1. ME 372 Final Project
Submitted to:
Dr. Jonathan D. Blotter
435Q CTB
Provo, UT 84602
Daniel J. Ramos
2. i
April 19, 2016
435Q CTB
Provo, UT 84602
Dear Dr. Jonathan D. Blotter,
This report is being submitted in order to demonstrate our competency in machine
design as outlined in the scope of ME 372 at BYU. This paper is for the graders of the
assignment, for the professor of the class, and for individuals whom want to see an
example of a design report. The purpose of this report is to demonstrate our ability in
machine design by considering all possible modes of failure, using computer aided
engineering, and using the appropriate failure theory; our machine design project will
focus on the sizing of a truss member system and a bracket design. Our report
concludes with the lightest truss structure and the smallest safe bracket.
We believe that, after reading our report, individuals will see an example of a good
engineering design in order to rate our knowledge in machine design or use it for
educational purposes. We hope that this report may adequately fulfill this purpose.
Thank you for taking the time to read and consider our report.
Sincerely,
Daniel J. Ramos
3. ii
Table of contents
Letter of Transmittal ............................................................................................i
List of Figures .................................................................................................... iii
List of Tables......................................................................................................iv
Abstract ...............................................................................................................v
Introduction ........................................................................................................1
Methodology and Preliminary Results .............................................................2
Truss Member Sizing ...........................................................................................2
Bracket Design .....................................................................................................5
Analysis ............................................................................................................12
Truss Member Analysis ......................................................................................12
Bracket Design Analysis .....................................................................................16
Conclusion ........................................................................................................18
Appendix ...........................................................................................................19
5. iv
List of Tables
Table 1 .................................................................................................................3
Table 2 .................................................................................................................3
Table 3 .................................................................................................................7
Table 4 ...............................................................................................................11
6. v
Abstract
Design of the mounting brackets and sizing of the members of a specified truss system
with the minimum size safe bracket and the lightest truss that will carry the intended
loads with a safety factor of 2. The process of the design is explained and all possible
modes of failure considered.
7. 1
Introduction
The purpose of this report is to present the design and sizing of a truss system and
corresponding brackets. The process by which the designs came to be is explained in
detail in order to demonstrate that a thorough and complete analysis was performed for
a safe design in all possible modes of failure.
The truss and brackets designed are for a certain type of scaffolding that can be raised
and lowered by cables. The objective of the design is to specify the minimum size safe
bracket and the lightest truss that will carry the intended loads with a safety factor of 2.
Figure 1: Truss system with brackets to be designed and sized.
8. 2
As seen in Figure 1 the mounting system consists of 2 brackets mounted to the top of
the truss. Bolts will go through the 1 inch diameter holes of the brackets. The base of
the truss is a simple compression joint. The truss members are square tubing.
The loading on the truss consists of two 500 lb. point loads, where specified in Figure 1,
and a uniformly distributed load of 7.14 lbs./ft2 over the entire surface area on the top
platform of the truss.
Methodology & Preliminary Results
The design process is divided in two main parts one for the truss and another for the
bracket. Several iterations were made in each case which will be summarized in table
form.
Truss Member Sizing
The first step in the truss design was the material selection. Since the design called for
minimizing the weight we selected a titanium alloy with a high strength to weight ratio:
Ti-6Al-4V, with a specific strength of 1E6 psi/lbs/in3. We found that the Ti alloy (Alpha-
Beta alloy) we selected, if solution treated (900-955C) and aged (540C), had the
following properties shown in the following table (www.matweb.com).
9. 3
Table 1: Ti-6Al-4V (Alpha-Beta alloy) properties.
Density 0.160 lb/in³
Tensile Strength 160,000 psi
Modulus of Elasticity (Average of tension & compression) 16.5E6 psi
Poisson’s Ratio 0.33
After the selection of the material we modeled the truss system parametrically in
ANSYS using BEAM188 element type. We tested several different widths and thickness
combinations until we found the best size that had a factor of safety of at least 2 and
was as light as possible. The following table is a summary of our iterations.
Table 2: Truss size iterations.
Max. Deflection
(in.)
Width
(in.)
Thickness
(in.)
Weight
(lbs.)
