Abstract

An effective method for demonstration of buckling in classroom conditions is lacking.

The following project was undertaken to design and develop a lightweight rig to

demonstrate the fundamental principles of buckling in classroom conditions.

Initially the existing products that were used for similar purposes were researched

and their problems outlined. A list of objectives was developed that incorporated

functions that were not available in current products. Buckling theories were used to

calculate the required dimensions for the rig. Research was carried out before the

design process to decide on the most suitable materials to use. The design process

involved developing initial ideas from which the most practical ones were developed

further into the prototype design. The prototype was manufactured and tested which

outlined the problems with the original design. Following the redesign of the

prototype, final design was manufactured and tested. Results demonstrated that the

rig closely conformed to the theoretical buckling principles.

The outcome of the project was a success as it fulfilled all the required objectives set

and provided an accurate visual representation of buckling. A range of

improvements can be made to the design if further work was to be carried out. All the

required drawings and CAD files were produced and attached.

Acknowledgements

I would like to thank Dr Anish Roy of Loughborough University for presenting me with

the opportunity to carry out this project. He always gave helpful feedback and made

great inputs into the project, without his support the project would have been of a

much poorer quality.

I would also like to take this opportunity to thank Professor Vadim Silberschmidt for

pointing out the problems with my initial design during the interim presentation and

the suggestions for the improvements that should be made.

Finally it is my pleasure to thank the Wolfson Technical Staff for providing enormous

support throughout the manufacturing of my product.

Table  of  Contents  CHAPTER  1  ............................................................................................................................................................  1  

1  Introduction  ......................................................................................................................................................  1  

1.1  Background  ..............................................................................................................................................  1  

1.2  Aims  and  Objectives  .............................................................................................................................  1  

1.3  Planning  .....................................................................................................................................................  2  

CHAPTER  2  ............................................................................................................................................................  3  

2  Literature  review  ............................................................................................................................................  3  

2.1  Euler  Theory  ............................................................................................................................................  3  

2.2  Rankine-­‐Gordon  Theory  .....................................................................................................................  5  

CHAPTER  3  ............................................................................................................................................................  7  

3.  Current  Products  ...........................................................................................................................................  7  

3.1  WP121  ........................................................................................................................................................  7  

3.2  WP120  ........................................................................................................................................................  8  

CHAPTER  4  ............................................................................................................................................................  9  

4  Design  &  Methodology  .................................................................................................................................  9  

4.1  Research  ....................................................................................................................................................  9  

4.1.1  Test  Piece  Material  ......................................................................................................................  9  

4.1.2  Boundary  Conditions  ...............................................................................................................  10  

4.1.3  Frame  Material  ...........................................................................................................................  11  

4.1.4  Loading  Masses  ..........................................................................................................................  11  

4.2  Research  Outcome  ..............................................................................................................................  12  

4.3  Calculations  ...........................................................................................................................................  13  

4.4  Initial  Ideas  ............................................................................................................................................  20  

4.4.1  Fixed  ................................................................................................................................................  20  

4.4.2  Pinned  ............................................................................................................................................  21  

4.4.3  Frame  ..............................................................................................................................................  22  

4.4.4  Top  fixed  ........................................................................................................................................  23  

4.4.5  Top  pinned  ...................................................................................................................................  25  

4.4.6  Short  strut  pinned  .....................................................................................................................  26  

4.5  Rig  Design  Development  ..................................................................................................................  28  

4.6  Final  Idea  CAD  ......................................................................................................................................  29  

 

 

 

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4.6.1  Frame  ..............................................................................................................................................  30  

4.6.2  Loading  plates  .............................................................................................................................  31  

4.6.3  Short  test  piece  holder  ............................................................................................................  32  

4.6.4  Stands  .............................................................................................................................................  32  

4.6.5  Pinned  Bottom  Bracket  ...........................................................................................................  33  

4.6.6  Corner  Bracket  ...........................................................................................................................  33  

4.6.7  Top  fixed  holder  .........................................................................................................................  34  

4.6.8  Bottom  fixed  holder  .................................................................................................................  34  

4.6.9  Top  pinned  bracket  ..................................................................................................................  35  

4.6.10  Test-­‐piece  attachment  ..........................................................................................................  35  

4.7  Engineering  Drawings  ......................................................................................................................  36  

CHAPTER  5  .........................................................................................................................................................  38  

5  Manufacturing  ...............................................................................................................................................  38  

5.1  Machinery  used  ....................................................................................................................................  38  

5.1.1  Lathe  Machine  .............................................................................................................................  38  

5.1.2  Milling  machine  ..........................................................................................................................  38  

5.1.3  Pillar  drill  ......................................................................................................................................  39  

5.1.4  Belt  Sander  ...................................................................................................................................  39  

CHAPTER  6  .........................................................................................................................................................  41  

6  Assembly  .........................................................................................................................................................  41  

6.1  Exploded  View  .....................................................................................................................................  41  

6.2  Step  by  Step  Assembly  ......................................................................................................................  42  

CHAPTER  7  .........................................................................................................................................................  45  

7  Results  and  observations  .........................................................................................................................  45  

7.1  Prototype  ................................................................................................................................................  45  

7.2  Prototype  Testing  ...............................................................................................................................  48  

7.3  Final  model  ............................................................................................................................................  49  

7.4  Final  Model  Testing  ............................................................................................................................  51  

7.5  Test  Results  ...........................................................................................................................................  52  

CHAPTER  8  .........................................................................................................................................................  55  

8  Discussion  .......................................................................................................................................................  55  

8.1  Buckling  Forces  ...................................................................................................................................  55  

Fixed-­‐Fixed  Strut  ..................................................................................................................................  55  

 

 

 

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Fixed-­‐Pinned  Strut  ...............................................................................................................................  55  

Pinned-­‐Pinned  Strut  ............................................................................................................................  56  

Short  Pinned-­‐Pinned  Strut  ...............................................................................................................  56  

8.2  Rig  Mass  ..................................................................................................................................................  57  

8.3  Problems  .................................................................................................................................................  57  

8.4  Design  Evaluation  ...............................................................................................................................  58  

Time  ............................................................................................................................................................  58  

Material  .....................................................................................................................................................  58  

Safety  ..........................................................................................................................................................  58  

CHAPTER  9  .........................................................................................................................................................  60  

9  Conclusions  ....................................................................................................................................................  60  

CHAPTER  10  ......................................................................................................................................................  62  

10  Further  work  ..............................................................................................................................................  62  

10.1  Further  Developments  and  Improvements  ..........................................................................  62  

10.2  Costs  .......................................................................................................................................................  63  

10.3  Distribution  ........................................................................................................................................  64  

References  ..........................................................................................................................................................  66  

Appendix  1  ............................................................................................  Error!  Bookmark  not  defined.  

Appendix  2  ............................................................................................  Error!  Bookmark  not  defined.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

iv  

 

Table  of  Figures  

Figure  1  -­‐  Buckling  shapes  [5]  ......................................................................................................................  4  

Figure  2  -­‐  Buckling  stress  against  slenderness  ratio  [3]  ...................................................................  5  

Figure  3  –  WP121  [7]  ........................................................................................................................................  7  

Figure  4  –  WP121  Diagram  [7]  .....................................................................................................................  7  

Figure  5  -­‐  WP120  [8]  ........................................................................................................................................  8  

Figure  6  -­‐  WP120  Diagram  [8]  .....................................................................................................................  8  

Figure  7  –  Aluminium  [10]  .............................................................................................................................  9  

Figure  8  –  Acrylic  [11]  ......................................................................................................................................  9  

Figure  9  –  Brass  [14]  ......................................................................................................................................  10  

Figure  10  –  Spring  Steel  [13]  ......................................................................................................................  10  

Figure  11  –  Door  Hinge  [15]  .......................................................................................................................  10  

Figure  12  –  Bench  Vice  [16]  ........................................................................................................................  10  

Figure  13  –  Slotted  Masses  [19]  ................................................................................................................  11  

Figure  14  -­‐  Logarithmic  Scale,  Overview  ..............................................................................................  16  

Figure  15  –  Linear,  Close  up  .......................................................................................................................  16  

Figure  16  –  Fixed  Concept  1  .......................................................................................................................  20  

Figure  17  –  Fixed  Concept  2  .......................................................................................................................  20  

Figure  18  –  Fixed  Concept  3  .......................................................................................................................  21  

Figure  19  –  Pinned  Concept  1  ....................................................................................................................  21  

Figure  20  –  Pinned  Concept  2  ....................................................................................................................  22  

Figure  21  –  Pinned  Concept  2.1  ................................................................................................................  22  

Figure  22  –  Pinned  Concept  2.2  ................................................................................................................  22  

Figure  23  –  Frame  Concept  .........................................................................................................................  23  

Figure  24  –  FEA  of  Top  Frame  Beam  ......................................................................................................  23  

Figure  25  –  Top  Fixed  Concept  1  ..............................................................................................................  24  

 

 

 

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Figure  26  –  Top  Fixed  Concept  2  ..............................................................................................................  24  

Figure  27  .............................................................................................................................................................  24  

Figure  28  –  Top  Fixed  Concept  3  ..............................................................................................................  25  

Figure  29  –  Top  Pinned  Concept  1  ...........................................................................................................  25  

Figure  30  –  Top  Pinned  Concept  2  ...........................................................................................................  25  

Figure  31  –  Top  Pinned  Concept  3  ...........................................................................................................  26  

Figure  32  –  Short  Strut  Concept  1  ............................................................................................................  26  

Figure  33  –  Short  Strut  Concept  1  ............................................................................................................  26  

Figure  34  –  Short  Strut  Concept  2  ............................................................................................................  27  

Figure  35  –  Rendered  Rig  Assembly  .......................................................................................................  30  

