Understanding Structural Concepts

Structural Concepts 2010│Page 1

Understanding Structural Concepts

Understanding, Developing, Learning… Structural Concepts 2010│Page 2


Preface This booklet is a collection of students’ coursework on, “Understanding structural concepts”, which is part of the module of Research Methods in 2011-12 at The University of Manchester. The booklet forms a source of learning for the students themselves enabling them to learn from each other rather than from lecturers and textbooks. It is hoped that students learn effectively and actively and this, in part, requires appropriate activities and/or stimulators being provided. Students were asked to study, Seeing and Touching Structural Concepts, at the website, www.structuralconcepts.org, where structural concepts are demonstrated by physical models and their applications are shown by practical examples. It was hoped that students could not only quickly revise a number of concepts they studied previously but could also gain an improved understanding of the structural concepts. Enhancing the understanding of structural concepts was introduced to the module in 2006 when the website was available internally and students were asked to do a piece of related individual coursework. After reading through the coursework, we felt that the individual submissions were interesting and varied and included some creative components. The coursework was revised and improved on the basis of the previous submissions in the years of 2007 and 2008. It was hoped that the revised coursework would encourage students to consider and explain structural concepts in a simple manner and to look for examples of structural concepts in everyday life motivating further study and the development of a greater understanding and awareness of structural concepts. All the submissions were made through Blackboard. They are slightly edited for the consistence of the format and compiled into one single PDF file. The booklet written by the students is ‘published’ through Blackboard so that they could learn from the work of each other and further improve their understanding of structural concepts. The booklet can be downloaded by the students and kept by them. The coursework return was very good. 60 submissions were received from a class of 60, including 39 model demonstrations and 21 examples. As the lecturer, I have enjoyed when reading through the coursework. There was no clear distinction between some of the models and examples provided and included in this booklet as some models can be treated as examples and vice versa. The titles in the contents page are directly copied from the coursework. The two covers of the booklet were voluntarily designed by Mr. Sencu Razvan and Mr. Parham Mohajerani, who are the students of the class. Mr. Qingwen Zhang, a PhD student, compiled all the submissions into one single word file and produced the contents page then compressed the huge file into a much smaller PDF file allowing downloading possible. We hope all students taking Research Methods will enjoy reading the presentation of their work in this booklet and will have learned from each other.

Tianjian Ji 9 November 2011




Contents Models...................................................................................................................... 9 1.1 Force Conversion ................................................................................................................ 10 1.2 Understanding The Concept Of Base Isolation .................................................................. 12 1.3 Neglecting Live Loads In Unfavourable Areas Causing Loss Of Equilibrium .................. 17 1.4 Shear Stress Concept And Its Application ......................................................................... 21 1.5 Increasing The Stiffness Creating Self-Balancing Structures ............................................ 24 1.6 Critical Load Of A Structure .............................................................................................. 27 1.7 Utilizing The Catenary Method To Determine The Rational Arch Axis Curve ................ 29 1.8 Static Equilibrium In Nail Clipper...................................................................................... 34 1.9 Cross Section Shape And The Parallel Axis Theorem. ...................................................... 36 1.10 The Concept Of Equilibrium And Centre Of Mass--Tumbler ......................................... 40 1.11 Improving Seismic Design ............................................................................................... 43 1.12 Force Increasing System ................................................................................................... 49 1.13 Proper Section To Improve Stiffness Of Structures ......................................................... 53 1.14 Arch Action In Egg Shells ................................................................................................ 55 1.15 Scaffolds-Widely Use Of Direct Force Path .................................................................... 57 1.16 Useful Structural Concept In Daily Life——Centre Of Mass ......................................... 59 1.17 The Concepts Of Prestress ................................................................................................ 62 1.18 Why The Bridges Are Designed To Be Convex?............................................................. 64 1.19 Principle Of Superposition ............................................................................................... 66 1.20 Why A Roly-Poly Toy Does Not Fall...???? .................................................................... 68 1.21 ―Cable Supported Structure‖Analysis .............................................................................. 70 1.22 Stress Distribution In Real Life ........................................................................................ 74 1.23 Using Global Buckling To Erect A Camping Tent .......................................................... 78 1.24 Bamboo Bionic Structure Application In The Buildings ................................................. 81 1.25 Post-Tensioned Concrete Concept.................................................................................... 84 1.26 Concept Of Vibration Reduction In A Structure Through Base Isolation ....................... 87

Understanding Structural Concepts 1.27 Element Of A Moment… The Lever Arm ....................................................................... 91 1.28 Easy Examples About The Equilibrium ........................................................................... 94 1.29 Bending Moment And Deflection .................................................................................... 96 1.30 Why A Roly-Poly Toy Can‘t Be Pushed Over ............................................................... 100 1.31 Critical Load Of A Structure .......................................................................................... 102 1.32 Understanding Structural Concepts ................................................................................ 104 1.33 The Physics Of Figure Skating ....................................................................................... 107 1.34 Jenga Block..................................................................................................................... 110 1.35 Demonstration Of Effect Of Water (Moisture) In Settlement Of Structures ................. 113 1.36 Relation Between Deflection And Length Of Rigid Nails Subjected To Concentrated Load At Free End. .................................................................................................................. 114 1.37 The Need Of The Worlds Biggest Structural Foundations............................................. 119 1.38 Applications Of Structural Concepts In Nature .............................................................. 121 1.39 Action Of Forces On Arches In Practical Way .............................................................. 123

Examples ............................................................................................................. 125 2.1 Equilibrium In Asymmetrical Cable-Stayed Bridge Alamillo Bridge And Sundial Bridge ................................................................................................................................................ 126 2.2 Tuned Mass Dampers ....................................................................................................... 128 2.3 Air-Formed Domes ........................................................................................................... 131 2.4 Improving The Understanding Of Structural Concepts .................................................... 134 2.5 Nature Frequency Of Structure With Position Of Mass ................................................... 136 2.6 The Centre Of Mass And Moment Of Inertia (Why Tightrope Walkers Carry Long Bent Poles) ...................................................................................................................................... 138 2.7 Mechanical Analysis Of Arch Bridge----Zhaozhou Bridge ............................................. 140 2.8 Tricks Of Man Sitting On Invisible Chair ........................................................................ 143 2.9 Load Conversion.............................................................................................................. 145 2.10 Overhangs : Reducing Bending Moments ...................................................................... 146 2.11 Stress Concentration In Daily Life ................................................................................. 149 2.12 Mechanical Analysis Of The Kitchen Knife .................................................................. 153 2.13 Centre Of Mass To Prevent Sway Of Tall Buildings ..................................................... 156 2.14 Birds Are Stable Even On One Foot .............................................................................. 158 2.15 The Concepts Of Equilibrium And Theapplication In Fish Tank .................................. 161 2.16 How The London Eye Works ......................................................................................... 164


2.17 Wire-Spoke Wheel ......................................................................................................... 167 2.18 Wind, Roof And A Aircraft ............................................................................................ 169 2.19 To Reduce Bending Moments ........................................................................................ 171 2.20 Tensegrity Structures ...................................................................................................... 173 2.21 The Effect Of Wind Loading On The Stability Of High Rise Twisted Structures ‗Infinity Tower‘ ...................................................................................................................... 175


Models


1.1 Force Conversion Bingqi Liu At present, the belts that people use everyday normally include two descriptions. It is easy to discover principle of one mechanism having holes and needle. And the another type of belt successfully utilizes the simple design of force conversion to stuck the leather and prevent the leather sliding out of belt buckle.

Belts With Holes

Belts Without Holes

The Mechanism of Buckle of Belt without Holes The core component of belt buckle is a steel cylinder，which can rotates around a steel bearing fixing on the buckle. A piece of rubber attaching on the steel cylinder would apply pressure and friction on the belt‘s leather when steel cylinder rotates towards clockwise direction. Inside of steel cylinder, a spring twining on the bearing makes the steel cylinder rotates clockwise naturally without any anticlockwise action exerted on it. (Details shows on the drawing below)

The Principle of Works Flipping the part highlighted by blue rectangle below can easily pull the belt owing to the release of pressure and friction. At this time, cylinder rotates anticlockwise.


When put off the switch, the rubber will touch the leather and exert pressure on the surface. Ultimately friction caused by pressure against and balances the force F. When the force F that attempts pull belt out of the belt buckle ascends, friction on the surface of leather and rubber will cause clockwise rotation of the cylinder, as a consequence, the pressure and the friction exerting on the leather increase contrary. This process can be demonstrated clearly with the formula below.

F is friction, P is pressure,

is friction factor.

is constant in this case. P increases with the

addition of F due to the reduction of the space between leather and rubber. At the time, rotation of the cylinder make rubber having more contact area with leather, which increase the friction between them as well.

Conclusion The design of this component balances the force F effectively and avoid belt sliding out of the belt buckle. And the idea of force conversion is used extensively to any system with pulley.


1.2 UNDERSTANDING THE CONCEPT OF BASE ISOLATION Mustafa EFILOGLU INTRODUCTION Base isolation is one of the most important concepts for earthquake engineering which can be defined as separating or decoupling the structure from its foundation. In other words, base isolation is a technique developed to prevent or minimise damage to buildings during an earthquake. In this essay, the concept of base isolation will be explained by giving some examples from other engineering and sport branches. These examples are automobile suspension systems and some defence techniques in boxing. Additionally, some experiments and analytic graphs will be demonstrated to provide better understanding of the concept of base isolation. USING THIS CONCEPT FOR EARTHQUAKE ENGINEERING “ BASE ISOLATION” It might be thought that structures can be protected from the destructive forces of earthquakes by increasing the strength of the structures so that they do not collapse during such events. In other words, more rigid attachment of a building to its foundation will result in less damage in an earthquake (the principle of strengthen to resist damage). However, if the foundation is rigidly attached to the building or any other structure, all of the earthquake forces will be transferred directly and without a change in frequency to the rest of the building. Providing a base isolation device between the building and the ground can minimize the level of earthquake force transmitted to the buildings.

Figure 1 (The effect of vibration to attached and non-attached jar) Figure 1 shows the effect of vibration to the attached and non-attached jars which are filled with coloured water. As can be seen from the Figure 1, since the green water is attached the ground, all the vibrations are transmitted to the jar directly and causes the water slosh up much higher than the non-attached one. This principle is exactly the same to the structures which have base isolation systems (non-attached jar) and the conventional ones (attached jar) (Figure 2)


Figure 2 As an earthquake shakes the soil laterally, the foundation moves with the soil and the seismic waves are transferred throughout the structure over time as the seismic wave travels up to the structure (Figure 2). ―If the earthquake has natural frequencies with high energy that match the natural frequencies of the building, it will cause the building to oscillate violently in harmony with the earthquake frequency. However, if the natural frequency of the building can be changed to a frequency that does not coincide with that of earthquakes, the building is less likely to fail‖. [1] This is exactly what a base isolator does. The base isolator reduces the stiffness of the structure and thereby lowers its natural frequency. In this condition, the building's superstructure will respond to the vibrations as a rigid unit instead of resonating with the vibrations. Simply put the building's foundation moves with the ground and the base isolator flexes to reduce the ground motion from affecting the superstructure‖ (superstructure is demonstrated in Figure 4).

Figure 3 Figure 3 illustrates how the base isolation system affects structures in a positive way. Base isolated structures are likely to have larger displacement, as they are separated from the ground.


In other words, base isolation lets buildings to move over the ground so that they have less frequency (Figure 3-A). Similarly, the graph B shows that non-isolated structures are subjected to much higher shear forces than the isolated ones which mean that structures are much more vulnerable to earthquake forces without a base isolation system.

Figure 4 As can be seen in Figure 4, a simple base isolation system consists of two basic components which are isolation bearings and damper. The former protects the superstructure from collapse because of lateral movements based on earthquake forces, whereas the latter absorbs or dissipates the energy that base obtains during an earthquake. APPLICATIONS OF THIS CONCEPT IN OTHER BRANCHES Automotive Suspension The isolators (damping and elastomeric bearings) work in a similar way to car suspension, which allows a car to travel over rough ground without the occupants of the car getting thrown around. In other words, a vehicle with no suspension system would transmit shocks from every bump and pothole in the road directly to the occupants. The suspension system has springs and dampers which modify the forces so the occupants feel very little of the motion as the wheels move over an uneven surface. As demonstrated in Figure 6, shock absorbers in automotives work exactly the same principle with the dampers in base isolation system.


Figure 6 (Car suspension system- shock absorber) Rolling with the punch A boxer can stand still and take the full force of a punch but a boxer with any sense will roll back so that the power of the punch is dissipated before it reaches its target (Figure 8). A structure without isolation is almost the same with the upright boxer (Figure 7), taking the full force of the earthquake; the isolated building rolls back to reduce the impact of the earthquake.

Figure 7

Figure 8


If the structures are designed the same principle of rolling back instead of increasing its strength and stiffness, earthquake forces will be dissipated by damper and elastomeric bearings. By using elastomeric bearings, it is provided that the structure will not be subjected to earthquake forces directly; all the forces will be transmitted to base isolation system. The party trick with the tablecloth The concept of base isolation is almost the same with party trick where the table cloth on a fully laden table is pulled out sideways very fast. If it is done right, everything on the table will remain in place and even unstable objects such as full glasses will not overturn (Figure 9a, 9b, 9c). The cloth forms a sliding isolation system so that the motion of the cloth is not transmitted into the objects above which are clearly similar earthquake forces are not transmitted to the structure above by the help of elastomeric bearings in base isolation system.

Figure 9a

Figure 9b

Figure 9c

CONCLUSION Base isolation has developed into a deep field requiring the work of many engineers and affecting the lives of people across the world, whether they are aware of it or not. By observing and analyzing the physical phenomena that cause buildings to crumble, engineers have devised an effective strategy to sidestep this problem. Besides, once the concept is understood, it is highly possible to use this concept for solving other engineering problems. As it is illustrated in this essay, a technique that has very effective solution to an engineering problem may help even a boxer to win a box match. This is called as seeing and touching the engineering concepts which aims to provide a better understanding of engineering principles through using simple physical models and appropriate practical examples.

