Calculation Design

1.0 Introduction A crane is a type of machine, generally equipped with a hoist, wire ropes or chains, and sheaves, that can be used both to lift and lower materials and to move them horizontally. Cranes has a large variety of forms- each designed to accommodate different types of functions in heavy industries. A jib crane is a type of crane where a horizontal member, supporting a movable hoist, is fixed to a wall or to a floor-mounted pillar. Jib cranes are used in industrial premises as well as military vehicles. The jib may swing through an arc, to give additional lateral movement, or be fixed. The various applications of a jib crane include suspension of tools as well as lifting of heavy machinery and equipment. The lifting capacity of jib cranes may vary from ½ ton to 200 ton and a span from a few meters to 50 meters, whereas the lifting height may be 30 meters or more. There are various types of jib cranes that are available in the market today. Some examples include wall mounted jib crane, hand operated Scotch Derrick type, Wharf cranes and mobile jib cranes. For our group, we are required to design a jib crane with height and span of 3m that can sustain 5000N of load and is able to rotate 360°. In this report, the complete design of the jib crane will be presented, which will be drawn manually and using the Solidwork program, showing the dimensions for every parts and components. Next, the required force calculation to determine suitable materials for the fabrication of jib crane. Furthermore, the components used for the fabrication of jib crane will also be listed in this report. We will also show a comparison between various dimensions during the selection of materials for the jib crane. Moreover, the types of fasteners and connections between components, such as bolt and nut or welding used and its size will also be listed in the report. Finally, the justification for each component selected will be explained in this report and a conclusion will be drawn from the overall outcome of this project. 2.0 Objective 1. To understand the conventional design of a jib crane 2. To be able to apply the various stress formulae when designing the jib crane 3. To analyze various types of material available in the market in order to find the suitable material to be used

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3.0 Problem Statement Design a jib crane which is used by small companies to load and unload objects on machines like Lathe machine. The height is about 3m. The T section is fixed on the vertical pillar to move around the pillar to move around the pillar with load. This can be about 3 meters to handle a load of 5000N.

4.0 Jib Crane Design Flow Chat

Figure 1: Jib crane design flow chart.

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Step 1: Material for Jib Crane The bending stresses for A36 steel at different conditions is shown in the table below. According to the table, the bending stress that should be applied for this case would be 152MPa.

Table 1: Bending stresses for A36 steel at different conditions Next, the Young’s Modulus,E, as well as yield strength at tension and compression are shown in the table below. Young’s Modulus, E (GPa) 200

Yield Strength (MPa) Tension

Compression

250

250

Table 2: The A36 Young’s Modulus and Yield Strength that refer from Mechanic of Materials, R.C. Hibbeler, 8th edition in SI units. Therefore, the material chosen for the fabrication of the jib crane would be structural steel A36. This is due to the fact that most industrial structures are made of that material. It will be more convenient for us in finding the respective parts with various dimensions for the jib crane as the material is easy to be found in the market.

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Step 2: Calculate the I-Beam 1) I-beam Base on the Mechanic of Materials, R.C. Hibbeler, 8th edition in SI units the wide-flange sections or W shapes SI units have been chosen. The designation was tested to choose the best I beam that can be used for this Jib Crane. The designation model has difference height and weight.

W200 X 36 Height (mm)

Weight (kg/m)

Figure 2: Meaning of the designation. y tf

d

X

X

y bf Figure 3: Wide – flange section or W shapes. Bending moment x = 3m M x1 = 1.5 m W = mg(x1)

5000 N

Figure 4: Free Body Diagram of I-Beam

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Bending Stress, σb The bending equation is given by

where M = bending moment acting at the beam σ = bending stress I = Moment of inertia of the cross section about the neutral axis y = the distance from the neutral axis to the extreme fiber E = Young’s Modulus of the material of the beam R = radius of curvature of the beam

Since E and R are constant, therefore within elastic limit, the stress at any point is directly proportional to y or the distance of the point from the neutral axis. The bending stress

is known as section modulus and is denoted by Z and the Z was depend to the designation that have been chosen. After the bending stress was found then compare it to the material steel 152 MPa and make sure it was not more than the material of the bending stress. The table below shows the designation that will be used was W200 X 36 because the bending stress was less than 152 MPa. Although the W250 X 36 I beam did not exceed the bending stress of the material, the dimension of W200 X 36 is more suitable as compared to W250 X 28. Moreover, the bending stress of W200 X 36 is also lesser than that of W250 X 28.