Figure  36  –  Frame  Final  CAD  .....................................................................................................................  31  

Figure  37  –  Loading  Plate  CAD  ..................................................................................................................  31  

Figure  38  –  Short  Test  Piece  Holder  CAD  .............................................................................................  32  

Figure  39  –  Stands  CAD  ................................................................................................................................  32  

Figure  40  –  Pinned  Bottom  Bracket  CAD  ..............................................................................................  33  

Figure  41  –  Corner  Bracket  CAD  ...............................................................................................................  34  

Figure  42  –  Top  Fixed  Holder  CAD  ..........................................................................................................  34  

Figure  43  –  Bottom  Fixed  Holder  CAD  ...................................................................................................  34  

Figure  44  –  Top  Pinned  Bracket  CAD  .....................................................................................................  35  

Figure  45  -­‐  Test  Piece  Attachment  CAD  .................................................................................................  35  

Figure  46  -­‐  Dimensioned  Assembly  Drawing  .....................................................................................  37  

Figure  47  –  Lathe  Machine  ..........................................................................................................................  38  

Figure  48  –  Milling  Machine  .......................................................................................................................  38  

Figure  49  –Pillar  Drill  ....................................................................................................................................  39  

Figure  50  –  Belt  Sander  ................................................................................................................................  39  

Figure  51  -­‐  Rig  Exploded  View  ..................................................................................................................  41  

Figure  52  -­‐  Frame  Assembly  .......................................................................................................................  42  

 

 

 

vi  

 

Figure  53  -­‐  Stand  Assembly  ........................................................................................................................  42  

Figure  54  -­‐  Bracket  Assembly  ....................................................................................................................  42  

Figure  55  -­‐  Test  Piece  Insertion  ................................................................................................................  43  

Figure  56  -­‐  Test  Piece  Insertion  2  ............................................................................................................  43  

Figure  57  -­‐  Test  Piece  Insertion  3  ............................................................................................................  43  

Figure  58  -­‐  Pin  Insertion  ..............................................................................................................................  44  

Figure  59  –  Prototype  ....................................................................................................................................  45  

Figure  60  –  Prototype  Top  ..........................................................................................................................  46  

Figure  61  –  Prototype  Close-­‐up  ................................................................................................................  46  

Figure  62  –  Test  Piece  Attachment  ..........................................................................................................  46  

Figure  63  –  Attachment  Redesign  ............................................................................................................  47  

Figure  64  –  Test  Piece  Comparisons  .......................................................................................................  47  

Figure  65  –  Fixed/Fixed  ...............................................................................................................................  48  

Figure  66  –  Fixed/Pinned  ............................................................................................................................  48  

Figure  67  -­‐Pinned/Pinned  ...........................................................................................................................  48  

Figure  68  –  Short  Pinned/Pinned  ............................................................................................................  48  

Figure  69  –  Limiting  Bush  ...........................................................................................................................  49  

Figure  70  -­‐  Modified  Mass  Holder  CAD  ..................................................................................................  49  

Figure  71  -­‐  Manufactured  bush  .................................................................................................................  50  

Figure  72  –  Manufactured  Weight  Plates  .............................................................................................  50  

Figure  73  –  Rig  on  Scales  .............................................................................................................................  51  

Figure  74  –  Scales  Readout  .........................................................................................................................  51  

Figure  75  –  Demonstration  of  Buckling  Shapes  .................................................................................  52  

Figure  76  –  Short  Test  Piece  Holder  Mass  ............................................................................................  53  

Figure  77  –  Pinned  Test  Piece  Holder  Mass  ........................................................................................  53  

Figure  78  –  Chart  Comparing  Experimental  and  Theoretical  Results  ......................................  54  

Figure  79  –  Original  Frame  .........................................................................................................................  62  

 

 

 

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Figure  80  –  Proposed  Redesign  ................................................................................................................  62  

Figure  81  –  Original  Holder  ........................................................................................................................  63  

Figure  82  –  Proposed  Redesign  ................................................................................................................  63  

 

 

 

 

 

1  

 

CHAPTER  1  

1  Introduction    

1.1  Background  Buckling is taught in variety of engineering degrees and the fundamentals are

very well established. When lecturing on the topic of buckling there are always

sections that describe the effect different boundary conditions have on the

maximum compressive force that can be applied to the slender member

before it buckles. In addition the maximum compressive force that the

member can be subjected to is length dependent. These principles can be

demonstrated in laboratories where specialized rigs are used which apply

compressive force to members of various lengths until they buckle. However it

is desired to be able to demonstrate similar things in a classroom/lecture

theatre. Smaller demonstration rigs are available on the market but are too

bulky to be carried around.

1.2  Aims  and  Objectives  The aim of the project was to design and manufacture a lightweight and

compact rig to demonstrate the fundamental principles of buckling for use in

classroom conditions. The rig had to be mechanically powered to ensure it

could be used without a power supply.

Following initial research that was carried out on existing products, the

following objectives were set:

• It was decided that the rig must not exceed 5kg in order to be easily

carried around. This however does not take into account the mass of

the weights that will be applied to the struts. [Required]

• The rig must represent Euler bucking [Required]

• Different strut conditions need to be demonstrated to show how the

attachment of the strut affects the buckling when a load is applied.

 

 

 

2  

 

Pinned-pinned, fixed-pinned etc. to show different buckling modes.

[Required]

• Displacement of the struts under load must be measured so numerical

comparison is available along with visual. [Desired]

• Euler buckling can sometimes be inaccurate when slenderness ratio is

less than 50, so demonstration of Rankine-Gordon buckling is desired.

[Desired]

• To prevent the strut from going beyond its elastic limit, safety support is

to be designed to limit the movement and prevent yielding. [Required]

• To fully demonstrate the buckling principles, use of different length bars

must be implemented. [Desired]

1.3  Planning    Before the project work commenced, a proposed plan of work was devised:

• Research into existing rigs available for demo – Research and analyse

available products on the market for demonstration of buckling

• Literature review of buckling principles – Review the fundamental

principles of buckling.

• Development of initial design ideas – Research into current designs

and current methods available to realise the objectives and develop

initial ideas. Evaluate initial ideas and develop them into final design.

• Prototyping and manufacture of design – Manufacture and test the

prototype. From testing conclusions and design changes can be made

which can be incorporated into final design.

• Testing – Thorough testing of the design against requirements set.

• Report writing – Report writing to be done progressively as new data

and results are acquired.

After the objectives have been set and the research was carried out a Gantt

chart was produced to ensure that the project was completed on time. The

copy of the Gantt chart can be viewed in Appendix 1.

 

 

 

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CHAPTER  2

2  Literature  review      

Buckling – “Long slender members subjected to an axial compressive force

are called columns, and the lateral deflection that occurs is called buckling”.

[1]

2.1  Euler  Theory  Euler theory is named after a Swiss mathematician Leonhard Euler and is one

of the main buckling theories used to calculate the maximum load that can be

applied to a column before it buckles [2]. This maximum load that can be

supported by a column before it buckles is called the critical load !!.

All calculations are performed on an ideal column, which means the following

assumptions [1, 2, 3] are made:

• The column is made from a homogeneous material i.e. the material

properties are constant throughout

• An ideal column is initially straight when unloaded

• The load is applied directly through the centroid of the cross-section of

the column

• The column is assumed to have a uniform cross-section

• The column behaves in a liner-elastic manner

• Upon buckling the yield stress is not exceeded

The critical load depends on the column cross-sectional dimensions, materials

modulus of elasticity and the length of the column. The greater the length of

the column the less force it takes before it buckles. The dimensions of the

column directly affect the value for the area moment of inertia. Therefore the

higher the moment of inertia ! at the cross-section, the greater the load that

can be supported by the member.

 

 

 

4  

 

Euler critical load (!!) is the maximum load that the column can be subjected

to before it buckles. [1,2,3]

!! =  !!!"!"!      (2− 1)  

Where ! is the modulus of elasticity, ! is the area moment of inertia and !" is

the effective length [4]. As can be seen in Table 1 the value for ! depends on

the boundary condition of the strut and ! is the unsupported length of the

column.

Table 1 – Effective Length [3]

Boundary Conditions Effective Length !"

Fixed - Fixed 0.5!

Fixed - Pinned 0.699!

Pinned - Pinned !

Fixed - Free 2!

Figure 1 shows the different buckling

shapes of the column depending on

the boundary conditions.

Even though Euler theory can provide

an accurate representation of the

buckling load there are some

limitations. Euler theory predicts that no deflection of the column occurs until

the critical load is reached, also the theory predicts that there is infinite

deflection possible at the critical load, and does not take yielding into account.

Figure  1  -­‐  Buckling  shapes  [5]

 

 

 

5  

 

2.2  Rankine-­‐Gordon  Theory  

Rankine-Gordon theory

is typically used for

shorter bars with

slenderness ratio (!)

less than 50. Figure 2

shows Euler, Rankine-

Gordon and

experimental buckling

stresses plotted against

slenderness ratio. It can

be seen that Euler theory

predicts a higher buckling stress than the experimental and the Rankine-

Gordon theory. As the slenderness ratio increases the predictions obtained

from Euler and Rankine-Gordon tend to equal each other.

Slenderness ratio (!) is the ratio of effective length (!!"") of a member to its

radius of gyration (!). [3]

! =  !!""!  (2− 2)

Where

! =  !!    (2− 3)

Figure  2  -­‐  Buckling  stress  against  slenderness  ratio  [3]

 

 

 

6  

 

Where ! is the cross-sectional area of the member and ! is the area moment

of inertia.

The Rankine-Gordon formula [3,6] for critical load (!!) is:

!! =  !!!

