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

Waddell “A” Truss …………………………………………………………………………………………………………. 5

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

Waddell “A” Truss

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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