REFERENCES [1] Johnson, E. (2004) Structural Dynamics (EESD). Vol. 32, pp. 1333-1352. [2] Kelly E. Trevor, (2001), Base Isolation of Structures, Design Guidelines. [3] http://jclahr.com/science/earth_science/shake/base%20isolation/index.html [4] http://auto.howstuffworks.com/car-suspension3.htm


1.3 Neglecting Live Loads in Unfavourable areas causing loss of Equilibrium Con Murray It is known that any load in a structure can be favourable or unfavourable (British Standards Institute 2002). To ensure that the load combination which gives you the most critical situation is accessed, eurocode has laid down guidelines to follow. Eurocode does this by minimising favourable loads and maximising unfavourable loads. Live loads can be favourable in some areas and unfavourable in other areas (British Standards Institute 2002). When checking equilibrium, the load combination format is similar to Ultimate Limit State, except safety factors are different because the calculations can be more accurately done. Equilibrium limit state is always checked ahead of ultimate limit state and serviceability limit state as loss of equilibrium in a structure is unacceptable. Example The following example will illustrate how failure to consider an unfavourable loading case resulted in a loss of equilibrium. Figure 1 shows a tractor pulling a trailer. In figure 2 the tractor and trailer have been simplified to establish whether the system is in equilibrium. Figure 1

Figure 2

Figure 3


The load in the trailer as well as the weight of the chassis is centred between the two wheels of the trailer. The trailer is therefore in equilibrium. The tractor however has both the self-weight of the tractor, which is centred between the two wheels, as well as weights on the front to give the front wheels more traction. Taking moments about the front wheel, the clockwise moments are (Weights × .3) + (Reaction at Back wheel × 2.3), and the counter clockwise moments are (dead load × 1.15). (6 × 0.3) + (Rb × 2.3) – (33 × 1.15) = 0 Rb + Rf = Dead load +Weight (1.8) + (2.3Rb) = 37.95 15.7 + Rf = 33 + 6 Rb = 15.7 Kn Rf = 23.3 Kn RTb = RTf = (Chassis weight+ Live load)/2 = (19 + 117)/2 = 68 When the trailer is level the system is in equilibrium. The critical case will be when the trailer begins tipping and as the centre of gravity of the live load moves behind the back wheel. If the load was to become stuck in the trailer the magnitude of the moment generated around the back wheel of the trailer could become large enough to cause uplift of the back wheel of the tractor. It is therefore essential to calculate at what angle this could happen at. Loss of equilibrium will be defined when Rb = 0 Taking moments around front wheel of tractor and assuming Rb = 0. (Weights × .3) + (Upward force at hitch × 2.7) – (Weight of tractor × 1.15) = 0 (6 × .3) + (Upward force at hitch × 2.7) – (33 × 1.15) = 0 1.8 + (Upward force at hitch × 2.7) = 37.95 Upward force at hitch = 13.38Kn Equilibrium will therefore be lost when a downward force of 13.38Kn applied at the hitch is needed to keep the trailer in equilibrium. RTf = 0. Taking moments around the back wheel of trailer in figure 3. X = distance to centre of gravity of live load. (Live load in trailer × X) – (Weight of chassis × .25) - (Downward force at hitch × 7) = 0 (117 × X) – (19 × .25) – (13.38 × 7) = 0 (117 × X) = 4.75 + 93.66 X = 98.41÷ 117 = .84m Figure 4


-1

The angle of the trailer when equilibrium is lost = Cos ((1.3-.84)/3.65) = 82˚ If the unfavourable loads are not factored the maximum allowable tipping angle ≤ 82˚

Figure 5

(www.youtube.com) Obviously this angle leaves no margin for error and as is illustrated in Figure 5 the result is very dangerous. The example will now be re calculated using the Eurocode guidelines. The unfavourable loads are the live load in the trailer and the weights on the tractor. The weights on the front of the tractor will be considered a variable load, as weights are added and removed depending on what the tractor is doing. It cannot be assumed they will always be removed when not wanted. Dead Loads in favourable areas are factored by 0.9 (British Standards Institute 2002). Taking moments about front wheel of tractor and assuming Rb = 0 (Weights × 1.5 × 0.3) + (Upward force at hitch × 2.7) – (Weight of tractor ×0.9 × 1.15) = 0 (6 × 1.5 × 0.3) + (Upward force of hitch × 2.7) – (33 × 0.9 × 1.15) = 0 2.7 + (Upward force of hitch × 2.7 ) = 34.155 Upward force of hitch = 11.65


Equilibrium will therefore be lost when a downward force of 11.65Kn applied at the hitch is needed to keep the trailer in equilibrium. RTf = 0. (Live load in trailer × 1.5 × X) – (Weight of Chassis × 0.9 × .25) – (Downward force of hitch × 7) = 0 (117 × 1.5 × X) – (19 × 0.9 ×.25) – (11.65 × 7) = 0 (175.5 × X) = 85.825 X = .48m The maximum allowable tipping angle allowed by Eurocode guidelines = -1 Cos ((1.3 - .48)/3.65) = 77˚ By factoring the favourable loads and unfavourable loads the maximum allowable tipping angle is reduced by from 82˚ to 77˚. This is obviously a far safer method to ensure equilibrium of a structural system is not lost. Modern trailers are also designed wider at the back to avoid the load getting caught.

References

www.youtube.com http://www.youtube.com/watch?v=zAqi8DCYnko&feature=related British Standards Institute (2002); Eurocode Basis of Structural Design (A1:2005) (Annex 1 Application for buildings 389 Chiswick High Road London UK W4AL British Standards Institute,:pg52


1.4 Shear stress concept and its application Cristian Scutaru Who said football has nothing to do with science? Surprisingly or not, many examples could be given to support this idea if an engineer is to be asked. Many people like watching football but few think about what happens from a scientific point of view and, furthermore, what does it have to do with structural engineering. One of the many examples an engineer will give you is the way players are able to accelerate, change direction and make sudden movements on the pitch and the way the studs on their boots behave.

Fig. 1: Football boots with studs

Fig. 2: Stud

Fig. 1 shows a pair of football boots with studs. Studs, as shown in the next figure, are the reason why players do not slip when they are making a run for the ball. But how do studs work? The answer to this question is provided by the concept of shear stress. As it can be seen from Fig.3, the loads acting on a stud are the horizontal load coming from the boot when a player tries to move forward, assuming that his foot is always perpendicular to the ground, and the distributed load coming from the resistance provided by the ground. This type of loads will induce a direct shearing in the stud. In order to better explain the phenomenon and to show its applications in structural engineering field we can consider a bolted connection between two metal parts pulled by a force P (as shown in Fig. 4).

Fig. 3: Loads acting on a stud


Fig. 4 Contact stresses develop which induce a direct shearing in the bolt. The contact stress  b is computed using the formula: F b  b Ab In our case Fb is equal the axial applied force P . The maximum contact stress is: P  b _ max   Fbr d * t min where d and t min are the bolt diameter and the minimum thickness of the two parts connected by the bolt. Fb r is a value obtained from laboratory tests and is uniquely determined for each type of connector. The shear force is transferred through the bolt section m n and the average shear stress  b _ avg is:

4* P  Fv  *d 2 where Fv is the also obtained from laboratory tests. (Simulescu I., 2004, Lectures in Mechanics of Materials)

 b _ avg 

A more practical example used in structural engineering of this kind of connection is the shear connectors used for connecting steel beams and composite slabs. Fig. 5


As seen in Fig. 5, the shear connector attached to the steel beam is very similar to the stud attached to the boot. The shear connector has to resist horizontal loads and provides stability. The concrete in the slab can be compared to the soil in which the stud enters. To conclude, there is no better understanding of a structural concept than trying to think of examples from everyday life and see how the same laws are applied when it comes to small things, otherwise not noticed, but which are of paramount importance. Furthermore, the relationship between structural engineering and everyday life examples proves that the above mentioned subject is no rocket science and it all resumes to simple structural and physical concepts.

Reference: www.structuralconcepts.org (accessed at 24th October 2011) Lectures in Mechanics of Materials (2004) by Simulescu I. Google images, search engine (accessed at 24th October 2011)


1.5 Increasing the Stiffness creating Self-Balancing structures Edurne Bilbao 1.Introduction In order to increase the stiffness of a structure without reducing its height or span, different elements that balance the internal forces can be incorporated. Due to the fact that they work only in tension, cables are among the most efficient elements that achieve this purpose. 2.Computer model and physical model A computer model and a physical model have been developed to prove how the stiffness is gradually increased after incorporating cables and some other additional structural elements. The following table shows the results obtained after having analysed four similar structures with these models. Self-weight of the structure and an additional load on the beam have been considered. COMPUTER MODEL Geometry and loading

Bending moment

PHYSICAL MODEL Deflected shape

Deflected shape (*)

Model 1

- The beam is rigidly jointed to the column. - The second moment of area (I) of the cross section of the beam has to be big enough so as to resist the bending moment and reduce the deflection at the free end. Model2

- The connection between the beam and the column is nominally pinned. - The second moment of area (I) of the cross section of the beam can be smaller that the one in "Model 1" as the design bending moment (MEd) is smaller. - If there were not a cable, the structure would be a mechanism. Therefore, the cable reduces the deflection at the free end.


Model 3

δ3 < δ2

- The bending moment of the column is smaller than in "Model 2" as the effect of the self-weight and the external load applied on the right beam is partially balanced by the self-weight of the left beam. - As a result, the deflection in"Model3" is smaller than the deflection in "Model 2".

Model4

δ4 < δ3 < δ2

- The bending moment of the column is almost completely self-balanced. - As the internal forces are much smaller than the ones in "Models 1, 2 and 3", the stiffness is bigger. (*) There is not a physical model due to the difficulty of creating a perfectly rigid joint.

3.Practical examples The models that have been previously described are widely used in very common structures: Model 1: Car park

Model 2: Car park

Model 3-4: Crane

The cross section of the beam is reinforced with a haunch at the joint (increased lever arm and I) in order to resist the bending moment.

The cross section of the beam is uniform, as the cable makes it possible to have a smaller bending moment in the beam.

The counterweight balances the internal forces of the structure.

However, this simple structural concept is also the basis of more complex and famous buildings such as the following ones in which bigger areas or heights are reached:


Renault Centre Swindon (Norman Foster, 1982):

The self-balancing structure is two-directional and creates a 24m2 module. The whole building is created by attaching several modules, which provides a huge flexibility on its shape and geometry, as well as allowing future expansion.

Headquarters for the Hongkong Shangai Banking Corporation (Norman Foster, 1986): This skyscreeper was conceived as a suspension structure that is based on the same principle of reducing the internal forces in order to provide lateral stability.

4.References  Tianjian, J. and Bell, A.(2008) Seeing and touching structural concepts.[e-book].Oxon: Taylor & Francis. Available from: http://www.dawsonera.com/ [accesed 22 October 2011]  Abel, C. (1991). Renault Centre Swindon 1982. Architect: Norman Foster. 1sted. London:Architecture design and Technology Press.  http://www.fosterandpartners.com/[accessed 22 October 2011]


1.6 Critical load of a structure Fanglei Jia (7411707)



1.7 Utilizing the Catenary Method to Determine the Rational Arch Axis Curve Yu Zheng Concept: Catenary Method Structure: Sagrada Familia Church Model: Self-support Arch Roof Introduction: Arch is widely used in structure design during our common life, which is not only beautiful in shape but efficient in mechanism as well. As a type of structure mainly in the condition of compression, arch is suggested to be designed with the theory of rational arch axis curve in order that axial force alone occur on cross-section (without bending moment and shear force). Those make the whole structure in the condition of uniform compression and the material will be fully in use ,which is most economic. Structural engineers nowadays depend on finite elements theory and computer technology to determine the rational arch axis curve. In fact, one century before, when computer was still a daydream, Antoni Gaudi, the master architect in Barcelona, created the catenary method to determine the shape of rational arch axis curve during design of one of his most famous masterpieces: Sagrada Familia Church.

Figure 1 : Sagrada Familia Church

Figure 2 : Antoni Gaudi

Analysis: The left image shown below is not a droplight. This is an analysis model Gaudi once used in drawing the optimizing shape of the arch roof .From the mirror we can see the real shape of arch roof .


Figure 3&4: Catenary Method in design of Arch Roof Catenary is the curve that an idealized hanging chain or cable, assuming when supported at its ends and acted on only by its own weight. As an idealized model, the crosssection should be same size and density be regular in full length. Figure 5 is an approximate example in our daily life.

Figure 5: Demonstration by Necklace The image upper in Figure 6 indicates that it is the force diagram for a chain which only consider self-weight as its load. Because chain only provides stiffness when in tension，we can easily find that under the effect of self-weight, all cross-section of the chain is in tension. The image lower in Figure 6 is a mirror model to the left one. Hence, they are in same force condition.


Figure 6 The two images shown below keep same structure shape and opposite direction of force. From the equilibrium formula we can easily reach the conclusion that under the effect of self-weight , all cross-section of the arch should be in compression.

Figure 7 Model: There is one model created by myself , utilizing the catenary method to determine the rational arch axis curve.


Figure 8: Model of Arch Roof

Figure 9: Model of Arch Roof (i)In this model , flexible tape is used to replace steel chain. (ii)Picture is taken from the bottom of desk. (iii)In order to enhance the accuracy of model, additional mass is suggested to add on the tape, which is not displayed in this model.


*Figures 5~9 are created by Yu Zheng. Figure 1~4 are searched from Existing data. Reference: 1.1 http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/ 1.1 http://en.wikipedia.org/wiki/Antoni_Gaudi 1.2 http://en.wikipedia.org/wiki/Catenary 1.3 http://zhuxiaobao.blog.163.com/blog/static/175475204201172043936820/ 1.4 http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia 1.5 http://hi.baidu.com/threesisters/blog/item/bc89bb018cb4e600738da557.html


1.8 Static Equilibrium in Nail Clipper Aaron Dikibo CONCEPT: MODEL:

STATIC EQUILIBRIUM NAIL CLIPPER

INTRODUCTION: Nail clippers are amazing devices used to help trim down overgrown finger or toe nails for safe and hygienic living. Two common types of nail clippers exist – the lever and plier. This piece of work shall be bordered around the principles/mechanisms of the lever type. DESCRIPTION: The nail clipper works by the lever mechanism. When some load is applied at the lever or handle, it moves downwards thereby causing the blade/cutting edges to tend towards each other (see Fig. 1).

Applied Load (F)

Fulcrum (C) Blades (B) Fig. 1: Pictorial description of a nail clipper

The greater the exerted load, the more likely the nail clipper would perform its operation of trimming the finger or toe nails. Just as it is with other first class lever systems, the nail clipper has its fulcrum located between the input (applied load) and the output (the touching blades).


F

L

a

Fig. 2: Schematic description of a nail clipper A nail clipper is a ‗simple machine‘, and as such, makes work easier. Now, work done is the product of the applied load (F) and the distance away (L) from the fulcrum (C) in the direction of F. That means (from Fig. 2), the greater L becomes, the smaller the angle under the lever arm (a), and the more effectively the blades would trim the nails (work done).

B

F*Cosa

C

L*Cosa Fig. 3: Free body diagram of the mechanism

REFERENCES: 1. http://www.tryengineering.org/lessons/clipper.pdf 2. http://www.livestrong.com/article/68362-nail-clipper-works/ 3. http://www.newworldencyclopedia.org/entry/Lever 4. http://www.gettyimages.co.uk/Search/Search.aspx?contractUrl=2&assetType=image&family=Cre ative&p=nail+clipper#2


1.9 CROSS SECTION SHAPE AND THE PARALLEL AXIS THEOREM. ALBEIRO MARQUEZ MARQUEZ Introduction. With this document is aimed to make easier to understand the concept involved with the second moment of area, and the importance of the shape and orientation of the cross section of an element without alter the quantity of material used. The Second Moment of Area or Moment of Inertia (I), depends only and exclusively in the area. It is just reflect the way in which the area spreads off the centroid, which value is proportional to it. A higher value of I represent a more spread area about the centroid. Consequently, the resistance to bending moment is inversely proportional to the deflection cause by the applied load along the element, and directly proportional to the resistance of bending moment, as shown in the formula:

From where, M is the Bending Moment, E is Young Modulus, I is Second Moment of area, and is the deflection along the element. Concept. According to many authors, he second moment of area termed as well as ―Moment of Inertia‖, ―finds application in the design of structural members, as it gives a measure of resistance to bending in the case of sections or plane areas. Depending of the distribution of this area, its resistance to bending moment varies.‖

However, in many cases we find ourselves in the situation in which we want to determinate the Second Moment of Area about a non-central axis which is parallel to the centroidal axis, in this case, we can get use of the parallel Axis theorem, also called, Transfer Formula‖. ―This formula relates the moment of inertia of a moment with respect to any axis in the plane of the area to the moment of inertia with respect to a parallel centroidal axis‖.

Understanding Structural Concepts As a conclusion, it can be deduced that ―Moment of inertia about an axis in the plane of the area is equal to the moment of inertia about an axis passing through the centroid and parallel to the given axis plus the product of the area and the square of the distance between the two parallel axis‖

Model demonstration.

Figure 1: The sequence in which a load is applied to a sheet of paper acting like a simple supported beam (picture on the left hand side) is shown above. It can be clearly observed the lack of resistance to bending when a force (in this case represented by a pencil, picture on the right side) is applied in the middle span of the beam.

Figure 2: Using the same sheet of paper, the shape was changed to a circular one instead, reducing its original width but increasing the high. As a result, the element gained capability to support an even higher applied load because of the increase on the value of the Second Moment of area (I) without alter the amount of material.


Real-life example.

Figure 3: A sheet of Guadua (Bamboo) is obtained after a longitudinal cut on the bar, simulating the way the concept of parallel axis has been naturally applied to the element.

Figure 4. The Guadua (an specie of Bamboo) in its original state. It consist on a series of hallow cells all along the longitude of the element.