1+ !!!  (2− 4)

Where !! is the yield stress of the material,  ! is the cross-sectional area, ! is

the slenderness ratio and ! is a constant depending on the material.

! =  !!!!!    

 

   

 

 

 

 

 

 

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CHAPTER  3  

3.  Current  Products  As was mentioned earlier there are some products existing on the market for

basic demonstration of the buckling principles. These products are made by

GUNT Hamburg, which is a German based company that produces

equipment for engineering education. Following are some of their products.

3.1  WP121            This product demonstrates four cases of

Euler buckling. As can be seen in Figure

3 the maximum mass that each strut can

be subjected to before it buckles depends

on the boundary condition. The white

backing provides a clear view of the

buckling shapes. The test bars are made

from stainless spring steel and remain

within the elastic range throughout the

experiment. The product comes with a set of graduated weights, which allow

a precise increase in mass until the

critical load is reached.

The strut length used in this product is

180mm and the dimensions of the

frame are 380x110x270mm (l x w x h).

The approximate weight of the rig is

10kg, not including the weight set.

Figure 41 shows the components that

the rig consists of.

                                                                                                                             

1  1 weight, 2 pinned support, 3 bar, 4 backing wall with grid pattern, 5 fixed support, 6 mount for weights  

Figure  3  –  WP121  [7]  

Figure  4  –  WP121  Diagram  [7]  

 

 

 

8  

 

3.2  WP120   This product demonstrates all cases of Euler

buckling, but can only do so for one

boundary condition at a time. The lateral

deflection of the member is measured

throughout the loading. The product allows

the stresses in the member to remain within

the elastic limit. The bar lengths supplied

with the product range from 350-700mm and

can be accommodated by adjusting the

height of the load-carrying arm. The test bars

supplied also come in a variety of materials

such as aluminium, copper, brass and steel.

The hand-operated spindle allows for progressive application of compressive

load to the bar. The load cell measures the applied force and displays the

value on the pressure gauge. Traverse loads can be applied to the test piece

to generate additional shear force

on the test piece. This lateral

deflection can be measured. The

dimensions for this product are

620 x 450 x 1150 mm (l x w x h)

and the approximate weight is

63kg. Additional sets allow

investigations of various cross-

sectional geometries, eccentric

application of force and also additional traverse loading. Figure 62 shows the

components the rig consists of.

                                                                                                                         

2 1 spindle, 2 height-adjustable load-carrying cross-arm, 3 dial gauge for lateral deflection of test bar, 4 load cell, 5 frame, 6 pressure gauge, 7 device to generate a transverse load, 8 test bar

 

Figure  5  -­‐  WP120  [8]

Figure  6  -­‐  WP120  Diagram  [8]  

 

 

 

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CHAPTER  4  

4  Design  &  Methodology  

4.1  Research  Before any initial design ideas were developed, research was carried out into

existing products. The product functionality and the materials used for each

part were studied carefully. One of the most demanding parts of the research

and design phase was developing methods of fixing the test pieces to the

frame and still allow for the end conditions to the attained. GUNT products

used steel for their frames and that made them somewhat heavy [7,8]. None

of the products researched compared different length test pieces side by side.

That had to be incorporated into the design, as that was one of the objectives

set. A suitable size for the frame had to be designed so it can easily be seen

from a distance.

4.1.1  Test  Piece  Material  There were various different materials that could

have been chosen for the test pieces. Aluminium

(Figure 7) was a very easy material to acquire

but due to low Young’s Modulus of 69GPa [9] it

was not suited for use as a test piece.

Aluminium yields under low forces and it is not

very flexible. Aluminium was not suited for this

application.

Acrylic (Figure 8)

was another material that was looked into for use

as a test piece. Young’s Modulus of 3.2GPa [9]

could have caused it to yield under low forces. It

could yield before noticeable deflection of the test

piece occurs.

Figure  7  –  Aluminium  [10]  

Figure  8  –  Acrylic  [11]  

 

 

 

10  

 

Brass (Figure 9) was also considered. With

Young’s Modulus of 100-125GPa [9] it can

provide effective demonstration buckling. One

material that was

suited for such an

application was

spring steel (Figure

10). It has a high

Young’s Modulus of

210GPa [12], which suggested that it will not

yield as easily as the materials discussed above.

In the existing products that are available on the market spring steel was used

as the material for the test pieces.

4.1.2  Boundary  Conditions  Research for the boundary conditions involved

methods that are in use today to achieve similar

things. For pinned boundary condition a

common door hinge (Figure 11) was considered.

This is a simple yet very effective design that is

used in various applications. It involves two

separate parts rotating around a common fixed

axis.

For a fixed boundary condition means of clamping

could be used. Available methods that currently

exist which provide clamping are vices (Figure 12)

and clamps. By implementing the same technique

into the design, a fixed boundary condition can be

attained by clamping the test piece and prevent it

rotating around the end point.

Figure  9  –  Brass  [14]  

Figure  10  –  Spring  Steel  [13]  

Figure  12  –  Bench  Vice  [16]  

Figure  11  –  Door  Hinge  [15]  

 

 

 

11  

 

4.1.3  Frame  Material There was a selection of materials that were considered for use in the frame

design. Aluminium has a density of 2712kg/m3 [17]. This is low compared to

steel, which has a density of 7850kg/m3 [17]. Carbon fiber was also

considered as the material for the frame as it would have made it very light

due to its density of 1740kg/m3 [18]. However carbon fiber was exceptionally

expensive and because of that was excluded from the material selection for

the frame. The frame had to be less than 5kg, as stated in the objectives.

Aluminium had a much lower density than steel therefore it was a more

favorable choice to be used as the material for the frame.

4.1.4  Loading  Masses  The test pieces had to be loaded to display the

maximum force that a strut could take before

buckling. This could be done using slotted

masses (Figure 13), which are available to

purchase from science equipment suppliers. The

maximum total mass of each set totals up to 1kg,

which is reached in 100g increments.

 

 

 

 

   

 

Figure  13  –  Slotted  Masses  [19]  

 

 

 

12  

 

4.2  Research  Outcome  Before the design ideas were developed some key design decisions were

made. For the rig to be less than 5kg the frame dimensions had to be

designed so that the mass did not exceed this value, for this reason

aluminium was chosen to be the material for the frame due to its low density.

The material for the test pieces had to be spring steel in order to prevent them

yielding under low force. The test pieces had to be dimensioned correctly so

that a reasonable amount of force had to be applied to cause buckling. After

further research and meeting the workshop staff it was noted that the test

piece holders would be under considerable stress. Therefore the rest of the

components had to be designed using mild steel as aluminium would not be

suited for such an application. For the rig to be easily seen a decision was

made that the height of the frame would approximately be 400mm and the

width of 500mm. Spring steel was the chosen material for the test pieces. The

available dimensions for spring steel strips were 0.5mm thick and 16mm wide

[20].

 

 

 

 

 

   

 

 

 

 

13  

 

4.3  Calculations  Using the decisions that were made during research, some basic calculations

were carried out to get the initial dimensions for the design. The design brief

stated that the jig had to demonstrate Euler buckling; therefore this theory was

used to calculate the test piece dimensions. The material used for test pieces

was spring steel with the following properties [12]:

Young’s modulus (!) – 210Gpa

Yield Strength (!!) – 1100Mpa

The strut cross-sectional dimensions remained as discussed earlier.

ℎ = 0.0005  !

! = 0.016  !

! = 0.4  !

The sample calculations were carried out for the strut with fixed-fixed

boundary conditions. So the effective length !!"" was

!!"" =  !2 = 0.2  !

x  

y  

 

 

 

14  

 

Worked out first was the area moment of inertia in x and y directions for a

rectangular cross-section [21,22]

!!! =  !ℎ!

12

!!! =  0.016×0.0005!

12 =    1.667×10!!"  !!

!!! =  !!ℎ12 = 1.067×10!!  !!

Therefore the strut will buckle about the x-axis as it has the lower value of !.

Next validity of Euler theory had to be worked out so the slenderness ratio

had to be calculated.

Using the cross-sectional dimensions that were stated earlier, the cross-

sectional area was calculated

! = !×ℎ

! = 0.016×0.0005 = 8×10!!  !!

To calculate the radius of gyration  ! equation (2− 3) was used

! =  !!!!

 

 

 

15  

 

! =  1.667×10!!"

8×10!! = 1.444×10!!  !

Therefore the slenderness ratio ! was

! =  !!""!

! =  0.2

1.444×10!! = 1385

A graph was plotted of slenderness ratio against the Euler [3] and Rankine-

Gordon [6] buckling forces using slenderness ratio (!) as the variable.

!! =!!!"!!

!! =  !!!

1+ !! !!!×!!

The following graphs show the variation in buckling force with slenderness

ratio (!) for Euler and Rankine-Gordon theories. Figure 14 shows a wide

range for the slenderness ratio and it can be seen how Euler and Rankine-

 

 

 

16  

 

Gordon curves correspond to each other up until the slenderness ratio (!)

drops below 150. This can be viewed in greater detail in Figure 15.

Figure  14  -­‐  Logarithmic  Scale,  Overview  

 

Figure  15  –  Linear,  Close  up  

1  

10  

100  

1000  

10000  

100000  

1000000  

10000000  

100000000  

0   500   1000   1500   2000   2500   3000  

Buckling  Force  

(N)  

Slenderness  Ratio  (k)  

Graph  Showing  Buckling  Force  Variation  with  Slenderness  Ratio    

Euler  

Rankine-­‐Gordon  

0  

2000  

4000  

6000  

8000  

10000  

0   50   100   150   200   250  

Buckling  Force  

(N)  

Slenderness  Ratio  

Graph  Showing  Buckling  Force  Variation  with  Slenderness  Ratio    

Euler  

Rankine-­‐Gordon  

 

 

 

17  

 

As can be seen in Figure 15, Euler theory began to deviate from the Rankine-

Gordon theory at a slenderness ratio ! of approximately 150. This means that

for this particular case the Euler theory should not be used for ! < 150. To

make the results more presentable a logarithmic scale was used for ‘Buckling

Force’ in Figure 14.

