The Waddell A-Truss Bridge

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. Let�s 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 carpenter�s 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 doesn�t 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 Method�Again Draw the two known vectors, the load and AB, at their proper lengths.

71. Graphical Method�Again 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 Method�Again 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 don�t) Let�s 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