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ENSC2004 Laboratory (Statics)
Laboratory Guide for Truss Analysis and Testing
Overview
The purpose of this project is to:
1. Practice analysis and design for a scale-model system truss;
2. Compare truss analysis with measurements from a truss-loading experiment;
3. Reflect on the impact of failure of engineering structures on people and the environment.
In this project students will work in groups of 5 to analyse and test a truss to failure. This will be
completed over two weeks.
Week 5 Lab Session
Each group will be assigned one of either a Pratt (Fig 1), Howe (Fig 2), or Warren truss (Fig 3) with a
unique loading combination.
Figure 1: Pratt truss. Dead Load Location: D; Dead Load Magnitude: 20 N or 50 N; Live Load
Location: E
Figure 2: Howe truss. Dead Load Location: D; Dead Load Magnitude: 20 N or 50 N; Live Load
Location: E
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Figure 3: Warren truss. Dead Load Location: D; Dead Load Magnitude: 20 N or 50 N; Live Load
Location: E
This loading combination will have a (constant) dead load and a (variable) live load. The live load will
be increased until a sacrificial plastic (PMMA) member fails in the testing rig (see Fig 4). (The PMMA
member will be provided in Week 6, on the day of testing). The application points of the dead and live
loads are detailed in Figures 1 – 3, along with the magnitude of the dead load.
Figure 4: Experimental rig showing dead and live loads
The magnitude of the live load (the weight of the sand) that results in failure is an unknown. It will be
predicted using the stress-strain properties of the PMMA members in tension, shown in Figure 5.
Your predicted failure load will be compared to the measured failure load.
Dead Load
(50 N or 20 N)
Live Load
(Sand)
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Figure 5: Stress-strain response of PMMA members
Procedure
In the first Lab Session, students will form groups of 5 students and be assigned a truss type (Pratt,
Howe or Warren) and a dead load value (20 or 50 Newtons), which will be applied to pin position D as
shown in Fig 1 to 3.
The members of the truss will be made out of aluminium with the horizontal and vertical members
having a nominal length of 10 cm and the diagonal members having a nominal length of 14 cm, the
cross-section dimensions of all members are the same.
Task 1
Determine the reaction forces at the ends of your truss as a function of the dead and live loads. You
may assume that the self-weight of the bridge is negligible. Compare your answers with the members
of your group.
Task 2
Use Method of Joints to determine the force in each member as a function of the dead and live loads.
Use Method of Sections to check your calculation based on Method of Joints for at least “one cut”. (The
purpose here is to put these analysis methods into practice and to make sure you know how to use them.)
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0
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0 0.005 0.01 0.015 0.02 0.025
St
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M
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Strain
Sample 5
Sample 4
Sample 3
Sample 2
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Task 3
Considering only the horizontal and vertical members in tension (or that will change from compression
to tension as the live load increases), plot the force in the members (y-axis) as a function of the live load
(x-axis).
Task 4
Your most critical member will be replaced with a sacrificial PMMA member during the second
workshop. This sacrificial member has a nominal cross-sectional area of 2 mm2 and tensile properties
shown Figure 5.
• Calculate the force at which the PMMA member is expected to fail, based on its properties and
dimensions, and plot this force as a constant line on your plot.
The critical-tension member is most at risk of failure in tension for the given loading condition. On
your plot of force in members under tension, the first member to have a force equal to the force expected
to cause failure in the PMMA member will be the critical member (on the graph the force in the member
line will cross the constant force line).
• Identify the location of the most critical member of your truss.
• Write down the critical member and the live load at which you expect it to fail and bring this
information with you to the second workshop.
If you cannot complete these tasks during the first lab session you must finish them before the
beginning of the second lab.
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Week 6 Lab Session
Procedure
Task 1
You will be given a sacrificial PMMA member. Use callipers to determine the cross-sectional area at
the narrowest point. Does it match the nominal 2 mm2 specifications? What is the uncertainty in your
measurement?
Task 2
You will be supplied with a partially completed truss and a sacrificial member. Each group, in turn,
will test their truss in the testing rig. Be very careful about keeping the sacrificial member under tension
when placing it into the testing rig; it is easy to accidentally cause the sacrificial member to buckle if
it’s placed under compression.