Since the calculated slenderness ratio ! for the fixed-fixed strut exceeded the

value of 150 it is accurate to use the Euler theory.

! = 210!"#

Using equation (2− 1)

!! =  !!!"!!""!

!! =  !!×210×10!×1.667×10!!"

0.2! = 8.638!

Next to ensure that yielding of strut did not occur under applied force

!!"# =  !!"! =

8.6388×10!! = 1.08!"#

!!"#   <  !! And the ratio of !!  !!"#

= 1019: 1  suggested the strut is extremely

unlikely to yield at any point during its operation lifecycle.

 

 

 

18  

 

The validity of Euler theory was verified even further by calculating the

Rankine-Gordon critical force using equation (2− 4)

!! =  !!!

1+ !! !!!×!!=

1100×10!×8×10!!

1+ 1100×10! !!×210×10!×1385!= 8.635!

The values obtained for the Euler buckling and the Rankine-Gordon buckling

loads are the same. Therefore Euler theory is valid for the chosen strut

dimensions.

The following calculations were carried out for all four struts. The results are

shown below in Table 2.

 

Table  2  –  Theoretical  Critical  Loads  

!  (!) !!""  (!) !!!  (!!) !!!  (!!) ! !!  (!) !!(!) Mass (kg)

0.4 0.2 1.667x10-13 1.067x10-8 1385 8.64 8.64 0.88

0.4 0.28 1.667x10-13 1.067x10-8 1937 4.42 4.42 0.45

0.4 0.4 1.667x10-13 1.067x10-8 2771 2.16 2.16 0.22

0.3 0.3 1.667x10-13 1.067x10-8 2078 3.84 3.84 0.39

 

 

 

19  

 

The longest test piece length was designed to be 400mm so the frame would

have to be built around that maximum dimension. The width was kept at

500mm. An excel spread sheet was created to calculate the final theoretical

mass of the frame depending on the inputs for the dimensions. The material

density for aluminium was taken to be 2700kg/m3 [17]. The chosen

dimensions were put into the spread sheet giving the theoretical mass of the

frame. Only the mass of the frame was calculated because it would contribute

the most to the mass of the rig.

The calculations involved basic equations such as

!"## = !"#$%&'  ×  !"#$%&

And

!"#$%& =!"#$ℎ  ×  !"#$ℎ!  ×  !"#$%ℎ

Table  3  –  Frame  Dimensions  and  Predicted  Mass  

Side Side Top Bottom

Width (m) 0.03 0.03 0.03 0.03

Length (m) 0.43 0.43 0.5 0.05

Thickness (m) 0.015 0.015 0.02 0.015

Volume (m3) 0.000194 0.000194 0.0003 0.000225

Mass (kg) 0.522 0.522 0.810 0.610

Total Theoretical Mass of Frame – 2.464kg

 

 

 

20  

 

4.4  Initial  Ideas    The initial design process started out with some rough sketches of ideas.

These sketches were dimensionless but showed the basic functionality of

each part.

4.4.1  Fixed  Figure 16 shows a basic method of

how a fixed boundary condition can be

attained. The block is cut in half and

slot is milled out in each half to hold

the test piece. The block is screwed

together. The test piece is clamped in

a block, which prevents it from

pivoting thus creating a fixed boundary

condition. One of the problems with

this design was that the holes that

were required to fix the block to the frame will have to be off-centre so

manufacturing would be complex. Figure 17 shows another alternative to

fixing the test piece. Instead of cutting the block in half and milling a slot in

both halves, a slot is simply milled

into the block near the edge.

However after some research on

tool sizes it was discovered that a

small enough diameter tool was

not available to mill out a slot that

wide, particularly through the whole

block.

So another variation of this design

was developed which also involved

clamping of the test piece.

Figure  16  –  Fixed  Concept  1

Figure  17  –  Fixed  Concept  2  

 

 

 

21  

 

As can be seen in

Figure 18 this is done

by milling out a slot in

the side of the block

and then clamping it

with a plate. The block

is securely attached to

the frame. This design

is relatively easy to

manufacture.

4.4.2  Pinned  Figure 19 displays a simple way of

recreating a pinned boundary

condition experimentally. A

triangular dip is made on the top

surface of the block. This can be

done by approaching the surface

of the block at a 45° angle with a

milling machine and milling into it.

The test piece can rest inside the

dip and pivot about the point

where it rests. The test piece will

be under compression so it will not slip out of the dip. The manufacture of this

design requires very proficient use of workshop equipment. While the test

piece will remain in the groove during operation of the rig it can easily fall out

when the rig is being transported.

Figure  18  –  Fixed  Concept  3

Figure  19  –  Pinned  Concept  1  

 

 

 

22  

 

To ensure the test piece remains fixed during transportation another method

was developed. This method can be seen in Figures 20,21&22.

Figure 20 shows a pinned

boundary. This method uses a

door hinge type mechanism

where the test piece pivots

around the pin, which is

stationary inside the block thus

creating a pinned boundary

condition. This is done by fitting

a bracket to the end of the test piece

(Figure 21), which has a hole in it for the

pin to fit through.

An alternative method for attaching the

test piece to the block can be seen in

Figure 22. This involves bending the end

of the test piece so a pin can fit through it

and be able to pivot. However because

the preferred

material for the test

piece is spring steel this would be difficult.

The only way that this could be achieved is by using

untreated spring steel and then heat-treating it once the

shaping procedure has been carried out. Fulfillment of

this idea was likely to be very time consuming.

 

4.4.3  Frame  

Figure  20  –  Pinned  Concept  2  

Figure  21  –  Pinned  Concept  2.1  

Figure  22  –  Pinned  Concept  2.2  

 

 

 

23  

 

Figure 23 shows a simplified idea

for a frame. The frame will hold

together all the components, which

will be fixed to it. The blocks are

fixed at the bottom and the top

beam will support the loading

plates as well as the mass that will

be applied to them. This means

that the top beam will need to be

thick enough to prevent any

deflection. To increase the frame

stability stands are added to it. An FEA simulation was carried out to

determine if the top beam was thick enough to support the mass of the

weights that were going to be applied to the rig. The result is shown in Figure

24 below. The thickness of the top beam was taken to be 0.02m. It can be

seen that when a load of 100N is applied evenly over the beam it deflects.

The simulation shows that the maximum deflection that occurs is 0.0228mm.

This ensures that the top beam is thick enough as the load is not going to be

as high as 100N at any point of the rigs operation.

 

4.4.4  Top  fixed    

Figure  23  –  Frame  Concept  

Figure  24  –  FEA  of  Top  Frame  Beam

 

 

 

24  

 

This section will talk about various methods that a

fixed boundary condition can be realised. It was

somewhat harder to recreate boundary condition for

the top of the test piece than the bottom since it

moves up and down. The idea was to use a round

bar as the starting point for the holder. This meant

that a hole can be drilled in the top part of the frame

and the holder can fit through it.

Figure 25 shows one of the initial ideas that was

originated. The holder uses a round bar and the end

is machined into a semi-circular shape. A hole is

drilled in the test piece and is then screwed to the

holder. This prevents the test piece pivoting and

therefore acts as a fixed joint.

Next idea (Figure 27) uses a similar concept

except the holder consists of two diameters. The

slot is milled into the larger diameter, which

provides side support

for the test piece. The

test piece is also bolted

to the holder, which

prevents pivoting. This

meant that it could be

easily manufactured

because there are only

a few basic turning and

milling operations that

needed to be carried

out.

Figure  25  –  Top  Fixed  Concept  1  

Figure  26  –  Top  Fixed  Concept  2  

 

Figure  27  

 

 

!

 

 

 

25  

 

Possible problems that can occur with these

designs is that the test piece is not completely

fixed when it is bolted down. As the test piece is

loaded it might move away from the holder. This

is shown exaggerated in Figure 26. It will result

in the joint becoming a mixture of fixed and

pinned. To prevent this from happening the

whole area of the test piece inside the holder

would have to be pressed down. Figure 28

demonstrates the method that will permit this. It

consisits of two parts and both have a semi-

circular shape. A slot is milled out in each part to

house the test piece and two parts are bolted

together pressing on the test piece, similar to a vice.

4.4.5  Top  pinned   Similar to the previous section this will discuss the

various ideas for realising a pinned boundary condition

at the top of the strut. Figure 29 shows an idea similar

to the one for the bottom pinned holder. It involves

milling a slot in the same way by approaching the

surface at a 45° angle. This however is not as effective

because the holder will

have to constantly apply

pressure to the test piece

to prevent it from

dropping out.

Figure  28  –  Top  Fixed  Concept  3

Figure  30  –  Top  Pinned  Concept  2  

Figure  29  –  Top  Pinned  Concept  1  

 

 

 

26  

 

Consequently another method had to be developed. Next idea (Figure 30)

was developed from a door hinge. It involves a circular bar similar to that from

previous ideas. The end of the bar is machined into a hinge. The circular end

fits through the frame and the other end attaches to a test piece. The hole in

the hinged piece allows for a nut and bolt to be used to secure the test piece.

This design would work very well but could be difficult and excessively time

consuming to manufacture. Another idea involved a similar method of using a

hinge, but in a much simpler way from a

manufacturing point of view.

This idea is seen in Figure 31 and it involves milling

out a slot in the wider end of the holder with a hole

drilled straight through. An attachment is fixed to

the test piece and a pin is then inserted through

which allows the test piece to pivot. This design will

be easy to manufacture as it involves a few basic

operations on the lathe and milling machine.

