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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.

EE0100464

02B

2.

ME0100614

02A

3.

EE0100465

02B

4.

EE0100482

02A

5.

ME0100617

02B

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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.

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

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.

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 = 0​​​AY + 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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