1. Truss Factor of Safety and Characterization
Member Cross-Sections
Effecting Tensile and Compressive Strengths
Characterizing Truss Members
The truss bridge internal force calculations resulted in the stresses on each truss member. To find the Factor of Safety for each member, you need to understand how much a load a given member will support before failing. The students will use a tool to measure the failing point for different sized paper bars and tubes.

2. Learning Objectives Calculate cross sectional area of a truss member
Explain factors that affect the tensile and compressive strength of a truss member
Explain the principle of the lever tool
Experimentally determine the tensile and compressive strengths of truss members
Graph and analyze the experimental data
Calculate Factor of Safety for every truss member
These learning objectives will be learned by completing the characterization of different sized truss bridge members.

3. Factor of Safety Design uncertainty
Excessive loads: vehicles exceeding specifications, wind, snow, earthquakes, etc
Construction: material variances, workmanship, etc
Design Models: accuracy of design simulations
These are some examples of things a designer must consider when designing a bridge. For example, even though a bridge may be posted with a 20 ton limit, the driver of a 30 ton truck may not heed the sign. And there will always be variances in building material strengths such as steel and concrete. Design modeling may have to make some assumptions. For our analysis, we will assume the bridge weight does not impact the loading and that every joint and beam is perfect.

4. Factor of Safety Designers make a bridge stronger than design target
Most codes require minimum Factor of Safety > 1.6
Failure Level
Actual Level
Also known as a ‘guardband’. Extra design considerations to compensate for the unknowns from the previous slide. For example, if a steel beam withstands 7,500 pounds of force and is subject to an internal force of 5,000 pounds, then the factor of safety is (7,500 pounds)/(5,000 pounds) = 1.5
Some structures have a factor of safety considerably higher than 1.6, depending on the requirements and expectations of the structure.

5. Truss Characterization and Factor of Safety
Actual level is calculated by Method of Joints
Need characterization data of the failure level for a truss member
Failure Level
Actual Level
The truss bridge internal force calculations resulted in the stresses on each truss member. To find the Factor of Safety for each member, you need to understand how much a load a given member will support before failing. The students will use a tool to measure the failing point for different sized paper bars and tubes.

6. Cross-Sections and Cross-Sectional Area
Four typical structural members are shown with their cross sectional area shown in black. The area of the solid rod is πr2, while the area of the solid rod is w*h. The hollow tube and I-Shape can be calculated by summing the area of multiple rectangles.
Tensile (stretching or pulling apart) strength has a direct relationship with the cross-sectional area. A solid bar and solid rod with the same cross-sectional area would have the exact same tensile strength. And of course material selection will effect the tensile strength.
Compression (crushing) strength is a function of cross-sectional area, cross-sectional shape, and member length as well as material selection.
More of this in a later slide.

7. Tensile Strength Characteristics
depends on the cross-sectional area
depends on the material
does not depend on the length
does not depend on the cross-sectional shape
These four characteristic affects are shown by the frayed rope. A bigger the cross sectional area (more strands) would make the rope stronger. If the rope material were comprised of stronger material, such as steel cable strands, the tensile strength would also be stronger.
The tensile strength is not a function of the rope length. There may be more chances of a rope defect such as nicked strands, but that would be considered a manufacturing defect. To address the independence of cross-sectional shape, if the same number of strands were shaped in a rectangle instead of a chord, the tensile strength would be the exact same.

8. Compressive Strength Characteristics
depends on the cross-sectional area
depends on the material
depends on the length
depends on the cross-sectional shape
There are a few quick ways to demonstrate some of these points.
To demonstrate the effects of length, procure a wooden yardstick and 12” ruler. Hold the yardstick vertically with one end on the floor and apply some compressive force on the yardstick by pushing it down on the other end. It will buckle, or bow out, with a little applied weight. Now try it with the 12” ruler, and it will withstand a lot more compressive force before it buckles.
To demonstrate the effects of cross-sectional shape, take two 5cm x 10cm sized pieces of manila file-folder, one shaped as a square tube and the other as a flat sheet. Hold the flat sheet between your thumb and forefinger and squeeze, observing little resistance before buckling. Then do the same with the tube and notice it is very strong in compression.

9. Summary of Material Effects on Tensile and Compressive Strengths
Cross-Sectional Shape No
Yes
Cross-Sectional Area
Material
Length
This table summarizes the prior slides. May be unnecessary to show.

10. Lever Concept Lever Relationship: F1 * L1 = F2 * L2 L1 L2 F1 F2
Potential example for the class: How much force could a 120 pound person generate with a 6 foot piece of pipe and a small log? If the above lever were setup with an L1 of 6” and L2 of 66”, this person could generate an F1 of 1320 pounds.
Lever Relationship: F1 * L1 = F2 * L2

11. Testing Machine This tester works on the lever principle
This testing machine needs to be built prior to Week 6. It can be made out of wood. The dimensions and instructions are in Appendix C, Building the Test Machine.
This tester works on the lever principle

12. Tensile Strength Characterization
Make test specimens, see Learning Activity #2
Clamp specimen to T-Line
Conduct tension tests
Read Learning Activity #2. Make sure the students differentiate between weight and mass in the calculations. The recommended testing program is specified in the manual. There are three different width bars to characterize for tensile strength. You might split the work between the different teams.

13. Tensile Strength Plot Tensile Strength (Newtons) vs. Member Width (mm)
Generate linear regression through (0,0)
Observe the small amount of ‘scatter’ among the three data points for each member width. This indicates some experimental error and natural variability among samples. The linear regression should show a linear relationship between the tensile strength and member width. This characterization data gives you extremely high confidence knowing the tensile strength of any member width between 0mm and 8mm. But beware of extrapolating much beyond 8mm without some more characterization data.
Use this data to calculate your Factor of Safety on members shaped as bars. Knowing the width of the bar you can easily find the tensile strength failing point.

14. Compression Strength Characterization
Make test specimens, see Learning Activity #2
Support specimen on felt pads at C-Line
Conduct compression tests
Read Learning Activity #2. Make sure the students differentiate between weight and mass in the calculations. The recommended testing program is specified in the manual. There are two different cross-sectional shapes and three different lengths to characterize for compressive strength. You might split the work between the different teams.

15. Compressive Strength
Plot Compressive Strength (Newtons) vs. Member Length (cm)
Generate best fit curve to data
This plot shows data from both cross-sectional shapes that were characterized.
Unlike the tensile strength data, the compression data is not strongly linear. Use a best fit curve to fit the data. Observe the smaller tube has less compressive strength than the larger tube, as expected due to the smaller cross-sectional area.
Use this data to calculate your Factor of Safety on members shaped as tubes. Knowing the length of the tube you can easily find the compressive strength failing point.

16. Acknowledgements
This presentation is based on Learning Activity #2, Test the Strength of Structural Members from the book by Colonel Stephen J. Ressler, P.E., Ph.D., Designing and Building File-Folder Bridges
This Civil Structures module is heavily based on this book which is found in the documents directory of the module.
To model an engineering project, we will start with the truss structural analysis (Learning Activity #3) which takes Weeks 3 and 4 or this curriculum. Then we begin bridge construction (Learning Activity #1) in Week 5. After the students get the feel of constructing their bridge members, during Week 6 they will characterize the strength of different sized members (Learning Activity #2) to be able to calculate the Factor of Safety. Week 6 is also used to complete their bridge construction and do the weight testing.
This module does not address Learning Activities #4 and #5, but you are encouraged to complete them if time allows.