both a magnitude and a direction.
Arrows are used to graphically represent vectors.
The arrow indicates the direction.
In trusses, the vector is always in the direction of the truss member (i.e. they follow the truss geometry).
The arrow length represents the magnitude.
Multiple vectors can be graphically added to determine one equivalent vector.
To maintain static equilibrium, forces meeting at a common point must add to zero.

**64. **Graphical Method First, select a joint at one of the reactions.
This selects three vectors; AD, AB & the reaction.

**65. **Graphical Method Draw the known vector, the reaction, at its proper length and direction.

**66. **Graphical Method Draw lines representing the direction of the remaining vectors.
Vectors must be connected tail to head.
The magnitudes are unknown, so the length doesnt matter at this point.
Since Joint A is a common point, the three vectors must add to zero.
This means that they must form a closed loop.

**67. **Graphical Method Measure the length of the unknown vectors.
Length = Magnitude

**68. **Graphical Method Move vectors to match actual joint geometry.

**69. **Graphical Method...Again Select another Joint.

**70. **Graphical MethodAgain Draw the two known vectors, the load and AB, at their proper lengths.

**71. **Graphical MethodAgain Draw the two unknown vectors, BD and BC.
Only possibility is a rectangle as shown.
Measure the lengths & move vectors to match geometry.

**72. **Graphical MethodAgain Continue same process for all other joints.
Caution: Select joints with no more than 2 unknowns.
Final results as shown.

**73. **Computer Modeling & Simulation Use computer modeling to support math and science concepts.
Many programs available; all require check on mathematical determinacy.
Truss Bars = 2(Truss Joints) 3 [ok]
Truss Bars > 2(Truss Joints) 3 [indeterminate]
Requires more advance analysis techniques
Truss Bars < 2(Truss Joints) 3 [unstable]
Truss will not support itself
Truss Analysis Wizard
http://mathonweb.com/
Freeware & easy to use
Provides numerical results (most dont)
Lets try it & check our previous answers......

**74. **Method of Joints Isolate a Joint.

**75. **Method of Joints

**76. **Equations of Equilibrium The sum of all forces acting in the x-direction must equal zero.
The sum of all forces acting in the y-direction must equal zero.
For forces that act in a diagonal direction, we must consider both the x-component and the y-component of the force.

**77. **Components of Force If magnitude of FAD is represented as the hypotenuse of a right triangle...
Then the magnitudes of (FAD)x and (FAD)y are represented by the lengths of the sides.

**80. **Equations of Equilibrium

**81. **Method of Joints...Again Isolate another Joint.

**82. **Equations of Equilibrium

**83. **Results of Structural Analysis

**84. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**85. **Assembly the Bridge

**86. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**87. **Tensile Strength of AB & BD

**88. **Strength of Member AD

**89. **Critiquing Our Design

**90. **Factor of Safety Ratio of Strength vs. Load.
Member with smallest ratio will likely fail first.
Our factors of safety:
AB = 2.11
AD = 4.62
BC = 2.11
BD = 2.12
CD = 4.62
Ratio should not be less than 1.5.
Members AD & CD likely oversized.
Modify design and repeat analysis

**91. **Our Agenda Engineering Design Process
Bridge Terminology and Basics
Design Requirements
Materials Testing
Start Building a Truss
Forces and Equilibrium
Continue Building the Truss
Structural Analysis
Finish the Bridge
Select Member Sizes
Test Bridge

**92. **Place the Structure into Service

**93. **Acknowledgements PowerPoint and Activity Adapted from Work Created by:
COL Stephen Ressler, P.E., Ph.D.
Department of Civil & Mechanical Engineering
U.S. Military Academy, West Point