Von Mises Stress
(psi)
n (Safety Factor)
1 1.08255 10.00000 0.00200 33.82900 26264.00000 6.09199
2 0.06976 10.00000 0.04000 674.01000 1555.67000 102.84958
3 0.16114 5.00000 0.04000 335.65000 5088.00000 31.44654
4 0.63587 2.50000 0.04000 166.47000 19783.50000 8.08755
5 1.11019 2.00000 0.04000 132.64000 30980.20000 5.16459
6 8.07256 1.00000 0.04000 90.86800 129173.00000 1.23865
7 600.32300 0.25000 0.06250 19.82600 2460000.00000 0.06504
8 51.97350 0.50000 0.06250 46.26000 424722.00000 0.37672
9 5.52847 1.00000 0.06250 99.12800 88623.40000 1.80539
10 2.78437 1.25000 0.06250 125.56000 54888.30000 2.91501
11 5.16384 1.25000 0.03125 64.43300 101526.00000 1.57595
12 3.03803 1.50000 0.03125 77.65000 69935.20000 2.28783
First we chose an arbitrary width and thickness to see what results we would get to give
ourselves a baseline of what to change in order to achieve our design goals. Although
we started with a thickness of 0.002 inches we believed that to be unreasonably thin
and so decided to use a minimum thickness of around 0.04 inches. We decreased the
width of the members to see its effect on the weight and safety factor until we were
10. 4
below the allowable safety factor. Afterwards we increased the thickness rounding up to
the next standard size, 0.0625 inches (1/16 in.), and varied the width again slowly
increasing it until we obtained a safety factor above 2. Throughout our iterations we saw
that the thickness of the members had a greater impact on the weight of the truss than
the width and so decided to decrease the thickness rounding down to the next standard
size, 0.03125 inches (1/32 in.), which was as thin as we were possibly considering for
our design. We then increased the width by standard sizing until obtaining a safety
factor above 2.
Throughout the iterations we also made sure to observe the maximum deflection in the
truss in order to make sure it was rigid enough that it would serve its purpose as a
support structure for a scaffolding.
Our preliminary results were that the members would be 1.5 inches wide and 0.03125
inches (1/32 in.) thick. These dimensions resulted in a safety factor of 2.29, a weight of
77.65 lbs. and, a maximum deflection of 3.03803 inches. We then proceeded to further
analysis discussed later in this report.
11. 5
Figure 2: Preliminary design for members with a width of 1.5 inches and 0.03125 inches thick. The maximum Von Mises stress is
shown, 69,935.2 psi.
Bracket design
For the bracket design we used the same Ti alloy because of its light weight and
strength. For the first 9 iterations we used a constant thickness of 1 inch and a diameter
size of 1.5 inches. The use of a 1.5 inch diameter instead of a 1 inch diameter as called
by in the specifications was due to human error while reading the instructions; however,
the information we obtained through these iterations were still useful to us to find the
best shape for the bracket and so are included as part of the design process.
All units shown in psi.
12. 6
Initially we used a simple rectangular bracket with a hole in the center to get an idea of
how the stresses were distributed throughout the part, labeled bracket 1. As seen in
Figure 3 below, the portion of the bracket furthest away from the weld and removed
from the hole area had very little stress within it.
Figure 3: Bracket1 stress distribution.
Since we found that there was very little stress in the before mentioned portion of the
first bracket for the next iterations, up to Bracket6, we tried to distribute the stress more
evenly throughout the bracket. The following table (Table 3) shows the different
iterations for the bracket. Table 3 also includes the x-y plane area of the bracket, the
All units shown in psi.
13. 7
safety factor, and the result of dividing the safety factor by the area (done in order to
compare the relative strength of the bracket compared to its weight).
Table 3: Preliminary bracket iterations.
Area (in2
) Von Mises Stress (psi) n (Safety Factor) n/A (1/in2
)
Bracket1 10.73300 3574.62000 44.76000 4.17032
Bracket2 10.57700 2905.92000 55.06002 5.20564
Bracket3 7.24700 2704.17000 59.16788 8.16446
Bracket4 6.01000 2849.35000 56.15316 9.34329
Bracket5 4.88800 2778.64000 57.58213 11.78030
Bracket6 4.88400 2857.72000 55.98869 11.46370
Bracket7 3.76200 2893.42000 55.29788 14.69907
Bracket8 3.34500 8114.46000 19.71789 5.89473
Bracket9 3.51500 4042.42000 39.58025 11.26038
When we got to Bracket6 we observed that the portion of the bracket closest to the weld
in the center of the bracket had very little stress compared to the other portions of the
bracket, this can be observed in Figure 4.
14. 8
Figure 4: Bracket6 stress distribution.
Since we observed a lack of a significant amount of stress in the portion mentioned for
Bracket 6 we decided to remove that portion and see what results we would get. So for
Bracket 7 we had an open bracket as shown below in Figure 5. However Bracket7
design was flawed in that there would be friction between the bolt and the truss on the
open section.
All units shown in psi.
15. 9
Figure 5: Bracket7 stress distribution and open bracket design.