 

4.4.6  Short  strut  pinned  The shorter strut had to have an extended top holder. Because of the

increased length of the holder some lateral support had to be provided to

prevent it from tilting, which can result in jamming. As can be seen in Figures

32&33 a bracket is fixed to the frame, which

provides support for the test piece holder.

One part of

the bracket is

secured to the

frame and the

other has a

hole through

which the

holder fits. This

Figure  31  –  Top  Pinned  Concept  3  

Figure  32  –  Short  Strut  Concept  1  

Figure  33  –  Short  Strut  Concept  1    

 

 

 

27  

 

provides two axially aligned points that support the holder forcing it to move

strictly in the vertical direction.

This is an excellent idea however if during the manufacturing process the

bracket is misaligned with the top hole, the

holder will jam and the rig will not function

properly. For this reason another idea was

produced, which can be seen in Figure 34.

This idea follows the same principle of

providing support for the holder but does it in

a slightly different way. The original hole in

the frame is made bigger and a bush is

inserted with the same internal diameter as

the diameter of the holder. This provides lateral support for the holder.

Concept 2 is simple to manufacture and does not require as much accuracy

as manufacturing a bracket.

Figure  34  –  Short  Strut  Concept  2    

 

 

 

28  

 

 

 

 

 

 

 

 

 

 

 

 

   

4.5  Rig  Design  Development Following evaluation of initial ideas, they then underwent a number of

revisions with added dimensions. The rig had to be self manufactured so

every part of the design had to be simplified to ensure that it was not too

complex to fabricate. This meant that every part had to be made using only

basic workshop machinery and in a realistic period of time.

The materials for the manufacture of the rig were provided by the university

workshop, so the available raw material dimensions had to be considered

when finalising the dimensions for the rig. This was to ensure that minimum

material wastage occurred and also to cut down the fabrication time, which

could increase if a lot of material had to be removed in order to end up with a

part.

Throughout the design process the simplicity of assembly was always

considered. All the parts had to be assembled with ease. The test pieces had

 

 

 

29  

 

to be easily replaced for whatever reason, such as yielding or changing the

material.

 

 

4.6  Final  Idea  CAD  Figure 35 shows the final rig assembly from two different angles. As can be

seen there are four test pieces each with a different boundary condition. The

masses are placed on the loading plates at the top. A detailed breakdown of

the components follows.

 

 

 

30  

 

 

Figure  35  –  Rendered  Rig  Assembly

4.6.1  Frame  The frame (Figure 36) had to support the mass that was going to be applied to

it and also house all the components, so it had to be rigid. The top part of the

frame was made thicker, 20mm compared to 15mm for the sides and the

bottom. This was in order to prevent noticeable deflection occurring. Another

way of achieving this would have been to place a support in the middle, hence

reducing the effective length of the top beam. But simply increasing the

thickness was enough to achieve this. The results acquired from FEA analysis

2  

3  

6  

5  

4  

8  

7  

1  

9  

 

 

 

31  

 

(Figure 24) showed that this thickness was enough to prevent the top beam

from deflecting under load. The frame was going to be assembled together by

bolting through the holes that can be seen in the image. The frame had all the

holes designed in precise positions so that all the components are aligned to

ensure accurate operation of the rig, for this reason the frame was designed

last.

 

Figure  36  –  Frame  Final  CAD

 

4.6.2  Loading  plates  The loading plates (Figure 37) were designed

to hold the mass that was going to be applied

to the test pieces. This had to be done so

that the weights did not fall off if the rig was

nudged. The plate was designed to be made

from one part and had a threaded rod at the

Figure  37  –  Loading  Plate  CAD  

 

 

 

32  

 

bottom of it so it can be attached to the test piece holders. Splitting the plate

and the holder into two parts was done in order to achieve easy assembly;

otherwise it would have been impossible to assemble it.

4.6.3  Short  test  piece  holder  As discussed in the initial design section the short test piece had to have extra

support in order to prevent it jamming inside the hole. There were two

alternatives for this application. One made use of the bracket, which attached

to the side of the frame and an alternative was a bush that had to be inserted

into the top beam of the frame.

The concept with the bush was

chosen (Figure 38). This was

done because the bracket

concept would have been

difficult to accomplish and

required use of different

manufacturing methods such

as welding, bending and drilling.

This simple concept shown only

required the use of a lathe.

This idea was chosen for its simplicity. The bush uses an aluminium rod with

an outside diameter of 14mm and a 10mm hole inside it. Which is press fitted

into the frame.

4.6.4  Stands  Evidently the rig had to stand by

itself on a flat surface and needed

to be stable. However due to the

mass limitation that was set, the

stands had to be low weight but

still provide a wide base. For this

Figure  38  –  Short  Test  Piece  Holder  CAD  

Figure  39  –  Stands  CAD

 

 

 

33  

 

reason a triangular stand was chosen and it was made from aluminium

(Figure 39).

It has a wide base and all the excess material is removed to reduce the mass

while still remaining rigid. The stands are made from 3mm thick aluminium

sheet and are manufactured using a milling machine. Alternatively this could

be done using CAM. The stands are attached to the frame using thee M3

screws.

4.6.5  Pinned  Bottom  Bracket  Initial design of the bracket considered the

use of aluminium. The final design (Figure

40) used mild steel as the material. This was

due to the fact that after discussions with

project supervisor it was decided that the

bracket would be under stress and aluminium

might not be suited for this. For safety and

durability of the part it was decided to use

mild steel. This design was chosen over

others because it was much easier to realise.

It allowed easy replacement of test pieces and didn’t require changing the

shape of the test piece in order to attach it to the bracket. Additionally it

provided a pinned condition and it could be easily fixed to the frame.

 

4.6.6  Corner  Bracket    The corner brackets (Figure 41) were made

from aluminium and were added to the

frame to increase its rigidity. They are fixed

to the corners where the horizontal and

vertical beams of the frame meet. The

brackets were made from 3mm thick

Figure  40  –  Pinned  Bottom  Bracket  CAD

 

 

 

34  

 

aluminium and attached to the frame using two M2 screws.

Theoretically the brackets do not weight much but significantly improve the

rigidity of the frame.

4.6.7  Top  fixed  holder  Figure 42 shows the top fixed holder. It uses

a steel rod of 20mm diameter on which the

top part is turned to 10mm.

The big end is milled to give a semi-circular

shape and the small part is manufactured

separately from a round bar. Two parts aren’t

exactly symmetrical and the removable side

has a slot milled in it. Because of this the

centre is slightly offset but this allowed the

test piece remain in line with the centre-line of

the holder. Initial idea of this design involved a slot being milled out in both

sides, but this was impractical because it was impossible to mill a rectangular

groove on the main part of the holder. That would have resulted in a circular

corner. The semi circular shape acts as a clamp, which locks the test piece.

This holder was made from mild steel since a lot of stress would be applied at

the point where the test piece is clamped. The top of the holder had a

threaded hole, which as discussed earlier allowed easy assembly for the

loading plate to be screwed in.

4.6.8  Bottom  fixed  holder  Similar to the pinned bottom bracket

this bracket (Figure 43) was made from

mild steel for the same reason. This

was chosen over other designs due to

its practicality. The holder consists of

two parts, the main block with a 10mm

wide slot milled out and a plate, which

Figure  41  –  Corner  Bracket  CAD

Figure  42  –  Top  Fixed  Holder  CAD

Figure  43  –  Bottom  Fixed  Holder  CAD

 

 

 

35  

 

is bolted to it using two M3 screws. The dimensions of the block are 30x20x15

mm, which are the same as pinned bracket block. This was to simplify the

design and allow faster manufacture since making a square bar the right

dimension and splitting it into four small blocks is more productive than

making them individually.

4.6.9  Top  pinned  bracket  The top bracket (Figure 44) has a 10mm slot milled out to accommodate the

test piece and the attachment that is

bolted to it. It is made from mild steel

and has a 2mm pin going through

around which the test piece pivots. At

the top it has a threaded hole in which

the loading plate is screwed. It was

designed to be turned from a round

bar of 20mm diameter. This was

selected over other ideas due to ease

of fabrication and simplicity.

 

 

   

4.6.10  Test-­‐piece  attachment  The part shown in Figure 45 attaches

to the test piece that will require a

pinned boundary condition. A slot was

milled out to accommodate the test

piece that was firmly secured by an M3

nut and bolt. And a 2mm hole for the

pin around which the test piece will

Figure  44  –  Top  Pinned  Bracket  CAD

Figure  45  -­‐  Test  Piece  Attachment  CAD

 

 

 

36  

 

pivot. This part is fabricated from mild steel to increase its durability.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

4.7  Engineering  Drawings  

 

 

 

37  

 

Because the design had to be manufactured engineering drawings of each

part were also produced from the CAD design. Figure 46 shows useful

dimension of the final rig design.

 

Figure  46  -­‐  Dimensioned  Assembly  Drawing

The remainder of the drawings can be viewed in Appendix 2.

 

 

 

 

 

 

38  

 

CHAPTER  5  

5  Manufacturing  Because the outcome of this project depended on the quality of manufacturing

the main equipment used for manufacture will be briefly covered in this

section.

5.1  Machinery  used  This section describes the machinery that was used throughout the

manufacturing process

5.1.1  Lathe  Machine  A lathe operates by rotating

the work piece about its axis.

The work piece is clamped

between self centering jaws

as can be seen in Figure 47

and is rotated at various

speeds depending of the work

piece dimensions. The tool is

moved in two horizontal axes

to remove the material about

the axis of rotation.

