MECH 2222 – MECHANICS OF MATERIALS
Lab 1: Forces in Single Plane Trusses
Prepared by: Azhriell Sta. Maria
Student Number: 7932624
Table of Contents
Abstract .............................................................................................................................................. 2
Introduction ........................................................................................................................................ 3
Objective ............................................................................................................................................ 3
Theory ................................................................................................................................................ 4
Experimental Method......................................................................................................................... 4
Data Collection .................................................................................................................................. 6
Discussion .......................................................................................................................................... 8
Conclusion ......................................................................................................................................... 9
References .......................................................................................................................................... 9
Appendix .......................................................................................................................................... 10
Abstract
For this laboratory experiment, a truss structure was built and the forces in each member
were recorded using strain gauges, which corresponds with the experiment’s purpose of measuring
the existing forces within the truss members and comparing them with the theoretical values that
were calculated using static equilibrium. This is accomplished by applying a tensile and a
compressive force, both with a magnitude of 120 N at different locations and recording the values.
The collected data were analyzed and compared with the calculated data yielding an average error
percentage of 2.43% for the tensile forces, and 2.71% for the compressive forces. According to the
results collected, it was concluded that performing the experiment using the truss structures and
strain gauges are therefore accurate as the measured values agree with the theoretical values.
Introduction
A single plane truss is made up of many two-force members that are all located in the same
plane. The goal of this experiment is to prove the that the measurement of forces within the truss
members is correct or close to the theoretical values, and by conducting an analysis of the trusses,
“zero-force members” can be identified as they are the members that don’t carry a load. The accuracy
and correctness of the calculations must be guaranteed because the forces in which the truss will
undergo depends on the mathematical result of the calculations. This knowledge is important in
designing structures that will need to meet the strength requirements and withstand the forces.
Objective
The main purpose of this laboratory experiment is to apply the fundamental theories of statics
into practical instruments. This will be accomplished by looking at how a single plane truss works,
with particular objectives being:
1) Measuring the forces that exist within the truss members under different loads.
2) Calculating the forces that exist within the truss members under different loads.
3) Comparing the measured forces with the calculated forces, calculate the error percentage and
determine the sources of errors.
4) Gaining knowledge about how strain gauges can be used to identify forces.
Theory
When trusses are subjected to external loads, its members experience forces that are either
in tension or in compression with the pins. For a truss in static equilibrium, it is assumed that the
sum of moments about any point and the sum of the forces acting on a pin in any direction is zero.
These concepts, along with using trigonometric tools that correspond with the assumptions such as
trigonometric functions, can be used to calculate the forces in each member.
Experimental Method
Required Equipment:
The laboratory used of the following equipment:
•
SE 112 Mounting Frame
•
Bars, Connectors, and Node Discs
•
Loading Jack (Load Application Device)
•
Multi-Channel Measurement Amplifier FL 151
•
Computer with FL151 and SE1X0 Software
Laboratory Set-up:
The experimental setup is composed of a representative truss, supported by a mounting frame
using the pin supports. The truss members are connected to the node discs with locking pins to
guarantee that all forces are simultaneous and that the members are properly attached. The strain
gauges are fixed to each member and are connected to the multi-channel amplifier (FL151) and the
computer. The truss is loaded manually using a loading jack, and the measurements are then recorded
using the SE1X0 software.
Experimental Procedure:
The experimental procedure consists of the following steps:
1) Setting up the truss plane as demonstrated in Fig. 6, matching the lengths of the members
with the required data.
2) Equilibrating the data acquisition system by switching it on without any load.
3) Calibrating the strain gauges by using the FL151 CD software.
4) Selecting the truss setup from the list in the SE1X0 software.
5) Setting all the strain gauge values into zero using the “Tare” button.
6) Applying a tensile load of 120 N by turning the loading jack knob and recording the forces
in various members.
7) Unloading the truss and recording the displayed force values in the unloaded members.
8) Calculating the adjusted force by subtracting the unloaded force from the measured force.
9) Calculating the % Error by comparing calculated and adjusted force values.
10) Repeating the procedure for a compressive load of 120 N.
11) Ensuring the maximum allowable load for members is not exceeded (500 N).
Data Collection
The tables below provide an overview of the member forces at both 120 N tensile and
compressive loads.
Table 1: Summary of Member Forces with Tension Load 120 N Down
Member No.
Calculated Force (N)
Measured Force (N)
Unloaded Force (N)
Adjusted Force (N)
Error (%)
1
-360
-364
1
-365
1.39
2
-240
-239
0
-239
0.42
3
-120
-116
1
-117
2.50
4
169.7
172
0
172
1.36
5
-120
-120
0
-120
0
6
169.7
169
0
169
0.41
7
-120
-127
0
-127
5.83
8
120
127
0
127
5.83
9
169.7
169
0
169
0.41
10
240
249
0
249
3.75
9
-169.7
-163
0
-163
3.95
10
-120
-119
0
-119
0.83
Table 2: Summary of Member Forces with Compression Load 120N Up
Member No.
Calculated Force (N)
Measured Force (N)
Unloaded Force (N)
Adjusted Force (N)
Error (%)
1
240
241
-1
242
0.83
2
120
115
0
115
4.17
3
0
-1
1
0
0
4
0
0
0
0
0
5
0
0
0
0
0
6
-169.7
-163
0
-163
3.95
7
120
117
0
117
2.50
8
0
0
0
0
0
Sample Calculations:
Figure 1:Sample Calculations for Table 1
Discussion
The experimental data collected matches the theoretical values calculated accurately. In the
first trial, there was an average error of 2.43% for each member, while in the second trial, there was
an average error of 2.71%, excluding the zero force members. Based on these data, the measured
results are true to their calculated results for the most part. This means that the truss structure is a
reliable tool to determine the forces in each member depending on where the load is applied and its
magnitude.
Sources of Error:
In every experiment, sources of errors are inevitable, as for this experiment, a potential error
might be the possibility of the members to bend or to flex, that would result in over-stretching or
over-compressing. This could affect the shape of the truss to change and impact the forces in each
member. Another source of error could be the assembly of the truss itself. The measurements the
measurements of the length between the nodes and the angles between them might be off, is why
there are what we call unloaded forces. The measurements could also have been altered due to
deformation through temperature change.
Difference Between Calculated Force and Experimental Adjusted Force:
The experimental adjusted force displays measured data, while the calculated forces are
entirely based on theoretical assumptions that may not agree with the real world, such as the fact
that the structure is two-dimensional which could have forces in another dimension that was assumed
to be negligible. The two are mostly similar but are not always the same because of the factors that
affect the values such as gravity, material deformation, or even the changes in air pressure that the
theoretical assumptions did not consider.
Conclusion
The purpose of this lab was to measure the forces of in the truss members using strain gauges
and comparing the measured data to the theoretical data. To further conclude this experiment, it can
be said that the goals were met and that it can be proved by stating that due to the average error
percentages of 2.73% and 2.71% in both truss locations, the theoretical values agree with the
collected data. By measuring, and comparing the forces within the truss members, we gain a clearer
view of the potential sources of error.
References
[1] Mech 2222 Laboratory Manual, Department of Mechanical Engineering, University of Manitoba,
2023
Appendix
Figure 2: Summary of Member Forces with Tension Load 120 N Down
Figure 3: Summary of Member Forces with Compression Load 120N Up
Figure 4: Full calculation for Truss 1 (Table 1)
Figure 5:: Full calculation for Truss 1 (Table 1)
Figure 6: Full calculation for Truss 2 (Table 2)
Figure 7: Full calculation for Truss 2 (Table 2)