Figure 5: From a sheet of Guadua to a simple supported bridge. The picture shows the longest bridge in Colombia built mainly of Guadua, taken advantage from the good understanding of the Structural Engineering.


Conclusions.  Throughout the document, the theory and concept of second moment of area was given and clearly justified with the model demonstration and real life examples.  It can be deduced, the importance of the shape of the cross sectional, which can be reflected on the resistance to bending moment.  A more resistant element does not represent a heavier or more expensive one, simply represent the good understanding of the Structural engineering.

References.  Engineering mechanics: Static and Dinamic. A. Nelson. 2009  Structures, from theory to practice. Alan Jennings. First edition. 2004.  http://construccionquindio.blogspot.com/2010/04/puente-en-guadua-mas-largo-delmundo.html Visited on Saturday the 29th of October 2011.


1.10 The concept of equilibrium and centre of mass--tumbler Li Chen Introduction The tumbler is a toy that rights itself when pushed over; it has a long history in China and gives many funs to people. In addition it also has many structural concepts in the small toy. We will analyze the equilibrium and the structure of the tumbler.

The theory The object which the upper structure is heavier than the lower structure is relatively stable, that is the center of mass lower, the more stable. When the tumbler is in the erect and balance position, the distance between the center of mass and adherent point is minimum. In this situation the center of the mass is lowest. Deviation from the equilibrium position, the center of the mass is always elevated. Therefore, this equilibrium position is stable and balanced. So in any case tumbler swing, not always inverted. All of these tumblers have the same characteristics: upper body as a hollow shell, the lower body is a solid hemisphere, bottom is round. These characteristics make them consistent with the basic mechanical structure, to achieve "no down" effect.

The physical structure of tumbler Tumbler is the hollow shell, the weight is low; lower body is a solid hemisphere, the weight is heavy, the tumbler‘s center of the mass is in the hemisphere. Between the bearing surface and the hemisphere, there is an adherent point; when the hemisphere is rolling on the bearing surface, the adherent point of the position will change. Tumbler is always using the adherent point stand on the bearing surface. A "tumbler" balance stability When a "tumbler" receives a external force, it will lose balance. After remove the external force, a "tumbler" will recover to balance position, this show a "tumbler" has resistance interference in balance ability outside external force, and this is the stability of the balance. The formation of resistance interference is to maintain a balance.


Three applied load situations of the tumbler First, the applied load of "tumbler" balance position. A "tumbler" on the desktop, receives two external forces: one is gravity; the earth to a tumbler‘s attractive force, the other is a supporting force. According to the object equilibrium situation, as long as the two force equal and opposite effect, in a straight line, a "tumbler" can maintain balance position. Second, the applied load of tumbler‘s tilt position. A "tumbler" tilted receive two moment, we call the role of external force is interference, external force form disturbance moment; another call resistance moment, formed by its own gravity.

At first the tumbler is upright, because the role of external force, the external force made the tumbler and adherent point produce moment, make a "tumbler" tilt, break the balance of the original. In addition, at first the gravity does not produce moment, because the "tumbler" is upright, the pull of gravity line and supporting point is located in the same line, moment is zero. Because the role of external force, a "tumbler" is tilt, hemispheroid to one side scrolling, the adherent point is move, and formed new adherent points, namely the formation of a new supporting point, right now the pull of gravity line and the original supporting point is not in the same line, becoming the moment, this is the resistance moment. It is because of the formation and development of the resistance moment, resistance and stopped interference effect of the external force. The direction of the resistance moment and the direction of the disturbing moment is exactly the opposite. At the same time, as a "tumbler" tilt Angle is continuously increasing, and the center of mass‘s action line offset is continuously increasing, and resistance of the moment value also unceasingly increases, when the resistance moment is equal to the disturbed moment, a "tumbler" into the new balance , this time the external force interference effect that also stop. Therefore, a "tumbler" by external force disturbance, the balance of the original damage, but the new balance then formed, a "tumbler" can keep in balance, although balance in different ways, but the essence of the balance unchanged, and this is the dynamic balance.

Third, the applied load of tumbler‘s recovery position. Consider aspect of potential energy, object which has lower potential energy is more stable, the object must change toward to low potential energy situation. If the tumbler goes down, it wills recovery to the original situation.


Because the base which is concentrated by most of center of mass has been bid up, the potential energy increased. Consider the aspect of lever principle, when the tumbler goes down, the action point of the centre of mass has been ends, wherever it is. Although the arm of force of base is shorter, but Moment= "force"* "arm of force‖, the tumbler will still go back to its original situation because of the higher moment which is around the base. In addition bottom of tumbler is circular and has lower friction; it is easy for tumbler to return to its situation. In the whole process above, to create a new balance is one of the main problems, because only this way can resist the disturbance of external force. Recovering to the original balance is the secondary problems, because the external disturbance has been removed at this time. In the whole process, the tumbler is always keep attribute of balance, which is "the stability of balance". Conclusion In summary, the key point of the theory is to make the line of action of the mass deviate from supporting point producing resistance moment. As a declining angle of tumbler is continuously increasing, and the offset the line of action of mass will also increase as well as resistance moment. In order to achieve the balance of external moment, so the ability of tumbler that can resistant interference and keep the balance of force is formed by upper theory The tumbler is not only giving the fun to us but also there are many applications in the real world, such as the toys and the base of the fan. Reference 1. Ji T and Bell A J,(2006), Seeing and Touching Structural Concept, University of Manchester,25/10/11,www.structuralconcepts.org


1.11 Improving Seismic Design Cawan Nero Miran Why is seismic engineering Important?

    

Seismic engineering is the study of ground motion, formed from the necessity to ensure safety and protection of occupants and assets. The study of seismic engineering can identify the required design criteria for earthquakeresistant buildings Seismic engineering has been around for 2000 years, and has been integrated into the building design and structures of the earliest civilizations such as Pyramids and temples Seismic activity is the vibration and waves generated from the motion or collision of a series of ―plates‖ which compose the Earth‘s crust. These complex ground motions are effects of the Earth‘s tectonic plate friction between the plate faults, as each slide, sub-duct and extend with another, generating tremendous stresses, which when released instantaneously, radiate through the plates as shockwaves, emanating from an epicentre point and may range in duration from a couple of seconds to minutes.

Preventive systems  Modern earthquake protection systems employ dampening devices within the building structure.  These devices aim to dissipate the forces exerted by the ground motion and can be categorized into active, passive and isolation devices.  Shear Walls and Braced Frames can be strategically placed to stiffen the walls and are capable of transferring lateral forces from floors and roofs to the foundation.

Understanding Structural Concepts 

However, ultimately the physical properties such as building shape, base to height ratio, uniformity, symmetry, ductility and stiffness are fundamental elements which compose a structures seismic characteristic.

NATURAL FREQUENCY  Let‘s take an example. Imagine you could push a building sideways at its top and then let go so that it swayed naturally. The number of times it swayed to and fro every second would be the fundamental frequency of vibration of the building.  If you repeated the experiment, but pushed the building a little harder or lighter, the fundamental frequency would stay the same.  The building distorts in a particular way when it vibrates at this frequency. The shape it takes up is called the fundamental mode shape. Δ Acceleration

 The Natural Frequency of a Building  The natural frequencies of vibration of a building depend on its mass and its stiffness.  The natural frequency for each mode of vibration follows this rule:

f 

1 2

K M

 f = natural frequency in Hertz. K = the stiffness of the building associated with this mode M = the mass of the building associated with this mode Buildings tend to have lower natural frequencies when they are:  Either heavier  Or more flexible

W

Seismic Force


FEM Theoretical analysis So let us look at the proposed design which best meets these outlined criteria B-B plan section 27m A-A plan section

5m

19.42m

27m

5m 19.42m A

A

B

B

Wall Inclination 74.05 degrees

Each Floor height at 3.5m spacing’s 35m 3.5m

[A]

[B]

Figure 1. Dimensions and layout of conventional and tapered structures. [A] Conventional 10 storey structure. [B] Tapered 10 storey structure with inclination of outer walls 

My study focuses on the effects of building shape, on the structural integrity under significantly large and rare seismic events. The study of the shape element of the building will compare conventional shape design and dimensions to those of nonconventional building shapes, specifically pyramids or taper shaped buildings in relation to their seismic properties.



The aim is to establish that such taper shaped or pyramidal buildings demonstrate a greater stability with lower centre of mass, while are also more restrained laterally and hence more resistant to displacements due to ground motion.



So let me present my findings for the analysis I have conducted using a FEM (Finite element method).




Here you can see the displaced shape of a conventional structure at the 1st mode or fundamental period. Which is occurring at 3.361Hz



Here you will see the pyramidal displaced shape at the fundamental Period occurring at 3.715 Hz




This Graph illustrates the extracted modes for each of the two structures studied 



ter walls provide lateral bracing to the whole structure increasing the stiffness of the structure.

Mode set No. CONV STRUC PYRIM STRUC

1 2.379 2.8756

2 3.3611 3.7149

3 4.5131 7.8746

4 7.1106 7.9222

Time/Freq 5 6 9.5321 9.9858 10.282 12.931

7 11.759 13.841

8 14.662 16.583

9 15.179 17.352

10 16.258 17.791


Conclusion  This Graph illustrates the extracted modes for each of the two structures studied and as shown the Pyramidal structure exhibits higher natural frequencies i.e. a greater stability to dynamic loading, this is due to a lower centre of gravity for this structure.  Also the inclined outer walls provide lateral bracing to the whole structure increasing the stiffness of the structure to seismic loading. References  ACI (2008). Building code requirements for structural concrete (ACI 318-08) and commentary, American Concrete Institute, Farmington Hills, MI.  AISC (2006). Seismic design manual, American Institute of Steel Construction, Inc., Chicago, IL.  Mezzi M., A. Parducci and P. Verducci , 2004. Architectural and Structural Configurations of Buildings with Innovative Aseismic Systems, 13th WCEE, Vancouver, Canada.  Arnold C. and R. Reitherman, 1982. Building Configuration and Seismic Design, John Wiley, New York.  Eurocode no.8, 2001. Design of Structures for Earthquake Resistance, prDraft No.3.  Thiel, Charles C., and James E. Beavers. The missing piece: improving seismic design and construction practices. Redwood City, Calif.: Applied Technology Council, 2003. Print.  Blume, J.A., Newmark, N.M., and Corning, L.H. (1961). Design of multi-storey reinforced concrete buildings for earthquake motions, Portland Cement Association, Chicago, IL.


1.12 FORCE INCREASING SYSTEM ANALYZING THE CONCEPTS OF MECHANICAL DEVICES DANIYAL CHUGHTAI An average person can lift almost equal to his or her body weight (Depending on how often you visit the gym; you may be able to lift more or less than that). Suppose you are asked to lift an object of 100Kg weight and you are sure there is no way you can lift this much weight you can use engineering principles to devise a force increasing system that allows you to lift more weight than the force you apply. Here is a simple system that could help in such a situation.

So you could apply a force W/2 and lift an object weighing W. In our case you could lift the 100 Kg object by applying only the force required to lift a 50 Kg object.

Here is a similar homemade system that lifts 4Kg weight by applying only 2Kg force. (Each bottle is 2Kg)

Understanding Structural Concepts If you still couldn‘t lift the weight, you need to devise a system with a bigger force increasing factor. (This factor is actually called the mechanical advantage of the system) You can use the following system.

If you used the above system, you could lift the 100 Kg force by applying the force required to lift only a 25 Kg object. (A force increasing factor or mechanical advantage of 4!!!)Further combinations could give you virtually as much mechanical advantage as you desire.

These systems have been known to man for a long time and ancient civilizations used them to build magnificent structures such as the pyramids. The adjacent figure is device that was used in construction by which a person could lift 15,000 Kg!!!

HOW DOES IT WORK. At first glance, these systems seem to contradict all the laws of conservation you could think of because you get more output force than the input force. But a careful analysis shows that this is not the case and laws of conservation still apply.


In the first system, moving the rope on the left (where you are applying force) by a distance ―d‖ will only lift the weight by a distance ―d/2‖. Hence the work done is constant.

In other words, using this system you can lift the 100 Kg weight by applying only 50 Kg force but to move the weight by 1 meter, you would have to pull the rope through a distance of 2 meters. So the work you would have to do (Force X Distance) is the same as you would if you lifted the weight without using this system. Similarly, in our second system which has a mechanical advantage of 4, you have to pull the rope through 4 meters to lift the weight by one meter.

THE LEVER FORCE INCREASING SYSTEM In lectures of Dr tianjian ji (2010-MACE 60005) it was discussed that a 25 gram and could lift a 4500 Kg elephant if the lever arm ratio was 1 to 18000.

This again seems like the system of lever increases the force of 25 gram to 4500Kg but a careful analysis of the system will prove that if the ant moves the lever down by 1 meter, the elephant will move up by only 1/18000 meters. Hence the work input and output are constant and no net gain of force is achieved.


REFERANCES Figures adapted from http://en.wikipedia.org/wiki/Pulley (Accessed 28-10-11) http://www.the-office.com/summerlift/pulleybasics.htm (Accessed 28-10-11) Figure for ancient pulley system taken from http://park.org/Korea/Pavilions/PublicPavilions/Public/nsm/eg/pe-3.html(Accessed 30-10-11) Lecture Notes MACE 6005 -2011


1.13 Proper Section to Improve Stiffness of structures HUANG Daifa 1. Introduction Stiffness is a basic character of structures or components which shows the ability to resist deformation. High stiffness means that structures or components have smaller deflections under certain loads. 2. Parameter E and I The stiffness of structure is closely related to the material properties and dimensions. Higher values of Young‘s modulus E and second moment of inertia I usually mean a higher stiffness. To all kinds of material, E should be a constant value. So enlarging second moment of inertia I is an effective way to improve the stiffness of a structure. 3. Cantilever w Figure 1 A

B

Figure 1 shows a cantilever with a total uniform load w. The length is L. Adopt the method of unit load, calculating the deflection of point B,

(1)

Δ= wL³/8EI

4. Example- Poker cards bridge Two models of cantilever bridge are made of poker cards in different sections, aiming to show how the second moment of inertia I functions to reduce the deflection of a structure. The dimension of a piece of poker card is 70mm*50mm*0.5mm.

h=10mm a=50mm t=0.5mm

a=30mm t=0.5mm

Figure 2 Figure 2 shows the different sections of the two models. The section of Model 1 is a normal poker card while the second model adopts a U-section which simply lifting the two sides for 10mm of the cards Calculate the second moment of inertia of the two models. Model 1 I=at³/12=0.52mm^4 Model 2


Neutral axis is 8mm from the top I‟=2*[0.5*10³/12+10*0.5*(8-5)²]+30*0.5³/12+30*0.5*(2-0.5/2)² =220mm^4 Δ= wL³/8EI, I‟/I=423 Hence, Δ‘/Δ=1/423, which means the deflection of Model 2 is 423 times less than Model 2. Figure 3 shows the deflection of the two models.

Figure 3 5. Summary To reduce the deflection of a structure or a component, the most direct way is to improve the stiffness. The improvement of stiffness can be realized by changing the section to get a higher value of second moment of inertia. As the experiment shows, the U-section features obvious. Stiffness enlarges 423 times.


1.14 ARCH ACTION IN EGG SHELLS IJAS MUHAMMED ALI OBJECTIVE: To demonstrate the load path in an egg shell and compare it to an arch. BRIEF: When an egg is loaded at its crown it tends to transfer loads to the bottom of the egg along the surface of the structure and this can be compared to how the load transfer takes place in an arch. When a small force is applied on the surface of the egg like when a spoon is struck on the surface to break the egg the force acting on the egg is normal to the surface and hence only a small force is required to break the egg. EXPERIMENT: Requirements: 1. Egg - 4 2. Egg Tray – 1 3. Weighing Scale – 1 4. Smooth surface(cutting board) – 1

Figure 1: Eggs before loading

Figure 2: Eggs at first crack

Procedure: place four eggs in an egg tray as shown in the figure. Place a smooth surface touching the top of each of the eggs so that it acts as a loading surface and transfers the load evenly to the eggs. Add books as weight until the first crack develops on the egg. RESULTS: Total weight of load = 14kgs Therefore weight on each egg = 3.5kgs


Figure 3 – Load path when the

Figure 4: Load path of a typical arch loaded

egg is loaded on top

at the crown

Another simple experiment is to hold an egg at its top and bottom with your fingers and try applying as much force as possible you will notice that the eggs can withstand a lot of pressure; this is because of the arch action displayed by the egg. INFERENCE: the reason why the egg can withstand a higher load when loaded on top is because of the shape which resembles the shape of an arch. When the load is transferred along the surface the stress that the egg can take increases as the surface area along which the load passes increases. Whereas in the case when the egg is struck with a small force on any of the sides the area in contact is very small and hence the force required to fail is less.