5.1.2  Milling  machine  The milling machine (Figure

48) operates by clamping the

work piece in the vice, which

is fixed to a table. This table

can be moved in x, y and z

axes. Milling machines are

typically used for planning,

Figure  47  –  Lathe  Machine  

Figure  48  –  Milling  Machine

 

 

 

39  

 

drilling and slot cutting.

5.1.3  Pillar  drill  A pillar drill (Figure 49) is a drill that is

mounted to a stand, which can be placed

on the floor or a workbench. The drill can

be moved up and down using a rack and

pinion. The work piece is placed on the

table that can be rotated vertically to allow

various geometries to be drilled.

5.1.4  Belt  Sander  Figure 50 shows a table based

belt sander. It involves a belt

consisting of abrasive material

and a hard grinding disk that are

powered simultaneously by an

electric motor.

Belt sanders are used to carry

out finishing touches on a

component by removing any

sharp edges or getting the

component to required dimensions.

Figure  49  –Pillar  Drill  

Figure  50  –  Belt  Sander  

 

 

 

40  

 

Table 4 shows the equipment used during manufacturing of specific components.

Table  4  –  Machinery  Used  

M

illin

g M

achi

ne

Lath

e M

achi

ne

Pill

ar D

rill

Bel

t San

der

Ban

d S

aw

Frame O

O O

Loading Plates

O

Short Test Piece Holder

O

O

Stands O

O

Pinned Bottom Bracket O

O O

Corner Bracket O

O

Top Fixed Holder O O O O

Bottom Fixed Holder O

O

Top Pinned Bracket O O O O

Test Piece Attachment O

O O O

 

 

 

41  

 

CHAPTER  6  

6  Assembly  This section will briefly describe the assembly process of the rig.

6.1  Exploded  View  Figure 51 below shows the exploded view of the rig before its assembly.

Figure  51  -­‐  Rig  Exploded  View  

 

 

   

 

 

 

42  

 

6.2  Step  by  Step  Assembly  In this section the

assembly process of the rig

will be briefly illustrated.

The assembly of the rig

must begin with the frame

(Figure 52). The frame will

house all the components

hence it is the first thing

that must be assembled.

Care must be taken while

assembling the frame

because it is very easy to

get the left and right side

beams mixed up. Three

holes on the on the side

beams have to be at the

bottom and facing outwards.

This is so the stands

(Figure 53) can be attached

to the frame.

While assembling the rig

attention must be paid to

the force that is used to

tighten the screws.

Because the frame is

made from aluminium it is

very easy to shred the

threads. As soon as

resistance is felt the

tightening can be stopped.

Figure  52  -­‐  Frame  Assembly  

Figure  53  -­‐  Stand  Assembly  

Figure  54  -­‐  Bracket  Assembly  

 

 

 

43  

 

Next step is to attach the bottom brackets to the frame (Figure 54). There is

no preferred orientation

to how this is done

because the brackets are

symmetrical. The main

thing to pay attention to

while attaching brackets

to the frame is the order

in which they go in. If the

frame is viewed from the

front, the order in which the

brackets attach in is fixed,

fixed, pinned, and pinned.

This will ensure that upon

completion the boundary

conditions turn out as

planned.

Once the bottom brackets

are in place the test piece

can be attached to holders

and attached to the frame.

Figure 55 shows how the

holders are inserted into

the frame. This is done

by deflecting the test

piece to the side while

inserting the holder into

the top part of the frame

(Figure 56). Lubricant

must be applied to the

holder prior to assembly.

Figure  55  -­‐  Test  Piece  Insertion  

Figure  57  -­‐  Test  Piece  Insertion  3  

Figure  56  -­‐  Test  Piece  Insertion  2  

 

 

 

44  

 

This will ensure smooth movement and reduce friction of the holder. Next step

is to insert the bottom of the test piece into the bottom holder. This can be

done in two ways. One way is to rest it inside the slot and screw the plate to it

or another way is to semi assemble the block and fit the test piece inside. This

can be seen in Figure 57. After that the screws are tightened to fix the test

piece in place. The process is repeated for other test pieces and the only

difference being that instead of the test piece being clamped a pin is inserted.

Figure 58 shows the pin

being inserted through

the block and the test

piece. Once all the test

pieces are in place the

mass holders are

attached to the top.

The rig took in the region of 5 minutes to assemble and only required two

Allen keys and a screwdriver. The attachment of components was very good

and no problems were encountered during assembly.

Figure  58  -­‐  Pin  Insertion  

 

 

 

45  

 

CHAPTER  7  

7  Results  and  observations  This section will discuss the prototype and the final model and their

corresponding testing results

7.1  Prototype  The prototype was made four weeks after the drawings were completed. This

closely conformed to the time plan that was created at the beginning of the

project. A few design

modifications were made

during the manufacturing

process. Figure 59 shows

the finished prototype. It

tested whether the design

works, how each

boundary condition

affected the shape of the

test piece. The prototype

was made with test

pieces from different

material, mild steel. There

was a limited supply of

spring steel strips so if anything needed to be redesigned, not enough

material would be available for the fabrication of additional test pieces. These

mild steel test pieces could have been heat treated to provide a closer

behavior to the spring steel however that was not necessary because these

test pieces were scrapped. The mild steel test pieces were a different

dimension to the test pieces that were going to be used in the final model. For

this reason it was meaningless testing how much force it took to buckle them.

The sole purpose of the prototype was to test correct function of all the

components. Because the material used was mild steel, it can be seen that

Figure  59  –  Prototype  

 

 

 

46  

 

the some of the test pieces have yielded. This is because the rig was

designed for the spring steel members in mind.

As can be seen in Figure 60,

there are no loading plates

attached to the test piece

holders. As stated earlier,

they were not required at

this point.

Throughout the

manufacturing process one

the parts that underwent

modification was the small

steel component that

attached to the pinned test

pieces (Figure 61).

Figure 62 shows the part that was discussed in the

paragraph above. As can be seen it is slightly

different from the final design (Figure 45). During

the manufacturing process some of the tools

required to make this were not available, therefore

the design was revised in the workshop and was

Figure  61  –  Prototype  Close-­‐up

Figure  60  –  Prototype  Top

Figure  62  –  Test  Piece  Attachment  

 

 

 

47  

 

decided that instead of milling a thin slot in the test piece it was easier to take

one side off and simply bolt the test piece to it (Figure 63). This also ensured

quick manufacture as the main profile was milled out in steel plate and then it

was split into five parts.

Figure 64 shows the comparison of the

spring steel test piece (left) and the

mild steel test piece (right). As can be

seen the spring steel test piece is half

the thickness of the mild steel test

piece. For this reason no extensive

testing was done on the prototype of

the rig

 

Figure  63  –  Attachment  Redesign  

 

 

Figure  64  –  Test  Piece  Comparisons

 

 

 

48  

 

 

7.2  Prototype  Testing  

As can be seen the experimental buckling modes corresponded to the

theoretical modes. Also at this stage the force that took to buckle each strut

was roughly tested. The fixed-fixed took the most force, followed by fixed-

pinned, short pinned-pinned and pinned-pinned.

There were a few modifications that were made to the prototype in order to

make it work properly. The top fixed-fixed support jammed inside the frame,

which provided inaccurate representation of the load that can be applied. The

holes drilled at the top of the frame were not very smooth, so a bush was

designed to be inserted which extended beyond the frame to provide more

lateral support in the same way as it is was for the short test piece.

Figure  67  -­‐Pinned/Pinned  

Figure  68  –  Short  Pinned/Pinned  

Figure  66  –  Fixed/Pinned  

Figure  65  –  Fixed/Fixed  

 

 

 

49  

 

7.3  Final  model  After some basic tests on the prototype were carried out some additions and

changes were made to the design.

One of the main problems with the prototype was that when force was applied

to the strut it would jam and not return to its initial position. So a bush (Figure

69) was designed to solve this problem. The initial hole was bored out from a

10mm to a 14mm diameter and the

bush was pressed inside from the top.

The bush played two roles. It

prevented the strut from buckling too

much by limiting the downward

movement of the mass and also

provided more lateral support for the

weight plate. This prevented the

weight plate tilting and jamming

inside the hole.

Another modification that

was added was an

extended bolt that

prevents the loading

masses from slipping off

as they are being loaded

on. It can be seen in

(Figure 70) how the bush

protrudes from the top

beam.

Figure  70  -­‐  Modified  Mass  Holder  CAD

Figure  69  –  Limiting  Bush

 

 

 

50  

 

By protruding it provides

more support and limits

the amount by which the

mass holder travels.

Figure 71&72 show the

final manufactured bushes

and weight plates.

 

 

 

   

Figure  71  -­‐  Manufactured  bush

Figure  72  –  Manufactured  Weight  Plates  

 

 

 

51  

 

 

7.4  Final  Model  Testing  After the final model was completed, testing was carried out to determine

whether the rig operated correctly and accurately. The objective of the testing

was to compare the practical results of loading the test pieces with the

theoretical results that were calculated before the design stage. Also the total

mass of the rig was measured, as one of the main required objectives was

that the rig does not exceed 5kg.

The rigs mass was measured. This was

done by simply placing the rig on scales

and recording the mass.

As can be seen in Figure 74 the total mass of the rig is 3.3kg not including the

loading masses.

Next to determine the experimental critical load the testing procedure was as

follows:

1. Gradually apply load to the strut in small increments. Increments

depend on the end condition of the strut.

