COLLEGE OF ENGINEERING
PUTRAJAYA CAMPUS
Semester 2 Year 2016/2017
MINI PROJECT REPORT
MECHANICS I : STATICS ( MEMB 123 )
Section: 02B
Project Tittle: BRIDGE TRUSS
Lecturer : EWE LAY SHENG, ASSOC. PROF. DR.
Group Members
NO.
NAME
ID
SECTION
1.
AHMAD AMMAR ASYRAAF B. JAINUDDIN
EE0100464
02B
2.
ADZHAR IMRAN BIN RUSLI
ME0100614
02A
3.
AMIR RIDHWAN BIN AHMAD FAUZI
EE0100465
02B
4.
MUHAMAD HAZIQ BIN ROSLI
EE0100482
02A
5.
AHMAD LUQMAN HAKIM
ME0100617
02B
17
TABLE OF CONTENT
1. Objective ……………………………………………1
2. Abstract……………………………………………..1
3. Introduction…………………………………………2
4. Methodology………………………………………..6
5. Truss Design………………………………………..7
6. Data Analysis……………………………………….9
a. Calculation……………………………………11
7. Discussion…………………………………………16
8. Conclusion………………………………………….16
9. Reference…………………………………………..17
OBJECTIVE
The aim for this project is for us to develop an understanding on how to design a bridge, knowing what type of truss to choose and solving problems found during the designing phase. It also help us to have better grasp of the knowledge learned during class such as static, trigonometry and physics as we must apply our knowledge in order to make a bridge that has high esthetic value with minimal material required. Furthermore, this project also help us improve our data collection and analysis to draw out useful conclusions, and acquire good communication skill for engineer by completing the memos, report and drawing.
ABSTRACT
The purpose of this project is to design a footbridge (bridge deisgned for pedestrian) and write a full report. In this project, three truss design were chosen to be selected and compared which is “Howe Truss”, “Warren Truss” and “Baltimore Truss”. For this project, we choose to corporate Warren Truss and Baltimore Truss with Warren Truss at the middle and Baltimore Truss at the side of the Warren Truss. The trusses were redesign to fit the given specification where the length and height cannot exceed 16m and 4m. The point J, I, H and G were subjected 5kN of vertical force. Then, the bridge was analyze using method of joint. Lastly the type and cost of the material for the bridge is also being considered as well.
INTRODUCTION
A Truss is a framework, usually use in roof design, bridge and other structure that are based on geometrical rigidity of a triangular shape and horizontal which it will experience tension or compression or both in the same time. Other geometrical shape is use to increase stability of the structure.
In engineering, a truss is a structure made out two-force members that are arranged geometrically to act as one body. Two force member is a component where force act at two point and usually arranged in a triangular unit where a truss can consist five or more with straight member connected to a joint. The reaction and external forces are considered applied at the joint only that result the member to subjected to either tensile or compression force or both.
About Truss Bridge
Truss bridge is the oldest type in the bridge design and are widely known example of truss usage. The simplest form of the truss bridge can be calculated easily by an engineer.
Bridge before the 19th century was made from stone and wood. wood can resist tension and compression better than the stone. Town lattice truss was one of the simplest form of truss and were patented in 1820. Bridge made out iron was rare in first half of the 19th century even though there is an iron truss patented at 1841. Iron replaced wood in the 1870s and replaced by steel in 1880s. From the first truss bridge, engineer experimented different design to find out the perfect shape that suit the problems. Because of that, now we have many types of truss bridge. A truss bridge can have a roadbed on top of the truss.
Example of Truss Bridge
Common Truss Type Used
• Howe Truss
The Howe truss was patented in 1840 by Massachusetts Millwright William Howe. The truss has vertical member that undergo tension, and a diagonal member that are angled upward the central vertical member and experience compression.
Example of the truss includes Jay bridge in Jay, New York and Sandy Creek in Jefferson County, Missouri.
Diagram of Basics Howe Truss
• Baltimore Truss
Baltimore Truss essentially is a modified Pratt Truss with extra diagonal element at the lower half of the truss to support against compression and help to control deflection.
Example of Baltimore Truss are Gould's Mill Bridge in Springfield and Penstock Bridge in Washington.
Diagram of Baltimore Truss
• Warren Truss
Warren Truss was invented by James Warren in 1848. It uses equilateral triangle that opposed the Neville Truss which use isosceles triangle. the member minimizes the force to compression but sometimes can change to tension. No vertical element in the truss. Mainly use in to create airframe for aircraft.
Example of Warren Truss uses in Piper J-3 Cub.