REFERENCES: 1.

www.structuralconcepts.org

2.

http://www.makingthemodernworld.org.uk/learning_modules/maths/02.TU.03/?section= 4

3.

http://reekoscience.com/Experiments/EggShellArches.aspx


1.15 Scaffolds-widely use of Direct Force Path Li Wang Individuals define stiffness as the ability of mechanical parts and components to resist deformation. Stiffness can be divided into static stiffness and dynamic stiffness. The formula: k=P/δ Where k---------stiffness P---------load δ---------deformation

Figure 1 Scaffolds, which are widely used in the Construction, enable individuals to work in the exterior and interior decoration area and high places. scaffolding materials are usually made by bamboo, wood, steel and synthetic materials.


Figure 2 To ensure workers‘ safety, it is standard practice for people to add cross braces (as the picture shows) to increase the stiffness of these tools because it increases as the internal force paths become direct, and this theory is playing a pivotal role in the construction area in this day and age. Reference: [1]Seeing and Touching Structural Concepts. University of Manchester. [online][30/10/2011] http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/ [2]Concept of Scaffold. [online][30/10/2011] http://baike.baidu.com/view/241327.htm [3] Concept of Stiffness. [online][30/10/2011] http://baike.baidu.com/view/121447.htm The figures are taken from the following addresses; [4]http://image.baidu.com/i?tn=baiduimage&ct=201326592&cl=2&lm=1&fr=&sf=1&fmq=&pv=&ic=0&z=&se=1&showtab=0&fb=0&width=&height=&face=0&isty pe=2&word=%BD%C5%CA%D6%BC%DC&s=0#pn=54 [5]http://image.baidu.com/i?ct=503316480&z=&tn=baiduimagedetail&word=%BD%C5%CA% D6%BC%DC&in=7323&cl=2&lm=-1&pn=193


1.16 Useful structural concept in daily life——centre of mass QIANQIAN MOU Introduction: As we all know, a body can be more stable when the location of its centre of mass is lower.And this concept do play a significant role in our daily life,such as sports match, general tools and so forth. Examples: For instance,tumbler,swaying all the time but never falls down,whose bottom is much more heavier than its top,which also means that its centre of mass is close to the base.(Sometimes the bottom is stuffed by some plasticine. Another method of increasing the weight of the bottom is to use those heavy materials.)Although the stability is also related to the frictionless round bottom and the change of the gravitational potential energy,I still believe that the centre of mass in the low place devotes most to this steady status.

Similarly,sumo athletes squatting down in the competition field,just like a pier standing there , can absolutely lower their centre of mass and then ensure stability of their bodys.


In addition,the same structural concept has been gradually applied to various fields in people's usual life creatively.

The benefits of the advanced "balance stick": It can be clearly seen from the photos above that the special design of the weight base can hold the self-weight of this stick .Thus the balance stick would not topple over and can stand very well ,so there is no need for the ages to bend down hardly to pick up the fallen stick any more.And balance stick can stand independently on slopes as well,it doesn't need to be held all the way .Hand free is benefit.


Dews toothbrush : The special design of the bottom has the ability of reducing tendency of overturn.And these novel toothbrushes not only have a good look in dews shape,but also convenient to be placed everywhere.

Conclusion: From examples all above,we can see amazing and miracle influence on every aspacts of our lives by this simple structural theory.If we keep taking good use of this useful concept ,more and more valuable structures will definitely appear in the near future.We will be provided much more benefits with those novel inventions ,too.

References: 1)Tianjian Ji, Adrian Bell, Seeing and Touching Structural Concepts. 2)The figures were taken from Baidu image search engine 3)http://youliv.com/products/7402305.aspx 4)http://www.e-jama.com/1882-page-asc.html


1.17 The concepts of prestress "Prestress is a technique that generates stresses in structural elements before they are loaded. "(Tianjian J,2008)

Prestress can be shown by the right figure.

We can

consider every book is the element of beam.

If

do not applied the load at the each end of

we

books.

We can not lift books at once. Figure 1: Row of

books

as a single unit During our daily life, there are lots of examples using prestressing. Like wooden barrel, people used metal bands or ropes around wooden staves.

Wooden barrel

wooden stave

half of metal band Figure 2: Principle of prestressing applied to barrel construction Lin, T Y, (1955),

The wooden barrel was consist of some wooden staves and fixed by two metal bands. The compressive prestress was caused between adjacent staves. Before bands and staves under any loads, both of them were prestressed. It could balance the internal liquid pressure and increase the barrel's using life.

Right now, prestressing is widely used, especially the prestressed concrete. The right figure below shows the principle of prestressing in concrete beam:


(a) Loading on the beam.

(b) The deflected beam subjected to a point load.

(c) The beam prestressed.

(d) The beam compressed after being prestressed.

(e) The deflected beam after being compressed.

(f) The prestressed beam subject to loads again.

Figure 3: Prestressed Concrete Beam

In conclusion, prestress can be used to improve anti-cracking property, durability, rigidity and bearing capacity of members.

Reference 1.

Lin, T Y, (1955), Design of Prestressed Concrete Structures, John Wiley & Sons, New York.

2.

Ji T and Bell A J,(2008), Seeing and Touching Structural Concepts, Taylor & Francis, ISBN 13: 978-0-415-39774-2.2008

3.

Threlfall A.J. (2002)

An Introduction to Prestressed Concrete

Cement Association. ISBN: 0 7210 1586 7.

(2nd edition). British


1.18 Why the bridges are designed to be convex? Yi Zhuo

We can assume that there are three identical cars moving with the same speed on the three types of the bridges respectively. The first one is moving on a plain bridge, the second one is moving on a concave bridge and the third one is moving on a convex bridge. When all the three cars are passing the midpoints of their respective bridges, then A. The supportive force from the plain bridge to the car is medium among the three B. The supportive force from the concave bridge to the car is maximum among the three C. The supportive force from the convex bridge to the car is minimum among the three. The reason why the three conclusions inferred will be explained as follow.

The Highest Point

The Lowest Point Fig.1 The simple bridge diagrams of the convex bridge and the concave bridge

According to the Fig.1, it can be imaged that the two cars are in the circular motion: the car at the highest point is present at the midpoint of the convex bridge and the other car at the lowest point is present at the midpoint of the concave bridge. As we know that Newton‘s first law of motion said that ―Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it‖. In other words, if a car is under without external forces, it will move uniformly in a direction tangential to the bridge (see Fig.2). However, there should be forces on the car which make it change the direction of motion. The force is called the centripetal force which can be calculated from mass * velocity / radius.


R

If a car is moving on convex bridge then, Resultant force = Centripetal force v

i.e. mg – R = mv^2 / r or, R = mg – mv^2 / r R is reactional force exerted by bridge on the body. m is the mass of the car. v is the linear velocity at the highest point

mg R

v

If a car is moving on concave bridge then, i.e. R - mg = mv^2 / r or, R = mg + mv^2 / r

mg R

v

If a car is moving on plain bridgr then, i.e. R = mg

mg Fig.2 Stress Analysis of the cars In summary, the calculation proves the three conclusions mentioned before, at the same time, it can be seen from the results that when the car is moving on convex bridge, the reactional force is less than another two bridges which means that convex bridge is beneficial to the bridge structure strength design. References: Frederic P. Miller (2009), Centripetal Force: Osculating Circle, Uniform Circular Motion, Circular Motion, Cross Product, Triple Product, Banked Turn, Reactive Centrifugal Force, Non-uniform Circular Motion, Generalized Forces, Curvilinear Coordinates, Generalized Coordinates, Alphascript Publishing. Tianjian J., Adrain B. 2011 Seeing and Touching Structural concepts, [online]. [Accessed 23Oct 2011], Available from: http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/


1.19 Principle of Superposition Adedayo Olanrewaju Adeniregun The principle of superposition according to Williams and Todd 2000 ―states that the total effects of two different inputs to a systems equal to the sum of their effects when applied separately.‖ Thus, if a beam deflects by a distance ∆1 under a load A and a distance ∆2 under a load B, then the beam‘s deflection under a load (A+B) will be ∆1+∆2. A ∆1

Fig 1.1: A Beam of length l with a vertical load A applied at l/2

B ∆2

Fig 1.2: Same Beam as in 1.1 but with a vertical load B applied at same position as 1.1 A+B

∆1+∆2

Fig 1.3: Same Beam as in 1.1 with a vertical load A+B applied at l/2 Assumptions of Super-position principle 1. The material is elastic and elastic limit is not exceeded during loading 2. The geometry of the material does not change or change in geometry is substantially small


Plate 1: A simply supported beam unloaded

Plate2: Deflection of beam loaded A

Plate3: Deflection of beam with load A+B References Williams M.S. & Todd J.D., (2000) Structures theory and analysis, Palgrave Macmillan


1.20 Why a Roly-Poly Toy does not fall...???? Amrit Pal Singh Concept: Stable Equilibrium by lowering the Centre of Gravity Definitions:Equilibrium- It is defined as the state of rest of a body, during which the net effect of forces on the body is zero i.e. F=0. Three states of equilibrium: a. Stable Equilibrium- A body is in stable equilibrium when the mass is concentrated at the bottom thus lowering the position of center of gravity. So when the body is tilted, the centre of gravity gets raised but the body moves back to its stable equilibrium position by making the centre of gravity as low as possible. Example – Roly ploy toy b. Unstable Equilibrium – A body is in unstable equilibrium when the mass is concentrated at the top, when a small force is applied on such a body it makes the body unstable and the body ultimately falls to make the centre of gravity as low as possible. Example – a person standing on one foot. c. Neutral equilibrium- – A body is in neutral equilibrium when the body is placed in such a position so that when a force acts on the body, centre of gravity is neither raised nor lowered. Example – A dumbbell lying on ground along its longer dimension Centre of gravity – A rigid body is made up of different members each having a specific weight. Center of gravity of a body is a point where we assume the weight of all the members of the body to be concentrated.

Understanding Structural Concepts Answer to Why…???? - Roly poly toy is generally hollow and spherical at the bottom with the entire weight concentrated at the bottom so the centre of gravity is in the middle of spherical section at the bottom as shown by red circle. At equilibrium centre of gravity is exactly above the point of contact with the ground as shown by the red line. ―When the toy is tilted the center of gravity rises from the green line to the orange line‖, and the center of gravity is no longer over the point of contact with the ground as clarified by the yellow line. . This produces a righting moment which returns the toy to the equilibrium position. . Such a Roly poly toys is not homogenous as its density varies across the body. An object like this has only one stable and unstable point so no matter how you move the toy it will return to its original position. Based on this example we can explain why it is so important for a Structure to have a broad base with its centre of gravity as low as possible and within the base of its support. If the centre of gravity of the structure lies outside the base of the support it may be unstable and it may fail but if centre of gravity is within the base of support and if a force is applied on the structure the structure will move around a fixed point at the base and retain its original position after some time therefore the position of the centre of gravity is crucial in a structure. Conclusion - If a system has its centre of gravity concentrated nearer the base of the support, it is in stable equilibrium, small disturbances to the system may lead to temporary changes in the position of the system but ultimately the system returns to its original position. So when the rolypoly toy is tilted at an angle it wobbles for some time and then attains its original position. References http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/[accessed on 24.10.2011] http://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c [accessed on 25.10.2011] http://en.wikipedia.org/wiki/Roly-poly_toy [accessed on 24.10.2011] http://www.phy.cmich.edu/people/andy/physics110/book/Chapters/Chapter7.htm [accessed on 27.10.2011] http://www.tutorvista.com/content/physics/physics-i/forces/equilibrium-and-stability.php [accessed on 27.10.2011]


1.21 “Cable supported structure”analysis BINGNAN SHEN ―Cable supported structure‖is a clear definition for both structural members and features―Cable‖ means the arched tension cables and ―supported‖denotes the effect of compression struts，while ―structure‖ represents the upper layer in the whole structure. Cable supported structures are defined as cable supported plane structure，separate cable supported spatial structure and inseparable supported spatial structure.

Fig.1 Cable supported portal frame Practical example:


Structure is composed by the rods and lasso composition. The lasso offer tension force so that the structure internal force get balance and the structure remain stable. The internal force path shows in the picture below.

Chord-tension beams example: Use common ruler as beams, both ends can be thought of as hinge support. Only use common ruler to support and put a load of 2.5kg at the middle of beam. It is clearly that the deflection is obvious.

Use cloth, ruler and plastic box constitute a chord-tension beam. As shown below:


Put a load of 4kg at the middle of beam.

Deflection of the structure is very small. Compared with the formal simply supported beams, stiffness improves a lot.

Load flow path of chord-tension beams: The bottom lasso sustain tension force, largely reduced the bending moment of the curved upper beams.


Assume the area of the uprights component is A1, the area of lower component is A2, the height of chord-tension beam is h. The second moment of area of the uprights component is I1. The second moment of area of lower component is I2 Then we can get the second moment of area of the whole structure:

Conclusion: 1. A string of the structure of the upper structure has certain stiffness, this makes the structure of the construction and the joint structure than the flexible structure will greatly simplified. 2. The forces path on the system structure is reasonable. High strength pressed lasso the introduction of the upper structure and lower cable-strut formed part of the whole, and work together; A type of the cable tension through the inner structure make the generation and load the opposite displacement, partly offset by the load. 3. In theory have to maximize the use of structure material characteristics, use of the least build large span steel structure of the building, etc.


1.22 Stress Distribution in Real Life Vlamakis Emmanouil Concept: Stress Distribution Structures: Simple column with footing, the using of snowshoes and a push-pin

Introduction: A common problem in Engineer‘s life but also in human‘s day to day life is the load enforcement in to non-cohesive ground. Particularly the stresses that are developed from a body from its weight or from the load which is acting on it may be produce disequilibrium or settlement in non-cohesive ground.

Practical Example 1: Simple column with footing

For F = 10KN


σ1 = F/A1 = 10KN/m2

and

σ2 = F/A2 = 100,000KN/m2

σ2 = 10,000 σ1 As it is illustrated in figure (1a-b) above, for a simple column foundation there are two cases, one with a large surface at the bottom of the column (figure 1a) and another without any extra surface at the bottom (figure1b). Consequently, according to figure 1a, we recognise that the applied force in the column is distributed in the whole area. As a result it is produced a stress distribution. On the other hand in figure 1b it is obvious that the column without footing produces high stress concentration which is 10 thousand times bigger than the first case.

Practical Example 2: The using of snowshoes. This is an example with the human body when someone wants to play with snow. How it is possible to walk on it?

Figure 2


As it is observed from figure above without snowshoes it is difficult to move because our feet settle in to the snow. This is the same problem as the previous. The snowshoe produces a stress distribution along its surface; as a result the surface of the snow which is come in contact with the snowshoe can resist easer the weight of the body.

Practical Example 2: Push-pin example

Figure 3

In this example we can observe the meaning of stress distribution by applying the same force. As we can see in figure 3 the finger applies force to the push-pin and the pin applies force to the board but the push-pin react from the resistance of the board so it is also applies the same force to our finger. As a result we have the same force but on the opposite site. The area of the head of the push-pin is Ap and the area of the nib is An but we know that Ap=400* An. Hence,

σfinger=F/ Ap

and

σboard=F/An

by dividing these two equations we have, σfinger /σboard = An /Ap


and by applying the previous assumptions we finally have, σboard = 400* σfinger Consequently the stress which is produced to the finger is 400 times smaller than the stress which is produced to the board. Thus this is the reason that the pin is fixed in to the board.