2. Record the force at which the strut buckled

3. Repeat 1&2 until ten sets of readings were acquired

Figure  73  –  Rig  on  Scales Figure  74  –  Scales  Readout

 

 

 

52  

 

7.5  Test  Results

Table  5-­‐  Testing  Results  

Test Number Fixed-Fixed (kg)

Fixed-Pinned (kg)

Pinned-Pinned (kg)

Short Pinned-Pinned (kg)

1 0.80 0.40 0.20 0.27

2 0.85 0.45 0.21 0.26

3 0.80 0.45 0.19 0.28

4 0.75 0.45 0.20 0.28

5 0.78 0.45 0.20 0.27

6 0.76 0.40 0.20 0.30

7 0.83 0.40 0.19 0.28

8 0.8 0.39 0.19 0.28

9 0.8 0.39 0.19 0.28

10 0.8 0.39 0.19 0.28

Average 0.797 0.417 0.196 0.278

Std Deviation 0.029 0.029 0.007 0.010

Theoretical 0.88 0.45 0.22 0.39

Figure 75 shows the masses

under which each strut buckles

and the buckling modes for

each boundary condition.

Figure  75  –  Demonstration  of  Buckling  Shapes

 

 

 

53  

 

The results were then edited to

include the mass of the test

piece holders because the

holders contribute to the force

that is needed to buckle the

strut. As can be seen in Figure

76 the mass of the holder for

the short pinned-pinned strut is

111.5g. This means that the

actual average mass applied to

the strut on is

0.278+ 0.112 = 0.39!"

Same applies for the struts with

other boundary conditions. As can

be seen in Figure 77 the other test

piece holder’s weight was around

49g. And the mass of the top fixed

holder was around 70g.

Table 6 shows the average

experimental mass with the mass

of the test piece holders included being compared to theoretical mass.

Table  6  –  Results  including  test  piece  holder  mass  

Fixed-Fixed

(kg)

Fixed-

Pinned (kg)

Pinned-

Pinned (kg)

Short Pinned-

Pinned (kg)

Experimental 0.867 0.466 0.245 0.39

Theoretical 0.88 0.45 0.22 0.39

Figure  77  –  Pinned  Test  Piece  Holder  Mass

Figure  76  –  Short  Test  Piece  Holder  Mass  

 

 

 

54  

 

Figure  78  –  Chart  Comparing  Experimental  and  Theoretical  Results  

 

 

 

 

   

 

 

Fixed-­‐Fixed   Fixed-­‐Pinned   Pinned-­‐Pinned  

Short  Pinned-­‐Pinned  

Experimental   0,867   0,466   0,245   0,39  Theoretical   0,88   0,45   0,22   0,39  

0  0,1  0,2  0,3  0,4  0,5  0,6  0,7  0,8  0,9  1  

Load  

(kg)  

Chart  Comparing  Experimental  and  Theoretical  Results  

 

 

 

55  

 

CHAPTER  8  

8  Discussion      

8.1  Buckling  Forces  As can be seen from the results obtained in testing, the actual buckling forces

for each strut were within 0.03kg of the theoretical values that were calculated.

This part of the discussion referred to Figure 78

Fixed-­‐Fixed  Strut  The experimental value for the fixed-fixed test piece was 0.867kg, which was

slightly lower than the theoretical value of 0.88kg. This was not unusual

because the results predicted by buckling theories are slightly higher than the

actual. Euler theory predicts that the strut is perfectly straight when unloaded.

The struts used in the rig are constantly under load due to the holder’s mass

acting down on them, this means that the struts already have some initial

deflection prior to loading. The load on the struts could have deviated from the

centroid of the cross-section, which negates another calculation assumption

that the load is applied directly through the centroid of the cross-section.

There is also a possibility that the materials properties aren’t constant

throughout the test piece. Some or all of these factors could have been the

cause of the lower experimental buckling force.

Fixed-­‐Pinned  Strut  The actual value for the fixed-pinned test piece was 0.466kg, which is greater

than the predicted value of 0.45kg. The reasons for this could be that there

was a frictional force due to the top holders sliding inside the bushes. This

caused an increase in the force that was needed to buckle the strut because

that frictional force had to be overcome. This greater frictional force was due

to manufacturing imperfections, which were mainly caused by the operator. In

this case the when holder was inserted inside the bush and moved some

resistance could be felt, this resistance was higher than that of the fixed-fixed

holder. Another possible reason for the greater actual load could be due to the

 

 

 

56  

 

test piece length and cross-sectional dimension variation. The test piece

attachment that was used to allow the test piece to be pinned adds height to

the cross-sectional area of the test piece. The length of the actual test piece

not including the attachment is 385mm compared to the length of 400mm

used in the calculations. It is known from the buckling theory that increasing

cross-sectional area increases the area moment of inertia, which increases

the buckling force that is required to buckle the strut. And decreasing the

length furthermore increases the maximum buckling force that the test piece

can be subjected to. Each one of these could have contributed to the higher

experimental buckling load.

Pinned-­‐Pinned  Strut  The experimental buckling load obtained from testing of the pinned-pinned

strut was 0.245kg. This was also higher than the predicted value of 0.22kg,

mainly for the same reasons as those discussed for the fixed-pinned strut.

This was due to friction and different strut length. The pinned-pinned strut

however has two test piece attachments because both the ends are pinned.

For this reason the actual length of the test piece is 370mm.

Short  Pinned-­‐Pinned  Strut  For the short pinned-pinned strut the actual buckling force equals the

predicted force. For this case it was believed that the change in the strut

length directly balances out the errors due to the assumptions made. The

actual length of the strut was 270mm compared to 300mm that was used for

the theoretical calculation. Because the holder moved really smoothly it can

be said that it had very low frictional force, similar to that of the fixed-fixed

holder. The loading could have been eccentric and the strut could have been

initially deflected prior to mass loading. This brings the actual buckling force

below the theoretical. The decrease in the actual length of the strut will bring

the value of the buckling force up therefore balancing out and making the

actual buckling force equal to the theoretical.

   

 

 

 

57  

 

 

8.2  Rig  Mass  It can be seen from the test results that the mass of the rig was 3.3kg. This

differed from the initial predictions of the mass because for the calculations

only the mass of the frame was considered and they were done as a rough

guideline to what the mass would be. The predicted mass of the frame was

2.464kg. The design objective stated that the rig needed to be less than 5kg.

8.3  Problems  Throughout the manufacturing process some complications were encountered

which changed the final outcome of the design.

The test pieces that were initially chosen were not available to purchase at the

necessary time as they were out of stock. So as an alternative, the strips of

steel that are used to wrap wooden parcel crates were used as the test pieces.

They had the same dimensions as the researched test pieces. However one

of the problems was that the test pieces were not perfectly straight so they

had to be hammered into shape. This could have changed the mechanical

properties of the material, which in turn could have affected the test results

that were obtained.

The fabrication of the pinned top holder (Fig 44, page 34) proved to be very

challenging. After the slot has been milled a hole had to be drilled

perpendicular to the slot in order for the pin to go through. This proved

problematic, as there were no exact ways of making sure that the hole was

going to be perpendicular to the slot. The solution to that was to use a spirit

level to ensure the slot is in horizontal orientation and drill the hole vertically

downwards, however the accuracy of that method depended on the skills of

the operator. The affect that a non-perpendicular hole had on the strut

behavior is that it caused rotation, which interfered with the desired results.

Similar problems were encountered while manufacturing the test piece

attachments for the pinned joint (Fig 45, page 35). Because the attachments

were cut on a band saw meant the edges were not exactly perpendicular to

 

 

 

58  

 

the hole for the pin. Also some material had to be left spare to allow room for

the width of the blade, so this had to be removed. The method for removing

material used a belt sander. This provided efficient removal but it was not the

most accurate and because of this the attachment shapes were not consistent

and the edges were not always perpendicular to the hole.

8.4  Design  Evaluation  The test pieces used in the design all had a slenderness ratio greater than

one thousand. That made it safe to assume that the rig represented both

Euler and Rankine-Gordon buckling theories.

Time  The manufacture of the design was very time-consuming, taking between

120-130 hours to complete the final product. This time could have been

greatly reduced if the experience level was greater at the planning and design

stage of the project. Due to the lack of experience in manufacturing and

equipment operation some parts designed were impossible to fabricate with

the available equipment. By solely designing each component to allow it to be

easily manufactured, time spent in the workshop could have been reduced

considerably.

Material  The choice of material for the rig was successful; the aluminium frame was

very durable but still light enough to be under specified weight. Spring steel

that was used as the test piece material did not yield and provided a good

representation of buckling. The remainder of components that were

manufactured from mild steel could have been redesigned using a different

material to make them lighter. This mainly applies to the top test piece holders

as they had significant masses that provided constant loads on the test pieces.

Safety  Operation of the rig necessitated in precautions to be taken. Even though

overall it was safe to operate care had to be taken to ensure the top loading

plates were secured firmly, to prevent the masses falling off and causing

injury to digits and toes. It was advised to wear hard footwear for protection.

 

 

 

59  

 

The rig was designed so that the test pieces remained within the elastic limit,

the bushes (Fig 69, page 48) aided this by limiting the amount by which the

struts deflect. Every boundary condition was demonstrated except the fixed-

free condition, this was left out because this would have made the rig wider

and heavier in order to accommodate five struts instead of four. Because the

fixed-free buckling shape is the simplest to understand it was replaced with a

short pinned-pinned strut. One of the desired objectives was to include the

demonstration of different length bars so the pinned-pinned condition was

used to demonstrate the effect that length has on the buckling force.

Another desired objective was to measure the lateral displacement of the

struts. This feature however was left out from the final design, as it would

have provided no advantageous feedback.

 

   

 

 

 

 

60  

 

CHAPTER  9  

9  Conclusions  The design fulfilled all the required objectives set by the project supervisor.

The rig successfully demonstrated the fundamentals of buckling since each

boundary condition was represented effectively and showed the

corresponding buckling shapes.