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Designation

Depth, Flange d

mm x kg/m

mm

x-x

Weight,

Moment,

Bending

width,

axis

W

M

Stress, σb

bf

Z

mm

103

N

Nm

MPa

Decision

mm3 a) W250 X 28

260

102.0

307

824.04

38736

126.2

Reject

b) W250 X 22

254

102.0

227

647.46

38471

169.5

Reject

c) W250 X 18

251

101.0

179

529.74

38295

213.9

Reject

d) W200 X 36

201

165.0

342

1059.48

39089

114.3

Accept

e) W200 X 22

206

102.0

194

647.46

38471

198.0

Reject

Table 3: Comparison the bending moment using different wide – flange section or W shapes

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Step 3: Calculate Shaft Diameter

x = 3m M H1

h

Shaft

x1 = 1.5 m W = mg(x1)

5000 N

H1 y1 = 0.15 m Ry Figure 5: Free Body Diagram of Shaft and I-Beam Since the I beam W200 – 36 has been chosen so, I-beam weight, W

Load, F

Total y-axis force, ∑Fy

Horizontal Force, H1

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Diameter of shaft, d

(Acceptable because the bending stress is less than the steel compression stress.) Calculate the shaft diameter:

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Step 4: Failure of the Column While designing the structure of the jib crane, we need to consider the failure of the column which the maximum of load can apply on the structure before it changes its shape. The load is called crippling load, Wcr. The equation, Euler’s Formula for calculating the load is stated as below:

Where,

End conditions of the column can be categorized into several kinds which are both the end fixed, one end is fixed and the other free, one is fixed and the other hinged and both the ends of the column hinged or pin jointed. It is important to choose the end condition well as we may know how the shaft buckles. The value of the end of condition constant is given as below:

Figure 6: The buckling of rod at different end conditions No

End Condition

End condition coefficient,C

a

Both ends hinged

1

b

Both ends fixed

4

c

One end fixed and other end free

0.25

d

One end fixed and other hinged

2

Table 4: The end condition coefficient, C, for different end conditions However, there are few assumption need to consider in order to apply Euler’s formula. The length of column must be long compared to its cross-sectional area and the load is applied 9

to the central of the structure with neglecting its own weight. Besides, we are assuming the column is perfectly straight and it is perfectly elastic and obeys Hooke’s Law. By our design of jib crane, we know that:

Therefore,

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Step 5: Choose the suitable bearing and pipe size from the market Bearing Size Since the shaft diameter is 70mm, then the bearing size that should be chosen is 70mm as well. The figure below showed the model from the market that suitable for this jib crane bearing size.

Figure 7: Bearing size base on the shaft diameter 70mm.

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Pipe Size Since the outer bearing diameter that have been chosen from the market is 152mm, consider the clearance ± 5mm for each side 0.116in

is the most suitable

dimension for design this jib crane design.

Figure 8: Pipe size that have been chosen was 0.116 in.

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Step 6: Calculate Bolt and Nut Size A

x = 3m

R

M

Shaft

H1

h

R

x1 = 1.5 m 5000 N

W = mg(x1)

H1 y1 = 0.15 m Ry

168 mm

z

197 mm

Figure 9: R is the force sustain by a single bolt.