Conclusion: In the conclusion the main concept of these examples are to understand how we can distribute the applied stress in order to avoid the settlement and also the disequilibrium. This is obvious from the simple examples above that by increasing the area we generate lower stress to the ground. Hence more stable structures.

References:  www.structuralconcepts.org  www.digitalschool.minedu.gov.gr/modules/ebook/show.  www.google.com


1.23 Using Global Buckling to Erect a Camping Tent Keiran Murphy A structural member that is loaded axially in compression is often referred to as a compression member and are the main members of modern day structures. A compression member is usually vertical and is known as a column. A column is said to be in stable equilibrium when it is under load and returns to its straight form even after a lateral force is applied and removed (See Figure 1.1). There comes a point however, when this compression load is increased and the column doesn‘t return to its original form after lateral forces are applied. This load is known as its critical or buckling load. A state of instability is reached when the column load is increased so much that uncontrollable deflection occurs in the lateral direction due to such application (See Figure 1.2). A short column will fail by direct compression, whereas a longer column under axial or eccentric loading will tend to reach this state of instability more easily resulting in it buckling / bending. This is due to their slender nature and so the load carrying capacity of a column depends on a ratio of length to cross-sectional area (often referred to as its slenderness ratio).

Fig. 1.2 State of instability showing buckling

Fig. 1.1 Stable equilibrium of a column

A formula derived by Euler to describe the maximum axial load a slender column can carry before buckling is shown below:

Where F = maximum or critical load on column E = modulus of elasticity I = area moment of inertia L = unsupported length of column K = column effective length factor (value depends on the conditions of end support of the column See Figure 1.3)

Fig. 1.3 Column effective length factors


Using the formula above to calculate the maximum load a column can withstand before buckling, is a vital stage within the design process. This is because if a state of instability where to occur within a structure, it could potentially be a life threatening situation and so global buckling is designed to be avoided at all costs. However, there are some applications in everyday life where this structural concept of global buckling is very useful. One of these applications is outdoor camping and the use of a tent. The theory behind this concept of erecting a camping tent works totally opposite to that used to prevent structural elements failing due to bending collapse. Tent poles are designed to be highly elastic and so can cope with huge amounts of eccentric loading past their critical load point without failing. This gives the tent huge diversity for the user without the need for them to worry about the safety of the product. Camping tents are also designed with slenderness ratio in mind. Once connected all together, the length of such is extremely greater in comparison to its cross sectional area, hence the force required to bend the pole is minimal (in accordance to Euler‘s formula). The smaller the value of EI, which is determined by the materials properties and dimensions, and the larger the length, L, will result in a smaller driving force required to buckle to section. This would give greater ease to the consumer, saving both time and work effort to erect the tent. A greater value of L also provides a larger living environment by creating a much wider circumference of arc (larger dome).

By testing this theory of global buckling with a camping tent will prove just how easy and effective the structural concept actually is. The photographic demonstration can be seen below:

1

Compression force is applied and pole is still in stable equilibrium.

F

F

2

>F

Force applied is increased so that section reaches a state of instability causing it to buckle about the pinned „joints‟, hence causing the desired dome shape.

>F


Stages 1 and 2 from above explaining the demonstration can now be repeated using the actual shell of a tent to show how the theory becomes reality.

1

Force applied at either end is not great enough, so pole stays in a state of equilibrium and tent doesn‟t erect.

F

F

2

>F

Greater driving force is applied causing the pole to buckle, raising the shell so that a dome is formed, and a new „home from home‟ is created.

>F

Using the theory of global buckling to erect camping tents has proven to be extremely useful, as not only is it a very simple idea in theory, but one that is exceptionally practical, functional and ingenious at the same time. The tent poles lightweight material properties and ease of construction methods make it an essential item on any camping holiday to create a perfect home from home. With very little effort, knowledge or experience needed to use, yet having huge benefits along with a great satisfaction of comfort due to its robustness and safety factors, the camping tent is an excellent example of how structural concepts are used in everyday lives. References: 1. BETZ, Professor Joseph AIAA, American Institute of Aeronautics and Astronautics Column Buckling DATE ACCESSED: 24/10/2011 via http://www.aiaa.org/tc/sd/education/physics_of_sd/experiments/column_buckling/index.htm 2. ENGINEERS EDGE 2000-2011 Ideal pinned column buckling, Euler‘s formula DATE ACCESSED: 27/10/2011 via http://www.engineersedge.com/column_buckling/column_ideal.htm 3. SRINIVAS, Professor Kodali Buckling of columns (28/03/2011) DATE ACCESSED: 24/10/2011 via http://profkodali.blogspot.com/2011/03/buckling-of-columns.html


1.24 Bamboo bionic structure application in the buildings

TANG li .

1. Introduction Bamboo widely used in China for many years, people use in life such as load-bearing; Building materials (figure 1, 2), because bamboo has good toughness and it was broad at the base also each segment gradually become thin with the increase of height, its like a ladder shape equal strength structural. (Figure 3)

Figure 1

Figure 2

Figure 3

2. Analysis From the view of mechanics, the each segment such as Horizontal resistance to twist box, and can improve Horizontal


resistance to squash and shearing ability so in the wind lord resistance on each paragraph bending deformation basically the same ability. The characteristics of thick at the bottom then top fine was also adapted to the bottom had stronger bending

moment than top.( figure 4 ) Figure 4 The bamboo’s structure is a good mechanics model, people quoted this kind of structure use in high-rise building design, such as “Taipei 101” (figure 5) and “Jin Mao Tower ” (figure 6)

Figure 5

Figure 6

These buildings are above 400 meters, in the design of high building, people met many problem and the main thing is that the strong winds caused the sway of the building, especially in the typhoon area but use the bamboo structure can solve this problem, because the “bamboo joint” structure like ring to truss and outrigger together effect on building, they will greatly enhance the structure’s stiffness and reduce lateral displacement. 3. Example


This is a simple structure do not have the “bamboo joint” (figure7) and another simple structure have “bamboo joint” (figure 8) in the same loads of performance.

Figure 7

Figure 8

In the obvious contrast we can found the “bamboo joint” in the role of high buildings is very important. 4. Conclusion The sum up, bamboo’s structure has good toughness and stiffness because it has bamboo joint. In the high building, outrigger and the ring to truss is building’s “bamboo joint”. Bamboo bionic structure use in modern buildings not only for beautiful but also practical. 5. References http://www.docin.com/p-225863664.html http://www.structuralconcepts.org http://ztzx.forestry.gov.cn/


1.25 Post-Tensioned Concrete Concept Răzvan SENCU

Pre-stressing is a method for overcoming concrete poor tensile strength (Wikipedia.com). This method implies some tendons, namely strands or high strength steel cables, which are the tensioned elements while they induce compression stresses to the concrete either by bonding or by ends anchorages.(Sami Khan, 1995). As the name sais ―pre‖ means before. However, there are known two main techniques, one being the pre-tensioning and the second post-tensioning. The difference between is that for the first case the cables are tensioned before concrete pouring and released once the concrete become cure, while for the second method usually the components are precast and tensioned by the tendons once they had been mounted in situ. In other words, the pre-stressed concrete is considered to be a combination between concrete and steel, similar to ordinary reinforced concrete, that comes to form a ―resisting couple of forces‖ that will counterbalance the ―external applied bending‖. (David Childs, 2010) ―Post-tensioning is a technique of pre-loading the concrete‖ in such a way that the ―tensile stresses that are induced by dead and live loads‖ will be eliminated or considerable reduced. (Sami Khan, 1995) The main advantage for using pre-stressing is that the concrete beams can span longer with reduced cross section.

Figure 1. Infinity Bridge across River Tees (free photos Flickr.com) A small research was carried out on The Infinity Bridge. The following picture shows the load transfer path of the bridge. It is fairly obvious that the twin-arches give not only vertical reactions but also horizontal thrusts.


Figure 2. Load transfer path (modified picture from http://geometrygym.blogspot.com/) A key feature of the design of The Infinity Bridge is that the horizontal reactions of the arches are not taken by the middle pier. They discharge on the lateral strands (see figure 1 right photo) which were provided to tie the bridge‘s concrete deck. In this elegant manner they achieve both the posttensioning of the deck and the stability of the arches at the same time.

The above images

explain the structural concept of the Infinity Bridge‘s post-tensioned concrete deck. Let us assume that we have a simple idealized arch with no initial loading as in the first image. At the both ends there is connected one wire each, different in colour with little helmets on their opposite ends. It can be observed in second image that once the arch is loaded will give lateral movement of


both ends. Having the two wires crossing each other, the distance between the little helmets will decrease, therefore it can be concluded that any member between this two helmets will be in compression. The beauty of the post-tension stays in the fact that engineers are able to use the internal forces induced by parts of their structure as favourable pre-tensioning forces. Conclusion Based on this small example and the thousands of successful pre-stressed bridges that have been built along the years for once we can state that the pre-stressing gives a more efficient and economic design. References: [1] Retrieved October 28, 2011, from Wikipedia.com: http://en.wikipedia.org/wiki/Prestressed_concrete [2] David Childs, Retrieved October 28, 2011, from www.childs-ceng.demon.co.uk [3] ]ami Khan, M. W. (1995). Post-tensioned concrete floors. Oxford: Hartnolls Limited, Bodmin, Cornwall [4] www.structuralconcepts.org [5] Research Methods – Dr. Dr Tianjian Ji, handouts - free photo Flickr.com - modified picture from http://geometrygym.blogspot.com/


1.26 Concept of vibration reduction in a structure through Base Isolation By Sam Higginson 1. Introduction Base Isolation is a method of reducing vibrations in a structure, commonly used when designing structures in earthquake prone environments. Base isolation essentially involves disconnecting the structure from the ground, protecting it from the seismic shear forces imposed by the movement of the ground surface. This is done by introducing elements into the structure that have a low horizontal stiffness. Energy is not passed into the structure and is instead deflected through the system dynamics.

2. A Method of Base Isolation Elastomeric bearings are a common modern method of base isolation, which are very effective. A diagram is shown below:

Figure 1

During seismic ground movement the rubber bearings flex and become stiffer, this pulls the structure back in the opposite direction, and eventually, once seismic activity has ceased, back into the structures original position. A lead core within the elastomeric bearing helps dampen the swaying force. Mechanical links are also needed to prevent the structure from moving under normal loading conditions; such as wind loading. In the case of elastomeric bearings, the mechanical link can take the form of polystyrene blocks placed either side of them. The picture below shows a base isolated structure under construction with elastomeric bearings:

Figure 2


3. Base Isolation Model The following is a demonstration as to the effectiveness of Base Isolation on a structural model. A model was built and shaker table used to simulate seismic actions on the model. There were two tests conducted:One without base isolation, using a fixed structure:

Figure 3

One with base isolation, using rollers:

Figure 4

For both tests the shaker table was run at the same constant amplitude and frequency. After 15 seconds the table was turned off, and the structure allowed come to a rest. Throughout each test two accelerometers at different positions on the structure calculated the sideways accelerations of the model. The results are shown below in graph form: Without Base Isolation:

Figure 5

With Base Isolation:

Figure 6


4. Results Analysis As shown by the graphs, accelerations in the structure were drastically reduced in the base isolated structure. For a real-world situation this would mean a huge reduction in the potential stresses on a structures main columns. After the shaker table was switched off at 15 seconds the base isolated structure took a much shorter amount of time to come to rest. This would limit the potential for damage to be caused to a structure in a real-world situation.

5. Conclusion A simple test demonstrates just how extremely effective base isolation is at preventing vibrations from being transmitted into a structure, and shows why it is so widely used in modern seismic engineering.


References Information Own work conducted during my BSc Civil Engineering course. Course notes – University of Salford. Seismic Engineering Bozorgnia, Y and Bertero, V (2004). Earthquake Engineering - From Engineering Seismology to Performance-Based Engineering. CRC Press, Boca Raton; United States

Edmund, B and Key, D (2006). Earthquake Design Practice for Builings. Second Edition. Thomas Telford, London Figures Figure 1 – Elastomeric Bearings: http://earthsci.org/processes/geopro/seismic/seismic.html Figure 2 – Bearing Construction: http://www.seismicisolation.com/ Figure 3 – Own Work Figure 4 – Own Work Figure 5 - Own Work Figure 6 - Own Work


1.27 Element of a Moment… THE LEVER ARM Yugal Angbo Definition: Moment is be defined as the measure of tendency to cause a body to rotate about a specific point at the distance from its action (Luebkeman, 1998). This is different from the tendency for the body to move in a vertical or horizontal plane or translate in the direction of the applied force. For moment to occur in a structure, the force must be applied upon the body in such a way that the part would begin to rotate. Moment occurs in a structure when the force applied does not pass through the centroid of the body. Anon (2010) confirms Luebkeman, 1998 by stating moment is equal to the product of the force and the perpendicular distance from its line of action to the point. Luebkeman (1998) on his article states that, there is a direct proportional relationship between the magnitude of moment of force acting on a specific point to the distance of the force which will be analysed in this paper. Moment can be calculated using the formula: Moment = Force x Lever arm Where, Force is the pressure being applied on the body Lever arm is the perpendicular distance from the force to the point of rotation.

Explanation by demonstration

Figure 1- long lever arm on the school bag

Figure 2- short lever arm on the school bag


A student carries equipment and books to school on a daily basis. The principal of moment applies when carrying a bag too. The length of the shoulder strap from the bag on figure 1 is much longer than on figure 2. Both the bags were applied a force of equal magnitude and it was observed that the amount of rotation on figure 1 was much more than on figure 2. Every aspect on this demonstration was kept constant for both experiments except the lever arm. This proves that the length of lever arm has a significant impact on the moment caused on the body.

Lever arm in accordance to equilibrium

Figure 3: equilibrium

Figure 4: moment on right is higher hence collapse of the body

Figure 5: equilibrium

Figure 3 clearly shows that the structure is in a state of equilibrium. The coins on each end of the ruler have same properties making the structure stay level. Figure 4 shows that extra coins has been added to the right hand side of the ruler. There is a movement in a clockwise direction of the ruler- which is a moment in the clockwise direction. There are several ways to bring the unbalanced structure shown on figure 4 and one of them is using the method of lever arm. Figure 5 also shows a state of equilibrium. Each of the coins weigh the same amount so despite having only four coins on the left- hand side and eight coins on the right-hand side, the structure is stable as the moment balances. Although the weight on the right hand side of the ruler is twice the weight on the left hand side, the moment asserted by both weights balances due to the difference in lever arm distance. The lever arm distance from the fulcrum of the left hand side is twice the lever arm distance of the left hand side. This being the case the moments asserted from the left hand side is equal to the right hand side hence is in a state of equilibrium.


Calculation to prove:

For the structure to be equilibrium the moment at both sides must equal: Moment at left = Moment at right 40 kN x 20 m = 80 kN x 10 m 80 kNm = 80 kNm hence in equilibrium.

Conclusion: The above demonstration and experiment shows that lever arm is a crucial element of moment and is vital in contributing towards the stability of a structure is there are any moments.

References: 

anon. (2010). Monet of a force. Available: http://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0016166.html. Last accessed 26th Oct 2011.



Luebkeman, C. (1998). Moment. Available: http://web.mit.edu/4.441/1_lectures/1_lecture5/1_lecture5.html. Last accessed 26th Oct 2011.

Bibliography 

Ryan, V. (2010). Forces. Available: http://www.technologystudent.com/forcmom/force2.htm. Last accessed 27th Oct 2011.


1.28 Easy Examples about the equilibrium ________RC Helicopter Yongzheng Yu（7962239）

Introduction: RC Helicopter, is short for radio-controlled helicopter,which caused crazy chasing since it was born.Most of children,especially for the boys,may dreamed about flying in the azure sky one day.With the development of technology,flying in the sky is not a dream any more,but have you considered of controlling a airplane or helicopter to hover freely. Just take a few minutes to have a look at this paper, and watch the video (the internet link) at the end of this paper, you must be facinated by that.