• With the truss in the testing rig, hang the correct dead load from pin D and the bucket for the
live load from pin E.
• Announce, based on your calculations, at what live-load value you anticipate the sacrificial
member will fail.
• Begin slowly adding sand to the live-load bucket until the sacrificial member fails.
• Weigh out the mass of sand and the bucket and record this value. Comment on and estimate the
uncertainty in your measurement of the total live-load mass.
Task 3
After the Tests
• Talk over the results of the experiment with your teammates and discuss if they met with your
expectations or not.
• If the actual cross section of the sacrificial member was different from the nominal 2 mm2
recalculate the force that the member was expected to fail at and the associated live load. Does
this better match your results?
• If the actual tensile strength of the PMMA was different than the expected value, how big would
the difference have to be to explain your results? Would it fall with a range of ± 15 %)?
Task 4
Three truss designs have been tested by group in your class. Research what are the advantages and
disadvantages of the three truss types used in this project (Pratt, Howe and Warren). Are the diagonals
in tension or compression for each of the different truss types?
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Task 5
(This will be completed outside of class) Review a documented example of engineering failure for a
structure, relevant to what you have been learning in the statics part of this course. Describe the cause
of failure (where did the design fail) and events that led to the failure situation. Consider the impact of
this failure event on people and the environment.
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Report
As a group, you will write a report of your findings using the format given in the next section.
This report must be the work of your own group, and all team members should be familiar with (and
ideally contribute to) all sections. Reports will be checked for similarity with reports from other classes
and other semesters. Any incident detected will be referred to the Academic Conduct Advisor.
Students will complete an individually-assessed quiz, testing your understanding and knowledge of
topics covered in the laboratory sessions and report.
Report Submission
Submit your report online to LMS by the deadline (Midnight, Friday week 7)
Each report must contain the following components:
a) University Assignment Cover Sheet.
b) Title page: include project title, your stream number, name of facilitator, and names of all
group members.
c) Introduction: A section briefly discussing the three different truss types, their advantages
and disadvantages. Pictures or schematic diagrams should be included to illustrate the truss
types.
d) Methodology: A section describing the truss your group analysed and providing the
background for the activity. Include a diagram of the truss, complete with sacrificial
member location, dead and live load locations and the predicted value of the dead load.
e) Results 1 – Modelling: A section on how you determined the critical member, to be replaced
by the sacrificial member. Include your original calculations for the force at which the
sacrificial member would fail based on the nominal 2 mm2 cross-sectional area and tensile
strength from the graph provided. Also include your original plot of the force in the vertical
and horizontal members under tension as a function of the live load and a statement of the
predicted terminal live load. (All other calculations should go into an appendix.)
f) Results 2 – Experiment: A section detailing the experiment and any sources of uncertainty
that could contribute to differences between the experimental results and your expectations.
g) Discussion: Comment on the comparison of your calculated and measured results. This
should include:
o Effects of cross-sectional area of the sacrificial member and how it would have
affected your predictions for the terminal value of the live load.
o Variations in the material properties of PMMA and its tensile strength. Give the
range for expected failure live load, if the range in the tensile strength was varied
by +/- 15%.
o Assessment of other uncertainties and variability in the experimental procedure
compared to calculations of the idealised model.
h) Case Study: Using an example of a documented event, discuss:
o The causes of failure of an engineering structure, relevant to what you have been
learning.
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o What went wrong in the design and/or construction process.
o The impact that this failure had on people and the environment.
o What changes (if any) were made to engineering practice.
i) References: A list of any and all references used in the report.
j) Appendix: including your calculations of:
(1) The reaction forces;
(2) The force in each member of the bridge as a function of D and L (even though you
will know the value of the dead load ahead of time please write force functions
symbolically using D for the dead load and L for the live load);
(3) Calculations of the force on the PMMA member at failure based on the measured
cross-sectional area and tensile strengths, and the specified tensile strength ± 15%;
(4) Calculations of the live loads associated with the forces you calculated in (3) for
the sacrificial member.