Diagram of Warren Truss
The Differences of “Pratt Truss”, “Howe Truss”, “Warren Truss”
There are many differences among the Warren truss, Pratt Truss and Howe Truss, and are presented below;
Warren Truss
Howe Truss
Baltimore Truss
Characteristic
Is a series of equilateral triangle with no vertical member.
Has vertical and diagonal member that slanted away from the center.
Has vertical and diagonal that are slanted to the center, and additional diagonal at the lower half of the body.
Shape
The diagonal member make a V-shaped along the body.
Equilateral Triangle throughout the body
At the middle of the body an inverted V-shaped while the rest of the body make a N-shape.
N-shape at the rest of the body
Inverted V-shape at the center
The rest of the body where the make a N-shape while the center make a V-shape and smaller V-shape of the bottom.
N-shape at the rest of the body
V-shape at the center
Lower V-shape
Ease of Construction
Easy and quick to build
Longer time to build and more complex than Warren Truss
METHODOLOGY
Procedure for analysis:
– The following is a procedure for analyzing a truss using the method of joints:
1. If possible, determine the support reactions.
2. Draw the free body diagram for each joint.
3. Write the equations of equilibrium for each joint,
,
4. If possible, begin solving the equilibrium equations at a joint where the least amount of members are connected to it. Work your way from joint to joint, selecting the new joint using the criterion where the least amount of members connected to it to the most amount of members connected to a joint.
5. Solve the joint equations of equilibrium simultaneously
To solve completely for the forces acting on a joint, a joint with least amount of members connected to it will be selected. We can assume any forces acting on a joint to be either tension or compression. If negative value is obtained, this means that the force is opposite in action to that of the assumed direction. Once the forces in one joint are determined, their effects on adjacent joints are known. Then continue solving on successive joints until all forces have been found
TRUSS DESIGN
For this project, we choose a combination of Warren Truss and Baltimore Truss. The Warren Truss is designed by James Warren as the design is to minimize the tensile force as it exerts force mostly compressive force. As for the Baltimore Truss, it is a modified Pratt Truss with extra diagonal element at the lower half of the truss to support against compression and help to control deflection.
This design was chosen because with Baltimore design at the side of the body to support Warren Truss since the Warren Truss will be executing too much of compressive forces. Then, the Baltimore Truss will reduce the compressive forces executed by Warren Truss as the Baltimore Truss’s properties is to prevent the buckling in the compression of the truss members.
As the design below, we can see that the Warren Truss and Baltimore Truss will support each other in spreading the compressive and tensile forces equally. The Warren Truss will execute the compressive force and the Baltimore Truss will prevent the buckling in the compression members.
POINT BC AND DE ARE SEPARATED BY 2m
Warren Truss
Baltimore Truss
How the Force Spread Out
Here are two diagram of each truss showing the force distributed when the hybrid truss is under load. In both diagram, the truss will be subjected to a load = 100. Therefore, we can take the number as percentage of the total load.
Spread load at the top
Load at the center
Like all truss design, when the load is located at the center the load is greater on the member than the load spread out on top of the structure.
DATA ANALYSIS
CALCULATION
Entire Truss
∑FX = 0 ∑FY = 0
AX = 0AY + FY – 20k = 0
AY = 12. 5 k∙N
∑MA = 0