Some Simple BasicModels 1.Gyro The blades,the most significant difference from other kind of planes,which consists of the primory souce of motivation. When the blades rotate in the clockwise direction, the tail also move to the left (Figure 1),which means there is needed a force to balance the tail’s rotation.What the engineering come up with a

Figure 1 Gyro

solution is to add one tail blades, usually lean about 7 degrees.The degrees needed is so comprehensive, denpends on different speed of blades’rotation, the wind speed, the total weight of the helicopter and so on. This the most simple case of balance.After the engineer banlance the main blades’ rotation and the force generated by the tail blades,the helicopter can move forward.

Understanding Structural Concepts 2. Death Spiral Death spiral,as the name suggested, through the controler let the helicopter’s main blades to be vertical ,then make the helicopter rotating as many as possible(just explained in the right graph). When the helicopter rotating around the circle,the force generated by the main brades should equal to the centripetal force.(showed in the figure 3)

F

F=m*v*v/r

Figure 3 Figure 2 The Death Spiral What showing above is just some simple movements of the RC helicopter, have you considered the real helicopter,what they can do? Of course they can , but in most circumstance, they do not allowed to do this movements,which is quite dangerous. (http://wn.com/REAL_Helicopter_does_BACKFLIP!) To find more information about the RC helicopter,just click the following links below.

http://www.rchelicopterfun.com/index.html http://rchelicopters3d.blogspot.com/ http://www.rchelicopter.com/


1.29 Bending Moment and Deflection Your Names: Shahabaldin Mazloom

EXAMPLE 1:

Fig. 1-1: Lumber in construction scaffold with distribution load by bricks.

w1

w2

MB A

D

B

RA

2.0 m

RB

2.0 m

C

RC

Fig. 2-1: Analytical Shape

Figure 1.1 shows the construction scaffold that is like a braced frame with two spans. The top lumbers can act as beams in this position which are connected to the pipes of scaffold at the first and end edges and middle. There are some bricks on the right hand's lumber. The weight of each brick is about 25 N then distribution load due to the weight of bricks will be 1750 N/m for w1 and 1250 N/m for w2. Number of bricks for w1: 35, and the length of loading (L1): 0.5m then distribution load (w1) will be 35×25/0.5 =1750 N/m. Also for w2, the numbers of bricks are 40 and L2 is 0.8m then w2 will be 40×25/0.8=1250 N/m. In figure 2.1 the shape of the first figure is converted to the structural analysis shape. By the analysing of the beam, the reaction forces, bending moments and deflection will be obtained. After analysing by software, magnitude of the supports' reactions and shear forces, bending moment and deflection diagrams are obtained. Maximum vertical displacement happens in B-C beam that its amount is about 8mm.


3.1. Reactions

4.1. Deflection

5.1. Bending Moment Diagram

6.1. Shear Force Diagram

EXAMPLE 2: EQUILIBRIUM EQUATION

Fig. 1.2: Sample of Tower Crane


In the figure 2.2, the tower-crane should move the construction material with the weight of W4 at distance of L4 from centre of tower's column. L4 is variable. b

Fig. 2.2: Analytical Shape

a


In tower-crane, beam and column design as a truss and the cables on top of column that connect truss beam to the column, help to distribute an amount of load to the column and decrease the tension in member of beam truss. Also some heavy concrete sinkers in the rear act as opposite loads in equilibrium equation. Equilibrium equation: SM=0 SFx=0 SFy=0

M5 = W4×L4 – W1×L1 – W2×L2 – W3×L3 Fx5 = 0 Fy5 = W1 + W2 + W3 + W4 + W5

The cables design according to maximum created tensions, T1 and T2. In each side there are two cables then the value of tension is divided in two parts to find amount of tension in each cable and design them. For design these kind of structures the height of column (H1, H2) and angle of cables (a, b) are important.


1.30 Why a roly-poly toy can’t be pushed over Yang Li 8048596 Introduction A roly-poly toy is a toy that rights itself when pushed over. The bottom of a roly-poly toy is round, roughly a hemisphere (Figure 1). Do you know why it can‘t be pushed over? The secret

Figure.1 A roly-poly toy

is that it has a centre of mass below the centre of the hemisphere. Actually, we know that the centre of gravity of a body is the point about which the body is balanced or the point through which the weight of the body acts and the location of the centre of gravity of a body coincides with the centre of mass of the body when the dimensions of the body are much smaller than those of the earth. Model demonstration

Figure.2


As shown by figure 2, when the roly-poly toy is pushed over, the position of the centre of mass rises compared with the upright one, thus causing a moment of resistance M which is M=G*d Then, considering its smooth bottom which means a small friction, the roly-poly toy will seek the upright orientation after wobbling for a few moments. Conclusion From the model, we can find the fact that the lower the centre of mass of a body is, the more stable is the body.

Reference 1. http://en.wikipedia.org/wiki/Roly-poly_toy.[Accessed 26 October 2011] 2. http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts.[Accessed 26 October 2011]


1.31 Critical load of a structure Fanglei Jia (7411707) Introduction Critical load is the load which creates the borderline between stable and unstable equilibrium of the structure or is the load that causes buckling of the structure. 1It also can be present numerically as Pcr=Π2 EI/Leff2. A following physical model is introduced to shows the above concept. Physical Model

Figure 1, experimental equipments Equipments  Two paper columns are removed from toilet roll. (One remains circular shaped cross-section and other one shaped to square cross-section.  Books  Scotch tape Experimental procedure

Figure 2, circular column and square column The figure 1 shows the two columns are fixed on a table by using scotch tape. Both columns have same young’s modulus (E) and effective length (Leff) but different second moment of area (I). Following experimental results performs which columns will buckle first when same load applied to the two columns.


Experimental result

Figure3, square column

Figure4, circular column

The result shows that the square column is buckled first when same load applied to the columns. Therefore, the square column have smaller critical load compare to circular column. However the critical loads of two columns can be compared theoretically. Theoretical result Both columns have same outside perimeter (D) and thickness (t), which is measured as: D=16.5 cm, t=0.1cm.The second moments of areas are calculated as: Isquare=4.37 cm4 Icircular=5.37 cm4 Both columns also have same young’s modulus (E) and effective length (Leff) .The critical loads are: Pcr (square) =4.37*(Π2 E/Leff2) Pcr (circular) =5.37* (Π2 E/Leff2) Therefore, the square cross-section column have smaller critical load compare to the circular one. The theoretical result is corresponding to above experimental result. Conclusion Cross-sectional shape can affects the buckling load of a column. The critical load is proportional to second moment of area (I); a greater critical load can be achieved effectively by increasing second moment of area.

Reference 1. Seeing and touching structural concepts website, http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/


1.32 UNDERSTANDING STRUCTURAL CONCEPTS Nur Bahiyah binti Mohd Shukuri DEFINITION OF EQUILIBRIUM Equilibrium is synonym with balance, stability and symmetry. The meaning of equilibrium is the equality of weight or forces, which is produce in a condition where all the acting influences are cancelled by one another, resulting in a balance, stable and unchanging reaction. In other words, equilibrium state can only be achieved when: 1. The summation of forces and moments, in a static system is equal to zero. 2. The summation of external forces is equal and opposite to the internal ones, thus the moment is also equal to zero. 3. The summation of horizontal forces from right is equal to the summation of forces to the left 4. The summation of vertical loads from upward direction is equal to the summation of loads downward direction.

STATIC EQUILIBRIUM & DYNAMIC EQUILIBRIUM Static Equilibrium refers to a condition where an object that have no movement forces acting on its potential energy either reverse or forward processes. By definition, in a static equilibrium there is balance, but no changes, disturbance or movement. Dynamic Equilibrium, however is similar with static equilibrium, but with movements. A dynamic equilibrium exist when a reversible reaction occur by changing its ratio of product. However, the equal rate remains the same. An easy example to understand is, a table has static equilibrium, and a car has dynamic equilibrium.

THE STATE OF EQUILIBRIUM The structural concept that i am using to prove the state of equilibrium is basically similar to a seesaw. This simple demonstration is done by using a ruler (15cm) and stick-on-paper which are all the same size and weight (0.1N). As you can see both side A and B are completely still because it is in the state of equilibrium. Since the reaction and length of A is the same as B, therefore the moment is zero. In other words, no movement will occur at either side.


If we applied more load at point B, for example by increasing the load to 0.2N, the ruler starts to move further down creating an anticlockwise moment. Therefore, in order to reach equilibrium, we have to determine the moment of clockwise as well.

Calculation: Anticlockwise moment at point A, (0.1N) x 10mm = 1Nmm Clockwise moment at point B, (0.2N) x 5mm =1Nmm  Hence, structure is in equilibrium.


CONCLUSION Based on the experiment, I can conclude that the equal value of moment distribution at both clockwise and anticlockwise direction must be made in order to achieve equilibrium. Therefore equilibrium describe perfectly clear that it is a state of an object in which all forces acting upon it are balanced. The forces mention includes both vertical and horizontal components.

REFERENCES 1.

http://ceae.colorado.edu/~saouma/Lecture-Notes/s4a.pdf

2.

http://dictionary.reference.com

3.

http://www.answers.com/topic/dynamic-equilibrium

4.

http://www.physicsclassroom.com/class/vectors/u3l3c.cfm

5.

http://www.technologystudent.com/forcmom/force2.htm

6.

http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/

7.

http://web.mit.edu/emech/dontindex-build/full-text/emechbk_2.pdf

8.

http://www.epito.bme.hu/me/kutat_prog/fajlok/10/al_thesis.pdf

9.

http://en.wikipedia.org/wiki/Static_equilibrium

10.

http://en.wikipedia.org/wiki/Dynamic_equilibrium


1.33 The Physics of Figure Skating Samar Raffoul Introduction: Have you ever wondered how figure skaters do their moves? How they seem to defy gravity, friction and all the other forces of nature? In fact these moves, however magical they appear, can be easily explained… In addition to strength, balance and practice, all these complicated steps are built on simple concepts in physics…

Speed Skating Speed skating is a type of skating used in competitive racing, hockey playing and sometimes figure skating. The aim of a speed skater would be to increase his speed as much as possible.

Charles Hamelin skates during the preliminary rounds of the ISU World Cup Short Track Speedskating Championships on November 13, 2009 in Marquette, Michigan. Jonathan Ferrey / Getty Images

Theory: Ice has negligible friction. According to Newton‘s first law, “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.” Newton In other words, the ice skater‘s motion will not be opposed by friction. Any tiny force can push the ice skater into a motion that remains almost constant hadn‘t it been for the air resistance… The air resistance is another force that can slow speed skaters down. In an effort to increase their speed, skaters crouch or stoop to decrease the area of contact of their bodies with air and thus increase their speeds.

Spinning Spinning is process where skaters spin around themselves at very high speeds. According to the Guinness world Records , The fastest spin on ice skates reached a rotational velocity of 308 RPM . Such speeds cannot be achieved by a human being without physics. Theory This phenomenon basically relies on angular momentum. The angular moment of a particle is given by : L=mvrsinѳ For a circular orbit , L=mvr


Where m is the mass of the particle, v the velocity, and r the radius of rotation (or the distance from each rotating particle to the rotational axis) Angular momentum is conserved . So, L1=L2 mv1r1=mv2r2 Since the mass of the skater is constant, the only way to increase the velocity and make a spin possible would be to decrease ―r‖ by pulling the body (arms and legs) closer together (bringing them closer to the center of the body). Below is a figure explaining this phenomenon.

from Nick Strobel's Astronomy Notes For a more visual explanation, please follow this link. http://www.youtube.com/watch?v=eCxFghwy5Rk

Spiral The Spiral , also known as the arabesque , is a very popular move among ice skaters and ballerinas. In a spiral, the skater slides on one foot, and extends the other foot above the hip level.

Painting Courtesy of Artist Larisa Gendernalik

Theory


In order to achieve a spiral, the skater has to position his body in such a manner that allows his center of gravity to be aligned with the reaction force coming through the foot in contact with the ground…

From the Bryn Mawr Library , “Physics of Sports”

This posture requires a lot of concentration , but once the forces are aligned, the net forces in the vertical direction become zero , no torque is created and the skater is in complete balance.

Bibliography

1-

"GUINNESS WORLD RECORDS-HOLDING FIGURE SKATERS GO FOR THE GOLD IN VANCOUVER." Guinness World Records. N.p., n.d. Web. 22 Oct. 2011. http://community.guinnessworldrecords.com/_GUINNESS-WORLD-RECORDSHOLDING-FIGURE-SKATERS-GO-FOR-THE-GOLD-INVANCOUVER/blog/1866731/7691.html 2- http://www.youtube.com/watch?v=eCxFghwy5Rk

3- Kluger, Jeffrey. "The Bryn Mawr School Library." Library - 25 Oct. 2011. http://207.239.98.44/Physics%20of%20sports.asp . 4- Reid, Evelyn. "1." Olympic Speed Skaters From Quebec at the 2010 Winter Olympics , 23 Oct. 2011.

1.34 Jenga Block YUCHEN FU A series of engineering technical applications are based on the fundamental structure concepts which combined mechanic theory and real phenomena. There are different kinds of structure concept models in the daily life and the model introduced in this project is the well-known Jenga Block. The Figure 1 indicates the famous game – Jenga Block which allows players to translate the blocks from any storey other than the top in turn. And the major purpose of the game is retaining the Jenga tower be stable. Jenga game demonstrates the basic mechanic theory in touching the structure concept because understanding the concept – Equilibrium is the key point to win this game. The stability of Jenga tower depends on the equilibrium between two neighbouring up and down blocks. To be more specific, each level of blocks is acting as both support for the upper blocks and dead load for the lower adjacent blocks at the same time. Therefore, analyzing the effective method to use the least of blocks as the support and dead load at the same time is the major issue. (1) Equilibrium condition of blocks acting as support As shown in Figure 2, three blocks are placed in each level and the mass and length of each block is M and L. It can be seen that there are only three different ways to move blocks from each level without causing collapse according to the mechanic analysis.

Figure 2 Mechanic analyses of blocks

The first method takes two blocks to be the support at two sides, which is as same as simply supported beam, and the reaction of each support is 3/2 Mg. Therefore the towel is equilibrium.


The second method is using only one block in the middle to hold the upper blocks. As shown in the Figure 2, the upper blocks in both left and right side are cantilevered and both of them could cause the moment in the same value but in different direction:

=

=1/9MgL.

Therefore, this method also can make tower be equilibrium. The last method is using two blocks in the one side to support the upper blocks and it has the same function as Method one and Method two since the moment caused by cantilevered side can be balanced by the other side of blocks, and the additional block will provide more stability for the upper blocks. (2) Equilibrium condition of blocks acting as dead load. Since the blocks are acting as support and dead load at the same time, the moving methods of ―dead load‖ blocks are as same as the condition (1). Therefore, there could be nine kinds of ways of removing blocks to keep the tower stable, which based on the theory of permutation and combination. (Figure 3)

Figure 3 Example of patterns of removing blocks

The Jenga Tower not only represents the application of equilibrium method but also express the concept of ‗More Uniform Stress‖ which means more stress distribution would lead to more effective design. That is to say, it is not necessary to use materials as many as possible to keep the structure stable because the small amount of materials applied in the effective position could make the structure stable. There are kinds of applications of the concept of Jenga tower in the real structure design.


As shown in the Figure 4, The building is the famous ―Jenga Tower Building‖ named 56 Leonard which located in New York, USA. The Building took advantages of Jenga Blocks tower and provided a wider field of view for residents. The building use the Jenga Blocks pattern which has the strong stability and it also makes the building looks fashion and beauty. The Jenga tower indicates a basic structure

concept

which

could

be

applied in the real life design. And it can be seen that every complex structure design is concluded and developed from basic theoretical model. Therefore, get better understanding of principle of the fundamental phenomenon would contribute a lot to the real structure design.

