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I have attached the file description of the project to this assignment, I just want you to do 2 sections which are abstract and future work. Let me know if you have any questions.Truss Analysis and Selection
Project Announcement
Authors
Gerald Angle II
Diane Raque
Engineering 102
Submitted To
ENGR 102 Students
Fundamentals of Engineering
Statler College of Engineering and Mineral Resources
West Virginia University
Morgantown, WV
Spring 2016
Todd Hamrick 2013
Abstract
The first project in ENGR 102 this semester is to analyze a series of trusses as possible replacements for
a Farm Bridge in Bollinger County, MO. The property owner has contracted an architect to replace the
bridge. The architect in turn sub-contracted with your project group, or “company” to determine which
of the four truss configurations that they like (Diamond, Warren, Howe, and Waddell Trusses) would be
the best for the application.
A sum of forces analysis has been completed and is provided for application using MATLAB as the
solution finding tool. The equations provided in this report represent when the vehicle is at the center of
the bridge, and your group should analyze the vehicle at multiple locations to simulate it moving across
the bridge. After determining the forces in each respective beam, the architect would like an initial
estimate of what material and size would suffice for the selected truss. As part of the results of this
project your team should have a scientific and/or mathematical reason for the selection you have made
for the truss configuration.
ii
Contents
Abstract ……………………………………………………………………………………………………………………………………… ii
1
Introduction ………………………………………………………………………………………………………………………… 1
2
Methodology……………………………………………………………………………………………………………………….. 2
2.1
Diamond Truss ……………………………………………………………………………………………………………… 2
2.2
Through Warren Truss …………………………………………………………………………………………………… 3
2.3
Modified Through Howe Truss ……………………………………………………………………………………….. 4
2.4
3
Results ………………………………………………………………………………………………………………………………… 6
4
Discussion……………………………………………………………………………………………………………………………. 6
5
Conclusion …………………………………………………………………………………………………………………………… 6
6
Future Work ………………………………………………………………………………………………………………………… 6
7
References ………………………………………………………………………………………………………………………….. 7
Appendix 1 …………………………………………………………………………………………………………………………………. 8
iii
1 Introduction
The assigned first project of the semester is to analyze the three truss configurations for a replacement
of small All-Terrain Vehicle (ATV) and Tractor Bridge in Bollinger County, Missouri as shown in Figure 1.
The landowner has approved four configurations for further analysis, a simple Diamond Truss, Through
Warren Truss, a Modified Through Howe Truss, and a Waddell “A” Truss.
Figure 1. Small Farm Bridge to be replaced by the analyzed bridge. (Southeast Missourian, 2006)
During the completion of this project each team member is expected to analyze one of the four
configurations to determine the forces that each structural element in the bridge will have to withstand.
After completing the analysis the group as a whole will select one of the configurations to recommend
and justify with their analysis results why that truss design was selected.
1
2 Methodology
The analysis of each of the truss systems becomes a sum of forces analysis, and these are detailed in this
section of the report. The first subsection describes the physics analysis for the Diamond Truss, followed
by the analysis for the Warren, Howe and Waddell trusses in the successive sub-sections. Each of the
truss sections were set-up using a sum of forces approach, Equation 1 and Equation 2, at each of the
node points, which are intersections of more than one structural member. A load was determined based
on the entire span of the bridge being covered with ATV’s which when converted to a point load at the
center of the bridge is approximately 4000 lbs. All of the bridges are to be analyzed as if they are simply
supported at both ends with the left hand side being pinned (apply horizontal and vertical forces) and
the right hand side placed on a roller (vertical force only).
� = 0
Equation 1
� = 0
Equation 2
During the analysis of the respective shapes, it is assumed that all structural members were placed in
compression, if you get a negative value as an answer that simply means the force is in the opposite
direction.
In order to simulate the vehicle moving across the bridge the force should be distributed at multiple
locations, at each lettered node, and halfway between nodes where the load is balanced between the
two end points as a minimum.
2.1
Diamond Truss
In the analysis of the Diamond Truss, Figure 2, there are 5 node points, which resulted in a 10 equation
system, as outlined in Table 1. The angle of the upper and lower beams with the horizontal is 15
degrees, and it is also assumed that when the load is at C then the vertical reaction forces at Node A and
Node E are equal.
B
F6
F1
F2
A
C
F4
F5
F3
F7
E
F8
D
Figure 2. Illustration of a Diamond Truss to be analyzed.
2
Table 1. Summary of the force equations for the Diamond Truss
Node
A (left support)
B (top center)
C (middle center)
D (bottom center)
E (right support)
2.2
X-Direction Equation
Y-Direction Equation
+ 1 cos(15) + 2 + 3 cos(15) = 0
+ 1 sin(15) − 3 sin(15) = 0
− 1 cos(15) + 6 cos(15) = 0
− 1 sin(15) − 4 − 6 sin(15) = 0
− 3 cos(15) + 8 cos(15) = 0
3 sin(15) + 5 + 8 sin(15) = 0
− 2 + 7 = 0
4 − 5 − 4000 = 0
− 6 cos(15) − 7 − 8 cos(15) = 0
+ 6 sin(15) − 8 sin(15) = 0
Through Warren Truss
A similar sum of forces approach on the Through Warren Truss, shown in Figure 3. The five nodes (A-E)
result in another 10 equation system as detailed in Table 2.
B
D
F4
F7
F5
F3
F1
A
E
F2
C
F6
Figure 3. Illustration of the Through Warren Truss to be analyzed.