FY (16) – 5k(4) – 5k(8) – 5k(12) = 0
FY = 7.5 k∙N
Joints:
∑FX = 0
FAB – FALCos(45)
FAJ
FAL
FAB = FALCos(45)
FAB = 0
∑FY = 0
AY + FAJ – FALSin(45) = 0
FAB
FAJ – FALSin(45) = -AY
FAJ = -AY
FAJ = -12.5 k∙N (T)
AY
5k∙N
FJI
∑FX = 0
FJI – FJLCos(45) = 0
FJI = FJLCos(45)
FJI = -7.502 k∙N (C)
FAJ
∑FY = 0
FJL
FJLSin(45) – FAJ -5k = 0
FJLSin(45) – FAJ = 5k
FJL = FAJ – 5k
FJL = -10.61 k∙N (T)
FJL
∑
J
FX = 0
FJLCos(45) + FALCos(45) – FBCCos(45) = 0
FJL + FAL = FBL ———-(1)
FJL = FBL = -10.61 k∙N (T)
∑
FBL
FAL
FY = 0
-FJLSin(45) + FBLSin(45) + FACSin(45) = 0
FBL + FAL = FJL ———(2)
Sub (1) into (2)
FJL + FAL + FAL = FJL
2FAL = 0
FAL =0
∑FX = 0
FBLCos(45) – FAB – FBC = 0
FBL
FBI
FBL = FAB + FBC
FBL = FBC = -10.61 k∙N (T)
∑FY = 0
FBC
FAB
FBI – FBLSin(45) = 0
FBI = -7.502 k∙N (C)
5k∙N
FIH
∑FX = 0
FJI
-FJI + FIH – FCICos(63) = 0
FIH – FCICos(63) = FJI
FBI
FCI
FIH = -8.78 k∙N (C)
∑FY = 0
C
-FCISin(63) – FBI – 5k = 0
FCI = -2.81 k∙N (T)
FCH
FCI
∑FX = 0
FBC – FCD + FCICos(63) – FCHCos(63) = 0
FBC +FCICos(63) = FCD +FCHCos(63)
FCD = -13.16 k∙N (T)
∑FY = 0
FBC
FCD
-FCISin(63) – FCHSin(63) = 0
FCH = -FCI = 2.81 k∙N (C)
FHG
FIH
5k∙N
∑FX = 0
FHG – FIH + FCHCos(63) – FHDCos(63) = 0
FHD
FCH
FHG – FHDCos(63) = FIH – FCHCos(63)
FHG = -11.63k∙N (C)
∑FY = 0
FHDSin(63) + FCHSin(63) – 5k = 0
FHD = 2.801 k∙N (C)
∑FX = 0
FFM
FFK
FFMCos(45) + FEF = 0
FEF = FFMCos(45) = 0
FY
FEF = 0
FBD (POINT F)
∑FY = 0
FY + FFK – FFMSin(45) = 0
FEF
-FFK + FFMSin(45) = FY
FFK = -7.50 k∙N (C)
FMK
∑FX = 0
FMECos(45) – FMKCos(45) – FFMCos(45) = 0
FME – FMK = FFM => FFM = 0
FFM
FME
∑FY = 0
-FMKSin(45) + FMESin(45) + FFMSin(45) = 0
FME + FFM = FMK => FME + FME – FMK = FMK
FME = FMK = -10.62 k.N (T)
FGK
∑FX = 0
FMKCos(45) – FGK = 0
FGK = -7.502 k∙N (C)
FFK
∑FY = 0
FMK
-FFK + FMKSin(45) = 0
FMKSin(45) = FFK
FMKSin(45) = -FY + FFMSin(45)
FMK = -10.61 k∙N (T)
5k∙N
FGK
FHG
∑FX = 0
FGK – FHG + FDGCos(63) = 0
FDG = -2.82k∙N (T)
FDG
∑FY = 0
FEG
FEG – 5k + FDGSin(63) = 0
FEG = 7.51 k∙N (C)
∑FX = 0
FME
FEG
FEF – FMECos(45) – FDE = 0
FDE = -FMECos(45)
FDE = 7.502k∙N (C)
∑
FDE
FY = 0
FEF
-FEG – FMESin(45) = 0
FME = -10.62 k.N (T)
( Please Referred The Table Attached At The Back )
DISCUSSION
Based on the bridge design, the usage of Baltimore Truss and Warren Truss had mathematically can support a large force. There are 4 zero force member that are uses for the stability of the structure. Another reason on why we chose the Baltimore Truss is because it provides a strong support towards the bridge design. The triangle shapes in the Baltimore Truss gives a strong support for the entire bridge design and it is also a great for very high traffic and heavy load areas.
Moving on to the Warren Truss, the reason on why we integrated this type of truss is because of the materials for this kind of truss are much less used compared to other complicated and expensive bridge designs, making it the same reason as the Baltimore Truss. With this, we can avoid from wasting extra and high costs materials. Besides low cost materials, the Warren Truss also enables the distribution of forces in a different kind of ways.
CONCLUSION
In conclusion, the hybrid truss bridge with four zero force member is very effective. This make the bridge affordable. As a result we choose material type B with nominal diameter of 25mm, maximum tensile strength of 40kN and maximum compressive strength of 20kN. Hence the bridge will be more sturdy and durable, and cost RM 2373.50.
REFERENCE
RAVINDRA, P. M. AND NAGARAJA, P. S.
THE INTERNATIONAL JOURNAL OF SCIENCE & TECHNOLEDGE
Your Bibliography: [1]P. Ravindra and P. Nagaraja, "THE INTERNATIONAL JOURNAL OF SCIENCE & TECHNOLEDGE", Strengthening Of Determinate Pratt Steel Truss By The Application Of Posttensioning Along Its Bottom Chord, vol. 1, no. 2, 2013.
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