References Figure of 56 Leonard Building, New York. http://www.56leonardtribeca.com/#/globallandmark-by-herzog-and-de-meuron. Figure of Jenga tower. http://www.doobybrain.com/2007/10/13/jenga-sitting-next-to-agiant-pile-of-wood/


1.35 DEMONSTRATION OF EFFECT OF WATER (MOISTURE) IN SETTLEMENT OF STRUCTURES Arun Ammini Amma Rajappan Nair Aim: To demonstrate the effect of water (moisture content) in the settlement of structures by a simple example. Equipments Used: Measuring Scale, Sponge, Cylindrical tin with water total weighing 300g. Theory of Settlement: Foundation Settlement is the shifting of foundation and the structures built upon it in to the soil. Areas with moist soil will face more settlement than dry areas. The more the moisture content of the soil, the more is the settlement. Experiment: The sponge is placed on the level surface and the cylindrical tin is placed centrally over it. Then the total height from the level surface is measured. Then the sponge was soaked in water (indicates saturated soil in site) by pouring water to the sponge from sides and the total height was measured using scale after 30 minutes. This time it is found to have settled more by 4 mm.It is found out by finding out the difference of first and second height measured. Experiment Figures:

Figure 1

Figure 2

Calculations: The initial measured height=15.6cm. The final height measured =14.1cm. Difference in height (Settlement) = 1.5cm. Settlement occurred when soaked in water= 1.5cm. Result: The experiment proved that the cylindrical tin settled in the sponge when the sponge was soaked in water to about 1.5 cm. Inference: It can be inferred from the above experiment that as the moisture content increases in the soil beneath foundations the rate of settlement of foundations too increases. This causes the settlement of the whole structure. The above experiment is a practical illustration of the actual settlement which takes place in the structure.


1.36 Relation between deflection and length of rigid nails subjected to concentrated load at free end. Anargyros Dasargyris Description of concept: In this concept, it will be examined the deflection of four rigid nails (nailed to a wall) according to the length of each one respectively as it is illustrated in the figure below. All the nails have the same material properties and geometry. Moreover, it will be determined the deflection in times of L (nail length) using the unit load method. Finally, a graph will be plotted in order to understand the relation between deflection and length.

Figure 1: Shows the experiment's concept

Experiment Process:


1. Proof of the cantilever deflection formula (

) using virtual work method.

P = 1 P

Mmax

SFD

BMD

Figure 2: Shows the deflection of a cantilever beam

Where: 

P= 1 (unit load)



VED= P



Mmax= PL

The bending moment for the nails is the same such as the above bending moment diagram. Due to the same material properties of the nails, geometry and load, which are subjected it is assumed that

U.

Where: 

P: concentrated load at free end



E: modulus of elasticity



I: moment of inertia

2. Determine the deflection: a) For L = L (1) b) For L = 3/2L (2) c) For L = 2L (3) d) For L = 3L


(4)

3. Plot the graph between δ and L: It is already known that the deflection graph should be similar as the figure below which is the function

whereα=1. However, in these experimental cases α≠1.In addition

only the positive values in the first quadrant are considered, because length=L is always positive with L>0. In order to be plotted the graph it is assumed that L= 1 unit.

Figure 3: Graph of f(x) =ax

The graph according to the determined values is: L

δ

0

0

1

0,333

1,5

1,125

2

2,667

3

9

3


Figure 4: Deflection graph of nails

4. Conclusion: The purpose of this experiment is to simulate the deflection of the nails with cantilever beams. It is proved that the deflection is proportional with the length and as the length increased, the deflection increased as well. It is not a linear proportion due to the cubic power of the L-value (length) in the deflection formula. Finally, as the figure below shows, the experimental deflection graph follows the main pattern with the general graph of

function with α=1.


Figure 5: Comparison of the two patterns

References Figure 1: Created using the Google Sketch Up 8 software Figures 2, 4, 5: Created using the Microsoft Office Excel software Figure 3: Created using Mac Grapher


1.37 The need of the worlds biggest structural foundations Nikolaos Vlachos Introduction:”Rion Antirion Bridge” is a cablestate bridge that exists in central Greece,at the gulf of Corinth.It is a simple structure?four concrete towers support a massive steel road spanning of 2200m throught cables and the total load of the structure transports from the towers to simply suported foundations and finally to the soil.The problem with the structure is the soil, that supports the load of the structure at dept of 80 meters below the sea level.There isn’t steady ground?There is only low bearing capasity soils.At 15 meters bellow seabed there is only silt,clay and sand.At 450 meters there is solidstate bedrock but the depht is prohibitive for any kind of foundation such as pile foundations.The solution was circle foundations with enormous footing area of 1,5 times a football stadioum that is aproximate 120x90x1.5=16200 m². Experimental procedure The experiment consists of two jelly stuffed donuts, one carton cup and a pen. Carton cup and pen have almost the same weight. Both pen and carton cup represent the pile of the bridge. The increasing load represents the increasing weight of the tower during construction phase. The donuts represent a non cohesive soil such silt or clay fully saturated. The force that is applied is the same on pen and carton cup. CASE 1: Small area foundation touching seabed and increasing load

LOADING  Pictures above shown small area tower before and after applying load to seabed CASE 2: Big area foundations touching seabed and increasing load

LOADING  Pictures above shown small area tower before and after applying load to seabed Conclusion: The small area foundation in case 1 has settlement that is prohibited. As the load increase the stress in the edge of the pen increase with result the pen to easily penetrate into the donut mass without resistance as the donut resisting stresses that apply on the pen are unable to resist due to a small resisting area. When area


decreases, pressure increases, with result the pressure to overcome the bearing capacity of the soil and the foundation to fail due to extreme settlement. This is dangerous in constructions because soft and anisotropic soil conditions or external physical parameters such as an earthquake or wind may cause the bridge tower to tilt under pure soil resistance. The bigger area of the carton cup distributes less pressure, in equal cup area on donut with result the donut stresses to resist as the stressess that apply cannot overcome the resistance stresses of the donut. Pressure equation  P=F/A where:  P is pressure  F is the load  A is the area. REFERENCES: National geographic rio antirio bridge < http://www.youtube.com/watch?v=dmwIjpjcPv0&feature=channel_video_title >


1.38 APPLICATIONS OF STRUCTURAL CONCEPTS IN NATURE SHSHANK RAINA CONCEPT In the case of a cantilever, due to the loading the beam bends in the direction of the load. One side of the beam is in tension while the other side is in compression. To reduce the tension in the beam strings are attached to take up the tensile forces and transferring it to the support. The bending of the beam thus reduces.

Figure 1 APPLICATION IN CIVIL ENGINEERING Similar is the case of a cable stayed bridge. In the case of a cable stayed bridge the cables that join the pillar to the bridge deck are in tension, the tensile forces are transferred through the columns to the foundation of the bridge. The purpose of transfer of the load and preventing the sagging of the bridge span is served.


Figure 2 APPLICATION IN NATURE

Figure 3 The above figure is a case of an animal with a long neck. Now the loads acting on the neck, i.e the head has a significant load. It can be understood as a cantilever action where the neck is the beam and the head acts as the point load. To prevent sagging of the neck nature provides the animals with a similar mechanism as tensioning of the cables. In the above figure the red lines are the tendons in the neck of the animal which act as tension members. The tendons are in tension when the animal bends down the neck and transfers the tensile force to the ground via the legs in a very simple manner. The body of the animal also resembles a type of cantilever bridge with the tendons from the neck and the tendons from the vertebral column of the animal transferring the tensile forces to the point A and eventually to the ground.

The mechanism is illustrated in the following videos. http://www.youtube.com/watch?v=u-uni3D2wNQ&feature=related http://www.youtube.com/watch?v=h5B71oBtjps

REFERENCES www.youtube.com www.wikipedia.com http://www.kollewin.com/blog/cable-stayed-bridge/ http://www.howtodrawit.com/animalmovement2.html


1.39 ACTION OF FORCES ON ARCHES IN PRACTICAL WAY FRANCIS A UKPEBOR AIM: TO PROOF THE ACTION OF FORCE ON ARCH EQUPMENT: PLAIN RECTANGUAL SHAPED PAPER 2mm THICK, CAMERA DEFINITION An Arch is a curved symmetrical structure spanning an opening and typically supporting the weight of a bridge, roof, or wall above it. An arch as a crown which is higher than the support, the support is at both ends called the thrust. CONCEPT Plain paper folded in a rectangular shape of 2mm thick. Paper is placed of the floor to take the shape of an arch which is simply supported at both ends of the ground. This illustration is shown in figure 1 below.

Fig 1 simply supported arch with no load Load is uniformly distributed from the top of the arch as shown in figure 2 and the result is illustrated in figure 3. As a result of the load that was applied, there is a collapse.

Fig 2 load exerted on the arch

Fig 3 collapse arch

At support, the horizontal force should be sufficient enough to keep the arch in its position whilst bearing load, else it would collapse. This is illustrated in the diagram below.


CONCLUSION The arch must be designed to safely withstand the severe combination of forces or load likely to be applied. REFERENCE 1.

“Structures: Theory and Analysis” by MS Williams and J D Todd Macmillan Press Ltd, London. ISBN 0-333-67760-9.

2. GOOGLE IMAGES.


Examples


2.1 Equilibrium in Asymmetrical Cable-stayed Bridge Alamillo Bridge and Sundial Bridge Hossam Mustafa Introduction: A body is said to be in equilibrium if sum of all reaction forces on a body is equal to the sum of all the action forces. This report explains the concept of equilibrium used in asymmetrical cable stayed bridges without any backstay supports. Alamillo Bridge: Alamillo Bridge is free standing cable-stayed bridge spanning 220m located in Spain. The bridge comprises of a single pylon of height 134m leaning at an angle of 58 degrees (figure 1). This is a selfbalancing bridge in which the pylon does not require backstays due to its self-reliance on its own weight to neutralise the forces exerted by the deck. As a result, this prevents moments from being produced at the pylon base allowing vertical forces to be transmitted to the bedrock beneath without overturning. The inclined tapered pylon causes the steel cables connecting pylon to transverse ends of the road deck to remain in tension When the cable stays and the deck exert a forward downward force, the weight and bend of the pylon exert a backward downward force to achieve equilibrium (figure 2). The steel box girder of the pylon and steel deck structure were filled with concrete, in order to counter balance the vertical downward forces. In addition to that, the horizontal forces of the roadway counteract the horizontal component of force due to bent pylon in order to keep the bridge stable.

Figure 6: Alamillo Bridge

Figure 7: Forces in Alamillo Bridge


Sundial Bridge: Sundial Bridge located in California is also cantilever spar asymmetric cable stayed bridge without back stay supports spanning 213m, having a pylon height of 66m inclined at an angle of 42 degrees (figure 3). The structural concept of equilibrium used in Sundial Bridge is same as mentioned above, but the steel deck in this bridge comprises of tubular truss members. Although the truss deck is capable to span the river, but steel cables are required to prevent deflection, which is expected to be 3m (without the cables) in order to keep the bridge in equilibrium. The small movement due to deflection increases its potential energy, but when load is released, it tends to move back to its original position, thus, keeping the bridge in equilibrium.

QuickTime™ and a decompressor are needed to see this picture.

Figure 8: Sundial Bridge

References: 1) Mort.R (2009), A critical analysis of Santiago calatrava’s turtle bay sundial bridge, Proceedings of Bridge Engineering 2 Conference 2009, University of Bath, UK. 2) Woodruff.S & Billington.D, Aesthetics and Ethics in Pedestrian Bridge Design, 2005. Available from: http://www.dist.unina.it/proc/2005/FOOTBRIDGE2/Billington%20Keynote1_/PAP_Billington.pdf, Last Accessed on 29/10/2011. 3) Seeing and touching Structural Concepts Available from: http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/contents/, Last accessed 27/10/2011.


2.2 Tuned Mass Dampers Likhin Hassan Dharmaraju Year by year buildings are racing against the height and setting up new records. But, building such a tall structure doesn‘t come easy. Tall structure means more problems; they have to overcome the nature‘s destructive forces such as wind and earthquake. Day by day, new structural systems are developed to handle these forces. Tuned Mass Damper is one such system which reduces the vibrations or sway in the building during heavy winds and earthquakes. The working principle behind these dampers is really amazing.

Figure 1: Tallest buildings [Ref: Wikipedia, Accessed online on 24th Oct 2011] During the heavy winds, tall structures sway to and fro up to several meters just like a tall tree subjected to heavy winds. This might even damage the structures and such a sway means discomfort and instability to the occupants. During the sway, the top of the structure moves away from the original position and it stores up the energy in the form of potential energy and this energy is later converted into kinetic energy then back to potential energy, causing to and fro motion until all the energy is dissipated , just like a simple pendulum. To cater this problem, Tuned Mass Dampers are installed in the tall structures. These dampers usually consist of a counter weight, which is suspended at the top of the building. During the sway motion, this suspended counter weight moves in the opposite direction of the sway and the counter weight stores up some energy and this energy is dissipated by the dampers connected to the counter weight. This reduces the sway of the building and hence the energy built up in the structure. This brings back the structure to normal position with less sway by the effect of dampening. These dampers can reduce the response by 40-50% (Kareem et al., 1999). A similar damper can be found in Taipei 101.


Figure 2:

a) Sway to left

b) No sway

c) Sway to right

Mass of the suspended counter weight depends on how tall the structure is and the horizontal wind forces for which it is designed. Sometimes these counter weights required are of huge masses and turn out to be very expensive. In such cases smaller counter weights powered by hydraulic jacks are installed. These hydraulic jacks are fitted with the sensors, which detect the sway and push the counter weight in the opposite direction by a greater distance to reduce the sway of the structure. These hydraulic jacks can push the counter weight in any required direction depending upon the direction of the wind.

Figure3: Tuned Mass Damper [Source: Extreme Engineering, Tokyo‘s sky city] Tuned Liquid Mass Dampers have also found their applications in recently constructed tall structures. One of the latest structures is One Rincon Tower; a residential complex which is built on the Rincon


Hill of California, United States (Wikipedia). This building is 697 feet above the San Francisco Bay and is subjected to heavy wind loads generated in the bay. One Rincon Tower houses a water tank of capacity of 50,000 gallons and this tank consist of the 2 baffle walls or the screens which modulate the flow of water. ―As the wind moves the building one way, the motion of water in two large tanks atop the building will roll in other direction causing the building to move less and the inhabitants to feel the less sway‖ (San Francisco chronicle, Dec 29, 2007). In this way the energy which would have been stored by the building and later dissipated in the consequent sways is used up by the water and spent by the motion from 1 section of the tank in to other section of the tank through baffle walls. Refrences Kareem, A., Kijewski, T. and Tamura, Y. (1999) Mitigation of Motions of Tall Buildings with Specific Examples of Recent Applications. Wind and Structures, Vol. 2, No. 3, pp. 201- 251. Wikipedia, http://upload.wikimedia.org/wikipedia/commons/e/e2/Tallest_Buildings_new2.png [accessed 24th Oct., 2011]. Wikipedia, http://en.wikipedia.org/wiki/One_Rincon_Hill [accessed 24th Oct., 2011]. San Francisco chronicle, 29th Dec., 2007. Tokyo‘s sky city, Extreme Engineering, Season 1 Episode 1.


2.3 Air-formed Domes Mohamed Nafil (8139202) Dome-“a rounded vault forming the roof of a building or structure, typically with a circular

base‖ (Oxford dictionary)

The Prophet’s mosque in Saudi Arabia

Dome of St.Peter‘s Basilica in Rome

Introduction Domes are the most difficult structure to build and design for an engineer. They are also one of the most expensive and time consuming structures to build. When complete, domes and hollow pyramid are self supporting and extremely stable. But while construction they are extremely unstable.

Dante Bini’s method Traditionally builders filled their domes with scaffolding. But in 1960’s, Dante Bini an architect came up with a new idea of erecting his domes in a simpler, quicker and less cost effective way known as Air-formed Domes (using only air). "I am able now to build a dome at lower cost even

than a conventional structure in no time because it takes about 60 minutes to lift and shape to the final position a dome a big as the Pantheon in Rome" - Dante Bini". A steady supply of air even at low pressure could lift and shape a heavy concrete dome structure.