In order to avoid friction of the bolt with the truss whilst having an open section we
decided to leave a gap of 0.11 inches for the subsequent iterations. We modeled
Bracket8, Bracket9, and Bracket10 to determine what the best angle between the truss
wall and the bracket top edge would be. We tried an obtuse angle (123° Bracket8), a
right angle (Bracket9), and a slightly acute angle (80° Bracket10). We didn’t want to
have a very acute angle since this would inevitably increase the x-y plane surface area
of the bracket and thus the weight of the bracket. We found that a slight acute angle of
80° was the best angle of the three and given its nominal value easier to manufacture—
All units shown in psi.
16. 10
opposed to 75°, 78°, 81.3°, etc. Below you can observe the differences in Braket8,
Bracket9, and Bracket10 (Figure 6).
Figure 6: Comparison between angles for the bracket. Bracket8 (Top left), with an obtuse angle of 123°; Bracket9 (Top right),
with a right angle; and Bracket10 (Bottom), with a slight acute angle of 80°.
We decided to use the geometric shape of Bracket10 for our design. We then
proceeded to find the smallest bracket we could create with our chosen design by
varying the hole diameter and thickness of the bracket. The following table summarizes
our iterations (Table 4).
All units shown in psi.
18. 12
Table 4 includes several categories which we took into consideration while finding the
best design for the bracket. We used the safety factor over the volume as a relative
comparison of strength per weight for each iteration. We also have %thickness over
maximum deflection and %inner diameter over maximum deflection; each of these
measurements are relative deflections compared to the thickness of the bracket and the
hole diameter respectively. Since we wanted to have sufficiently stiff brackets we only
considered brackets with relative deflections less than 0.1%. Table 4 also has
highlighted the criteria why each iteration was rejected. Only 4 iterations met all the
criteria (including the 1 inch hole diameter specification): Bracket10-7, Bracket10-9-1,
Bracket10-9-2, Bracket10-9-3, and Bracket10-9-4; out of which Bracket10-9-4 was the
lightest of them all.
Analysis
In this section we analyze possible failure modes for our preliminary designs for the
truss system and the bracket in order to make any necessary modifications, if any.
Truss Member Analysis
We first used theoretical analysis to find the reaction forces under the assumption of a
rigid structure, shown in Figure 7.
20. 14
After finding the reaction forces we found the forces in each member of the truss system
shown in Figure 8 shown below; a table of all the member forces are included in the
Appendix.
Figure 8: Internal member forces of the truss system.
21. 15
From the internal member forces we found that the largest compressive forces felt by
the members were members EI and FJ both of 1,088.60 lbs., neglecting weight or
1,144.07 lbs.with the weight included. We then proceeded to test for buckling of these
members shown below in Figure 9.
Figure 9: Checking for buckling.
22. 16
We first found the allowable critical buckling load and then compared it to the actual
loads of members EI and FJ; we made sure that the members indeed followed the Euler
buckling failure and not the Johnson buckling failure. We found that EI and FJ were
above the allowable buckling load given the safety factor of 2. We then proceeded to
increase the member width up until the next standard size, 1.75 inches, and reevaluate
the allowable buckling load. We found that the allowable buckling load would be
1,196.63 lbs which is less than 1,176.28 lbs., the new member force given the
increased width size. Finally we checked the validity of our ANSYS model by comparing
the reaction forces in the y direction from the theoretical analysis (with the weight
included) and the ANSYS model. We found that there was a difference of 1.6 lbs. which
we attributed to round off error and the size of our elements; we found the ANSYS
model to be fairly accurate.
The best sizing for the truss members that would have the lightest structure and would
be safe with a safety factor of at least 2 is 1.75 inch wide Ti-6Al-4V square tubing with
0.03125 inches (1/32 inches) wall thickness. The weight of the truss structure ended up
being 90.868 lbs.
Bracket Design Analysis
We continued our analysis with the bracket accounting for all possible failure modes
shown below in Figure 10: bolt bearing, bracket bearing, bolt shear, edge shearing,
tensile yielding, bolt bending.
23. 17
Figure 10: Checking different modes of bracket failure: bolt bearing, bracket bearing, bolt shear, edge shearing, tensile yielding,
bolt bending.
The bracket was sufficiently strong in all modes of failure. The best design for the
smallest safe bracket is outlined in the following engineering drawing shown in Figure
11.
24. 18
Figure 11: Engineering drawing for smallest safe bracket.
Conclusion
We found that for the truss member sizing the critical failure mode was buckling which
we accounted for in the analysis portion of this report. For the bracket, the stiffness was
the most limiting constraint factor. In conclusion, we found that the best sizing for the
truss members for the lightest structure and the smallest safe bracket given a safety
factor of 2 had a combined weight of 90.99472 lbs.