152 mm 197 mm Figure 10: Bolt and plat. Length of z = 214.9605 mm = 0. 2150 m Taking moment at A,

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Formula for stresses of bolt due to external forces:

Where, = root or core diameter of the thread = proof load for the bolt material

Using steel bolt, class 10.9 Hence, proof load of steel bolt of class 10.9, σp = 830 MPa

From table below, M20 bolt is selected. Bolt length = 80 mm

Figure 11: The suitable bolt is M20 have been chosen from this jib crane base on the

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Dimension of bolt and nut for size M20 BOLT

Figure 12: Bolt specification dimension. Size for bolt M20 H=12.285mm −12.715mm T=22.4mm R=46mm L=80mm G=33.53mm F=29.67mm −30mm NUT

Figure 13: Nut specification size. G=33.53mm F=29.67mm −30mm Thickness= 16mm

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Step 7: Welding Calculation I-beam

Welding area

y

Block X

Welding area

X

y

Figure 14: Front view of the I-beam and welding area block. Total y-axis force, ∑Fy = Bending Moment = 37733 N.m To obtain the throat thickness, S from the shear stress of welding, equation below is used. (eqn 1)

For (eqn 2) Area considered is the area of welding, A (eqn 3) Substitute (3) into (2), (eqn 4)

For (eqn 5)

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Moment of inertia from parallel axis theorem,

has very small value and thus is assume negligible. Since 4 layer of welding with 2 different length is used, addition of the inertia for longer length and shorter length is included. (eqn 6) Substitute (6) into (5), (eqn 7) Substitute (7) & (4) into (1),

(eqn 8)

Welding electrodes used is S – 7016 H yield strength = 490 N/mm2 permissible shear stress (eqn 9)

S= 3.95

Substitute (9) into (8)

t

S =3.95 Figure 15: S is the welding height and t is throat thickness

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Hollow Shaft Outer Welding Part Horizontal Force, H1

To obtain the throat thickness, S from the shear stress of welding, equation below is used. (eqn 1)

For (eqn 2) Area, A considered is the area of welding on the outer circumference of hollow shaft

(eqn 3) Substitute (3) into (2), (eqn 4)

For (eqn 5) Moment of inertia for the circular hollow shaft (eqn 6) Substiture (6) into (7)

(eqn 7)

Substitute (7) & (4) into (1),

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S = 16.97

Permissible Shear Stress

t

S =16.97 Figure 16: S is the height of the welding and t is the throat thickness

Cover Plate Welding area

Pipe

Figure 17: The circular welding part

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5.0 Illustration of Design

Figure 18: Isometric view of jib crane design

Figure 19: Front view of jib crane design

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Figure 20: Design for jib crane mechanism

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6.0 List of Design Components and Dimensions No.

Component

1

I-beam

2

Solid shaft

3

Pipe

4

Cover Plate

Dimension

22

5

Solid Block

6

Bolt & Nut

7

Bearing

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7.0 Conclusion In conclusion, from this mini design project, it is discovered that designing any mechanical structure need to take a lot of aspects and conditions into consideration. Factors such as the permissible stresses of materials as well as the requirements needed by the design play a very important part in constructing the design. Through this mini design project, our group has managed to understand more about the process in designing a mechanical structure. It also gave us an opportunity to learn how to apply different types of formulae in order to determine parameters such as the diameter of shaft or the dimension of the I-beam. We need to acquire a lot of information regarding both the materials and the requirements of the design itself. Furthermore, we were also able to understand more about the design of a conventional jib crane.

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8.0 Reference 1) http://www.roymech.co.uk/Useful_Tables/Screws/Hex_Screws.htm 2) http://www.edgefasteners.com/bolts/Hex_Bolts_Grade_A_B_Metric.pdf 3)http://books.google.com.my/books?id=Giyf7wk3qv0C&pg=PA179&dq=allowable+bending +stress+of+a36+steel&hl=en&sa=X&ei=TRmoUpTlK4LWrQevloGAAw&redir_esc=y#v=one page&q=allowable%20bending%20stress%20of%20a36%20steel&f=false 4)http://books.google.com.my/books?id=5my9ysp9eiAC&pg=PA229&dq=allowable+bending +stress+of+a36+steel&hl=en&sa=X&ei=TRmoUpTlK4LWrQevloGAAw&redir_esc=y#v=one page&q=allowable%20bending%20stress%20of%20a36%20steel&f=false 5) http://www.metalsdepot.com/products/hrsteel2.phtml?page=plate 6) http://www.dearborncrane.com/crane-ium/articles_directory.htm 7) https://www.gorbel.com/Solutions/designstandards.aspx 8) http://www.astm.org/Standards/A36.htm 9) http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm

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