The buckling loads for the fixed-fixed and fixed-pinned struts were within 1.5%

and 3.4% of the theoretical values respectively. The error for the pinned-

pinned buckling load was 10% of the theoretical; this was due to the fact load

applied was small, so even small deviations from the theoretical values gave

high percentage errors. The short pinned-pinned strut gave the buckling load

value that was exactly the same as the predicted buckling load. While the

practical results obtained were averaged from ten sets of readings, it can be

seen how greatly they fluctuated. The buckling load greatly depended on the

way that the operator loaded the strut.

The errors were caused due to defects in the design that were created during

the manufacturing process. These errors could have been greatly reduced if

the rig was made to a greater accuracy.

The main objective that was set stated that the rig could not exceed 5kg. The

final model weighed 3.3kg and even if the loading masses (1kg3) that were

required for demonstration were considered the total mass was still less than

5kg. When this was compared to the products that are currently on the market

it was seen that produced rig was 50% lighter than competing product.

In conclusion a mechanically powered rig was designed and manufactured

that was under 5kg, represented Euler buckling, demonstrated the effect of

                                                                                                                         

3  (500g)  x  1,  (200g)  x  1,  (100g)  x  2,  (50g)  x  2  

 

 

 

61  

 

different boundary conditions on the buckling load and allowed different length

bars to be subjected to testing.

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

62  

 

CHAPTER  10  

10  Further  work    

10.1  Further  Developments  and  Improvements    

After the design was finished a few ideas have come up that could have

improved the final outcome. So the following are some ideas that could be

incorporated in the design if it is to be manufactured again.

White backing can be added to provide a clear view of the struts behavior

while buckling. A grid can also be added to the backing in order to show how

boundary conditions affect at which point the strut deflects laterally.

Different test piece materials can be selected for demonstration purposes.

The materials that were covered in the research section such as brass,

aluminium and acrylic can be used to display their behavior under

compression. However the strut dimensions would have to be kept the same

in order to show how changing the material affects the value for critical force.

The mass of the rig can be reduced to around 2.5kg and still maintain the

rigidity of the current design. Reducing the dimensions of the frame as can be

seen in Figures 79&80 below can do this. Cutting down the dimensions would

mean that one screw would

have to be used to attach the

beams to each other.

However the bracket at the

back of the frame would

provide the extra support

required.

Figure  80  –  Proposed  Redesign  

Figure  79  –  Original  Frame  

 

 

 

63  

 

Additional improvement that can be made is to reduce the mass of the top test

piece holders by making them out of a combination of materials. Stronger

material can be used where more stress is present and lighter material where

minimal stress is present. So a top pinned holder would

be made of a combination of steel and aluminium. As

shown the Figure 81 the highlighted part should be

made from steel and the smaller diameter to be made

from aluminium to reduce its mass. In addition this will

reduce the initial load on the struts.

To take the demonstration of buckling principles further,

various additions can be

incorporated into the rig such as

adding a torsion element to the compression. This can be

integrated by milling a slot across the surface of the

holder as shown in Figure 82 by a red line. Then a grub

screw can be screwed in to fit in the slot. As the holder

moves downwards the slot will force the holder to rotate

due to the grub screw sitting in it. This will add torsion to

the strut being compressed.

10.2  Costs  If the rig was to be manufactured again the cost of materials for one rig are

shown in Table 7 below. All prices quoted from MetalsDepot [23]. Table  7  –  Material  Costs  

Material Cost Estimate

Aluminium Bar – 30x20mm £4

Steel Square Bar – 30x30mm £0.3

Steel Round Bar – 20mm £0.5

Aluminium Plate – 3mm £6

Spring Steel (Test Pieces) £6

Total Cost £16.8

Figure  81  –  Original  Holder  

Figure  82  –  Proposed  Redesign  

 

 

 

64  

 

A sample business plan has been written to show the possibilities if this

design is introduced into the market. The business plan can be accessed from

the CD supplied with the report. The file is titled ‘Compact Jig for Buckling of

Struts Business Plan’.

10.3  Distribution  If the rig is going to be distributed to other universities in order to assist with

lecturing then an instruction manual will have to be written to outline the

assembly procedure and operation instructions. A brief operation instruction is

outlined below:

The rig will be supplied with custom made masses that range from 500g to

50g. (500g x 1, 200g x 1, 100g x 2, 50g x 2)

Fixed – Fixed

1. Place 500g mass on

the weight plate

2. Carefully add 200g

on top, some

movement of the

strut should be seen

3. Place 100g mass on

top and the strut

should give way and

buckle. If it does not

then follow step 4

4. Place a further 50g

on top.

 

 

 

65  

 

Fixed – Pinned

1. Place 200g mass on the weight plate

2. Add 100g mass on top, some deflection of the strut should be observed

3. Add a further 100g mass on top and the strut should buckle, if it does

not then follow step 4

4. Place 50g on top

Pinned – Pinned

1. Place 100g mass on the weight plate

2. Add another 100g and the strut should buckle, however if it does not,

follow step 3

3. Place a further 50g on top

Short Pinned – Pinned

1. Place 200g mass on the weight pate

2. Place a further 100g on the weight plate, the strut should buckle. If

buckling does not occur then follow step 3

3. Place 50g on top

The drawings and dimensions for the masses can be viewed in Appendix 2.

 

 

 

66  

 

References  

1. Hibbeler R. C. Mechanics of Materials. Third Edition. New Jersey:

Prentice Hall; 1997. p. 654-656

2. Logan D. L. Mechanics of Materials. New York: Harper Collins; 1991. p.

563-565

3. Roy A. Buckling: Bars in Compression [Lecture Notes]. Loughborough:

Loughborough University. [Accessed November 2010]

4. Hibbeler R. C. Mechanics of Materials. Third Edition. New Jersey:

Prentice Hall; 1997. p. 659

5. Logan D. L. Mechanics of Materials. New York: Harper Collins; 1991. p.

573

6. Hearn E. J. Mechanics of Materials 2. Third Edition. Oxford:

Butterworth-Heinemann; 1997. p.28

7. GUNT Hamburg. Company Website:

http://www.gunt.de/static/s3246_1.php?p1=&p2=&pN=#. [Accessed

April 2011]

8. GUNT Hamburg. Company Website:

http://www.gunt.de/static/s3248_1.php?p1=&p2=&pN=;;#. [Accessed

April 2011]

9. Engineering Toolbox Database. Website:

http://www.engineeringtoolbox.com/young-modulus-d_417.html .

[Accessed April 2011]

10. Image: Globo Supply. Website:

http://globosupply.com/index.php?main_page=index&cPath=50_150 .

[Accessed April 2011]

11. Image: http://www.signsbynature.co.uk/images/acrylic-sheet-.jpg .

[Accessed May 2011]

12. Matbase. Material Database. Website:

http://www.matbase.com/material/ferrous-metals/spring-

steel/55si7/properties. [Accessed April 2011]

 

 

 

67  

 

13. Image: http://www.tsmods.com/images/spring_steel.jpg . [Accessed

May 2011]

14. Image: Quick Ship Metals;

http://www.quickshipmetals.com/brass/Brass-sheet.jpg. [Accessed May

2011]

15. Image: http://product-image.esuppliersindia.com/00269746/b/0/Genset-

Canopy-Door-Hinge.jpg. [Accessed May 2011]

16. Image: http://image.made-in-china.com/2f0j00mBdaMoRJlGue/Bench-

Vice-Vise-3-4-5-6-8-.jpg. [Accessed May 2011]

17. Engineering Toolbox Database. Website:

http://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html.

[Accessed April 2011]

18. Carbon Fiber Properties. Website: http://www.carbon-fiber-hood.net/cf-

information. [Accessed May 2011]

19. Image: http://www.philipharris.co.uk/primary/physical-processes/forces-

and-energy/slotted-masses-1kg/?ev=search . [Accessed April 2011]

20. Supplier. Website: http://springsteelstrip.co.uk/2009/11/04/spring-steel-

strip/. [Accessed March 2011]

21. Logan D. L. Mechanics of Materials. New York: Harper Collins; 1991.

[properties of plane areas]

22. Hibbeler R. C. Mechanics of Materials. Third Edition. New Jersey:

Prentice Hall; 1997. [geometric properties of area elements]

23. Supplier. Website: http://www.metalsdepot.com. [Accessed May 2011]

 

 

Individual Project Gannt Chart

Compact Jig for Buckling of Beams - Peter Hamilton

Start Date 4.10.2010

Week Number 1 2 3 4 5 6 7 8 9 10

11 Christmas

12

13

14

15 1 2 3 4 5 6 7 Easter 8 9

10

11

12

Week Starting 04.1

0.2

010

11.1

0.2

010

18.1

0.2

010

25.1

0.2

010

01.1

1.2

010

08.1

1.2

010

15.1

1.2

010

22.1

1.2

010

29.1

1.2

010

06.1

2.2

010

13.1

2.2

010

20.1

2.2

010

27.1

2.2

010

03.0

1.2

011

10.0

1.2

011

17.0

1.2

011

24.0

1.2

011

31.0

1.2

011

07.0

2.2

011

14.0

2.2

011

21.0

2.2

011

28.0

2.2

011

07.0

3.2

011

14.0

3.2

011

21.0

3.2

011

28.0

3.2

011

04.0

4.2

011

11.0

4.2

011

18.0

4.2

011

25.0

4.2

011

02.0

5.2

011

09.0

5.2

011

16.0

5.2

011

23.0

5.2

011

30.0

5.2

011

Hand in Objectives Form

Literature Review

Products Review

Workshop Meeting

Generating Initial Design Ideas

Interim Report

Evaluation of Ideas

Interim Presentation

Design Development

Design Documentation

Manufacturing

Testing

Report Writing

Viva voce/Poster

Work Plan

Deadline