Table 2. Summary of the force equations for the Warren Truss
Node
A (left support)
B (top left)
C (bottom center)
D (top right)
E (right support)
X-Direction Equation
Y-Direction Equation
+ 1 cos(60) + 2 = 0
+ 1 sin(60) = 0
− 1 cos(60) + 3 cos(60) + 4 = 0
− 1 sin(60) − 3 sin(60) = 0
− 2 − 3 cos(60) + 5 cos(60) + 6 = 0
3 sin(60) + 5 sin(60) − 4000 = 0
− 6 − 7 cos(60) = 0
+ 7 sin(60) = 0
− 4 − 5 cos(60) + 7 cos(60) = 0
− 5 sin(60) − 7 sin(60) = 0
3
2.3
Modified Through Howe Truss
For the analysis of the Howe Truss, the weight of the point load was equally divided (2000 lbs each)
between the Nodes C and G to determine the forces in the members when the loading is symmetric.
Also, due to the symmetric loading, the vertical reaction forces supporting the bridge at A and G are
equivalent. Table 3 shows the equations derived based on the seven nodes as labeled in Figure 4 for the
Modified Howe Truss to be analyzed during the completion of this project.
F7
B
F8
F4
F1
F11
D
F3
F2
C
F10
F9
F5
A
E
F6
G
F12
H
Figure 4. Illustration of the Modified Howe Truss to be analyzed.
Table 3. Summary of the force equations for the Howe Truss
Node
A (left support)
B (top left)
C (bot.left-center)
D (middle center)
E (top right)
G (bot.right-center)
H (right support)
X-Direction Equation
Y-Direction Equation
+ 1 cos(45) + 2 = 0
+ 1 sin(45) = 0
− 1 cos(45) + 4 cos(45) + 7 = 0
− 1 sin(45) − 3 − 4 sin(45) = 0
− 4 cos(45) − 5 cos(45) + 8 cos(45) + 9 cos(45) = 0
4 sin(45) − 5 sin(45) + 8 sin(45) − 9 sin(45) = 0
− 6 − 9 cos(45) + 12 = 0
9 sin(45) + 10 − 2000 = 0
− 2 + 5 cos(45) + 6 = 0
− 7 − 8 cos(45) + 11 cos(45) = 0
− 12 − 11 cos(45) = 0
3 + 5 sin(45) − 2000 = 0
− 8 sin(45) − 10 − 11 sin(45) = 0
+ 11 sin(45) = 0
4
2.4
The Waddell “A” Truss, shown in Figure 5, contains eight locations where links in the truss are
connected, and thus a 16 equation system needs to be solved. The X- and Y- direction equations for this
system of equations is outlined in Table 4, in setting up these equations the point load considered in the
initial description was placed back at the center point of the bridge deck (horizontal surface).
D
F4
F8
B
G
F7
F5
F1
F9
F12
F11
F3
A
K
F2
C
F6
E
F10
H
F13
Figure 5. Illustration of the Waddell “A” Truss to be analyzed.
Table 4. Summary of the force equations for the Waddell Truss
Node
A (left support)
B (mid-upper left)
C (mid-bot left)
D (top center)
E (bottom center)
G (mid-upper right)
H (mid-bot right)
K (right support)
X-Direction Equation
Y-Direction Equation
+ 1 cos(45) + 2 = 0
+ 1 sin(45) = 0
− 1 cos(45) + 4 cos(45) + 5 cos(45) = 0
− 1 sin(45) − 3 + 4 sin(45) − 5 sin(45) = 0
− 4 cos(45) + 8 cos(45) = 0
− 4 sin(45) − 7 − 8 sin(45) = 0
− 2 + 6 = 0
− 6 − 5 cos(45) + 9 cos(45) + 10 = 0
3 = 0
−4000 + 5 sin(45) + 7 + 9 sin(45) = 0
− 8 cos(45) − 9 cos(45) + 12 cos(45) = 0
8 sin(45) − 9 sin(45) − 11 − 12 sin(45) = 0
− 13 − 12 cos(45) = 0
+ 12 sin(45) = 0
− 10 + 13 = 0
11 = 0
5
3 Results
As results for this project, it is expected that Matlab will be used as the analysis tool for each of the four
trusses by different members of the project group. The results section should describe the answers
determined from each of the four respective analyses in detail (with numbers). Graphs could be
beneficial to help illustrate the differences between the bridges.
4 Discussion
For the discussion section, the expectation is that this section will describe what the group has done
with the information gathered through the analyses and step the reader through how the best truss for
the bridge was determined. In this section sub-headings can be used as a means of dividing up the
features/items that were utilized for a more detailed, but easy to follow selection process.
5 Conclusion
For the conclusion of this project, the recommended truss configuration should be named. In addition, it
is acceptable to reiterate the determining factors that led to this truss selection.
6 Future Work
The future work section, is similar to a recommendation section in that you should describe what the
next step(s) are in continuing the replacement process for the ATV Bridge in Bollinger County, MO and
how to improve the analysis method that your group used in this project.
6
7 References
Southeast Missourian. (2006, February 6). Blog: The Bridges of Bollinger County. Retrieved from
Southeast Missourian: http://www.semissourian.com/blogs/pavementends/entry/25398
7
Appendix 1
Deliverables:
Description
Group/Individual
Point Value
Team Planning(Team Charter and Gantt Chart)
Group
10
Background Research for Report
Individual
10
Project Code
Individual
30
Powerpoint File
Group
15
Presentation
Group
10
Final Technical Report
Group
25
Due Date
1st Friday
of class
2nd Wed
of class
3rd Wed of
class
3rd Friday
of class
3rd Friday
of class
3rd Friday
of class
8

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