At first the ground is leveled and a circular ring pit is dug for foundation. Then circular foundations are filled and leveled. Meanwhile the main inflatable formwork known as the balloon is tested side by side. Then they are brought back to G.L in a set of sequence and folded like a rectangular or square sheets. Over the formwork membrane many 3m*3m PVC sheets are


placed (overlapped) to reduce the friction. Concrete has to be reinforced to acquire its maximum strength. So a series of spring are stretched to required length and are laid across the inflatable formwork in a pre-determined pattern. They are pulled and connected to the outer spring in the circular foundation. As each springs are paced in a proper manner, length of conventional rods pass through them. This looks like a skeleton with hinged joints laid out on the ground, and the balloon inflated underneath it to lift it into place. We know that springs have no structural function; however they ensure that the structural rods achieve their designed position of the dome. This system controls the dome shape, the concrete thickness and also restricts the concrete from slumping down.

1. Placing the springs and reinforcement.

2. Pouring the concrete.

The next step is concrete pour. A special type of concrete is used in this method. The concrete is poured evenly throughout the base. Once the base is filled with concrete, an outer membrane is rolled over the wet concrete surface. Before the pumping is done, an vibrator is placed on the centre of the circular base with strings attached to make it move freely. Now the pumping starts. Air is blown into with a pressure no more than to puff a cigarette. It is the only power which lifts the concrete in to the desired shape. The final shape of the dome is acquired depending on the size of the dome structure. Once the shell is up, the vibrators are moved around the external surface of the dome in a desired path. By doing this, it ensures that the concrete is properly packed and spread evenly within the inner and outer surface of the dome. Now the air pressure is maintained inside the dome depending on the diameter of the structure. This is the setting period of the concrete.

3. Inflating the membrane.

4. Using the roller vibrators.

After few hours the inner and outer membrane are removed. These membranes can be reused for further projects. Once the concrete is fully set, the position of the doors and windows are made by breaking and drilling that portion. A vapor barrier is applied over the dome and also painted with waterproofing materials. Using this concept Dante Bini has built more than 1,600 buildings in 23 countries.


5. A computer model of Morden Bini shell.

Conclusion We come to know form Dante Bini‘s method that even heavier loads such as concrete can be lifted easily with just applying air pressure in a uniform manner. This can be also applied to erect even heavier loads like steel (trusses/beams/columns etc.). These shell structures are also capable of resisting earthquakes and other natural disaster.

References 1. Media Wiki. 2011. Air-formed domes. [ONLINE] Available at: http://opensourceecology.org/wiki/Air-formed_domes. [Accessed 23 October 11]. 2. BINISYSTEMS. 2011. BINISYSTEMS. [ONLINE] Available at: http://www.binisystems.com. [Accessed 23 October 11]. 3. BINISHELLS. 2011. BINISHELLS. [ONLINE] Available at: http://www.binishells.com. [Accessed 23 October 11]. 4. Wikipedia. 2011. Dome . [ONLINE] Available at: http://en.wikipedia.org/wiki/Domes. [Accessed 23 October 11]. 5. All the images are taken from reference no.2, no.3 and no.4.


2.4 Improving the understanding of structural concepts Mohammadreza Bayran Direct Force Path in a simple picnic chair:

A picnic chair however it is so simple and small, it has got a structure system for itself and follows the rules of structures. A picnic chair when it is not being used, has a unstable structure which you can easily bend it and make it smaller but when you put it on the ground it will be stable and you can use it with no concern of chair failing. Here I will try to explain what the differences between these situations are and what changes that make it stable.

When chair is not being used, it can be considered like the frame shown in the picture below:


C

D

A

B

So when you impose load on the surface, because it is not restricted in any way (x, y, θ), if we consider the surface as beam which is not restricted and a force is applying on it, it will have buckling and we will have tension in the beam which causes two ends to get closer to each other and it closes, because the beam only can handle tension not compression so it causes bulking. But when it is being used and has been put it on the ground, the connection between the chair legs and ground will makes friction and it will work as a restriction for the structure and transfer the imposed forces to the ground which works like a foundation. Also because we don‘t have columns in the chair so we have to prevent it from falling down vertically, so at braces cross section we will put a restriction in the middle of diagonal members to prevent them from rotating more than for example 30ο. In the picture below I will show you how the loads are imposed on the chair and how they will be transferred to the bottom of the structure by diagonal members.

C

A

D

B

As you can see vertical force which at the first part caused the structure collapsed, right now is being transferred to the supports and transferred to the ground. If the we did not have diagonal members, and had vertical members instead such as column, the structure would fall again, because however we are imposing vertical load on the structure, but we get horizontal load also, so in order to transfer them to the foundation we would need members to handle them.

Conclusion: in every structure we design we should consider the horizontal load restriction even though there is no horizontal load, because there will be horizontal force because of member`s actions and turn the vertical load to horizontal load.


2.5 Nature frequency of structure with position of mass K.C.H,TSOI The following modeling illustrates how position of mass affects the nature frequency of a simple structure, which link to positioning the mass damper to resolve resonance in practice.

Model property Material

Steel plate and strip

Storey

3

Storey Height

0.2 metre

Width in x-x direction

0.32 metre

Width in y-y direction

0.09 metre

Total weight

1.006kg

The model was tested under a horizontal force in X-X plane of the model using finite element analysis software (ANSYS). A total load of 2.5 kg was placed within the structure with different arrangement of mass positioning. During the test, only consider the first mode of vibration.

Figure 1


Result obtained from ANSYS

Loading position arrangement (Figure 1)

Nature Frequency of first mode (Hz)

A

3.065

B+A

1.567

C+A

1.645

D+A

1.715

2.5 kg at top floor + A

1.323

2.5 kg at middle floor + A

7.278

2.5 kg at bottom floor + A

4.833

In this experiment, high concentration of mass located at middle floor of the model and it requested higher excitation to reach to resonance. It was due to the position at the mid-height of the structure which created smallest sideway motion to the model and acting as a restraint to the top and bottom floor movement, so the mass damped the structure. From the results obtained, the nature frequencies of the structure are governed by the height of the mass and the location of concentration, even the total weight of structure is the same.


2.6 The Centre of Mass and Moment of Inertia (Why tightrope walkers carry long bent poles) Sofiane Mesbahi Why does Tightrope walkers carry long bent down ward‘s poles? The answer is obvious for most of the people. To increase their stability!! Yes but how? The principles that keep the tightrope walkers in a state of stability are: 1. The pole‘s bend lowers their centre of gravity. 2. The pole increases the tightrope walker‘s moment of inertia.

In 1974, Philippe Petit undertook a tightrope walk between the twin towers carrying a long pole.

The centre of gravity (centre of mass): The lower the centre of gravity the more stable a body is. The centre of gravity is the point about which all the weight is evenly distributed in an object. While it is easy to find it in a round object, a human body is not symmetrically distributed. However, the centre of gravity of a standing human body is about 5cm below the belly button. The concept of centre of gravity is used by many athletes to improve their performance since a low centre of gravity in the body means a more stable body. Fosbury flow, a high jump athlete is a good illustration of this concept. In the other hand, the same idea is applied to buildings, where the centre of gravity is kept low. Formula 1 cars also use the same concept, as they are flat in the ground, and have large wheel base so that they won‘t easily turn over in the corners. There is a change in centre of mass as the shape of human body changes when the body is moving. For a tightrope walker, its centre of gravity must be kept directly over the narrow and constantly moving wire to stay balanced.


However, when the centre of gravity is directly above the support point, physicists call the balance an unstable equilibrium. The fact is, the higher the centre of gravity, the less force is required to upset the equilibrium. Taking a bend pole at its end make the centre of gravity of the system lower. Moreover, by applying weight on the ends of the pole, the centre of mass will be even lower.

Moment of Inertia: Take two objects, one is a solid sphere, the other is a hollow sphere, suppose they have same mass and same size. The hollow sphere will always be harder to move and rolls more slowly than the solid sphere if put down a hill. Inertia or moment of inertia reflects how the mass is distributed. When the mass is far from centre, the object has high inertia, which means that it resist being moved more than does an object where the mass is distributed evenly throughout.

High Inertia

Low Inertia

Slow

Fast

Move away mass far from an object will make it harder to move or move slowly. Tightrope Walker by holding the long pole is increasing moment of inertia by moving mass away from centre. When the system wobbles, it wobbles more slowly and has more time to correct and restore the balance. In conclusion, the lower the centre of mass combined with a higher moment of inertia, the more stable the tightrope walker will be.

References:  Heckert, P. (2010) Why Tightrope Walkers Carry Long Bent Poles [online]. [Accessed 23 rd October 2011]. Available at: < http://paul-a-heckert.suite101.com/why-tightrope-walkerscarry-long-bent-poles-a185632>.  Jenkins, D. (2008) Balancing Act: Finding Your Center Of Gravity [online]. [Accessed 23 rd October 2011]. Available at: .  Physics Of (2001) Tight Rope Walking [online]. [Accessed 20th October 2011]. Available at: < http://physicsofcircus.homestead.com/files/tightrope3.htm>.  Plus Magazine (2003) A sense of balance: solution [online]. [Accessed 19th October 2011]. Available at: < http://plus.maths.org/content/os/issue26/outerspace/solution>.


2.7 Mechanical analysis of arch bridge----Zhaozhou Bridge Xin Liu . 1.Construction of Zhaozhou bridge The Zhaozhou Bridge is the world's oldest open-spandrel stone segmental arch bridge.It is also the oldest standing bridge in China, although the Chinese had built bridges over waterways since the ancient Zhou Dynasty.

The zhaozhou bridge is about 50 m long with a central span of 37.37 m. It stands 7.3 m tall and has a width of 9 m. The arch covers a circular segment less than half of a semicircle (84°) and with a radius of 27.27 m, has a rise-to-span ratio of approximately 0.197 (7.3 to 37 m). This is considerably smaller than the rise-to-span ratio of 0.5 of a semicircular arch bridge and slightly smaller than the rise-to-span ratio of 0.207 of a quarter circle. The arch length to span ratio is 1.1, less than the arch-to-span ratio of 1.57 of a semicircle arch bridge by 43%, thus the saving in material is about 40%, making the bridge lighter in weight. The elevation of the arch is about 45°, which subjects the abutments of the bridge to downward force and sideways force. The central arch is made of 28 thin, curved limestone slabs .This allows the arch to adjust to shifts in its supports, and prevents the bridge from collapsing even when a segment of the arch breaks. The bridge has two small side arches on either side of the main arch. These side arches serve two important functions: First, they reduce the total weight of the bridge by about 15.3% or approximately 700 tons, which is vital because of the low rise-to-span ratio and the large forces on the abutments it creates. Second, when the bridge is submerged during a flood, they


allow water to pass through, thereby reducing the forces on the structure of the bridge.

2.About the arch structure Conception of arch： Structure whose rod axis is curve and under the action of vertical load it results in horizontal force . Conmon form：

three-hinged arch two hinged arch

arch without articulation

mechanical characteristic of arch： 1) It produces horizontal trust under the action of vertical load. 2) Three hinged arch section bending moment is smaller than corresponding beam bending moment. 3) Under the action of vertical load,on the section of the arch there exists larger axial force and it is always presents strain. 3.Internal force calculation of arch Bearing force calculation：


The action of vertical load of arch under specified section internal force calculation formula：


2.8 Tricks of Man Sitting on Invisible Chair IL-SIK YUN In the city centre of Manchester, we can sometimes see the street performer sitting on the invisible chair and makes illusion as if he is very comfortable on the invisible chair. People always gathering around him and try to find the trick of magic. However, this is not illusion or magic but there are structural concepts behind its performance. Rather than directly having an answer of secrets of invisible chair, we could firstly think about it as a structure in order to find the clues. From figure 1, we can observe blue coloured plate at his feet and it can be assumed that there are some secrets on that as well. Therefore draw a free body diagram including blue plate as shown in figure 2. Figure 1 Man on Invisible Chair http://www.flickr.com/photos/justsunshineandblueskies/5370907042/

From figure 2, we can think it as a structure and divide into three main parts 1 (blue plate), 2 (legs), and 3(body and head). As the weight of head and body are much heavier than legs, we can assume that centre of mass pass through the body as shown in figure1 and think the weight of head and body as a load applied on the half-frame structure as shown in figure 2. Additionally, if we assume that blue plate is infinitively large and fully fixed with shoes, then we can treat it as fixed condition and could draw simplified free body diagram of structure as shown in figure 3.

Figure 2

Figure 3

From figure 3, we can see that reaction forces and moments due to weight of body occur at the fixed point between plate and foot. However, there are two main problems in this assumption.  First, one leg is not stiff enough to resist the weight of body.  Second, blue plate is not actually infinitely large, and we cannot actually think it as a fixed support condition.


Second problem can be resolved by thinking concepts of centre of mass. Centre of mass is defined as ―point about which the body is balanced or the point through which the weight of the body acts” (Ji and Bell 2008). We can now think that plate is fixed with foot and it is the part of structure as shown in figure 4.

Figure 4 Centre of mass of structure

If we find the centre of mass of two cases in figure 4, we can clearly see that centre of mass is lower and more stable when mass of plate is larger/heavier. This is why pyramid is more stable than uniform cross-section of the building. By applying this concept into invisible chair we could put more mass (in high density) in the plate in order to make it more stable. First Problem can be solved by stiffen the legs. Concept of Stiffness is defined as ability of the structure to resist changes in shape (Wikipedia) and relationship between stiffness and elasticity can be represented as below. k = EA/L (Where k = stiffness, E=Youngs modulus, L= length, A=Cross section area) From the equation above, we can clearly see that by adding materials with high Youngs modulus can increases the stiffness of material/structure. This concept can be applied into invisible chair by adding pole/beam, which has high Youngs modulus, fixed with plate and tied with legs. Now legs are stiffer than before and therefore resist the weight of body. Pole can be hided in trousers in order to make illumination effect.

By resolving two main problems, now we can see how man on invisible chair is works as stable structure as shown in figure 5.

Figure 5

References  Ji T & Bell A, 2008, Seeing and Touching Structural Concepts, Taylor & Francis, Oxon.  Wikipedia, Stiffness, http://en.wikipedia.org/wiki/Stiffness, last accessed 30 OCT 2011


2.9 Load Conversion Basir Alavi

The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time. For an isolated system, this law means that energy can change its location within the system, and that it can change form within the system. (WIKIPEDIA)

In this Module the night latch convert the moment load to the horizontal load (axial load) through some procedures.


2.10 Overhangs : reducing bending moments HAO LUN Introduction Economic is always a significant factor in structural design,and it is a fairly important requirement for structural engineer to design the practical structure meeting the economic demand of the sponsor.Application of structural concept can optimize the structure design to achieve the target of saving material and safe.Overhangs is a cost effective example of reducing bending moments in numbers of practical engineerings.

The figure shows a steel-framed multi-story carpark,in which overhangs are used in this structure reducing the bending moments.It is found that in the first overhang,two steel wires being fixed to link the free end of it and the concrete support,provide a downward force on the free end.In this paper,basing on this example, the simplified model would be demonstrated this structural concept. Figure 9 :Overhangs used to reduce bending moments (courtesy of Mr. J Calverley )

Simplified model: 4 -span beam

Figure 2 : 4-span beam


Figure 3 : Bending moment of 4-span beam The span of 4-span beam is 20 unit and the uniform load is 10 unit .It is found by calculation that the bending moment of 1st midspan is much high than 2st midspan,and the bending moment of 2nd bearing negative moment is close to 3rd bearing.In the structure,this beam has to be designed sufficient stiff to meet the requirement of this load, the great gap in bending between different span would lead to that the material is not been fully utilized.

Figure 4 : 4-span beam with overhangs

Figure 5 : Bending moment of 4-span beam with overhangs In the second model, 4-span beam with overhangs,the tensile downward force is added on the free end of overhang,which cause different output compared to the former one.Not only the bending moment of 1st midspan decreased,but also the gap on bending moment between 1st and 3rd span did.And here is the comparison :


Figure 6 : Comparison on bending moment between these two models From the comparison above,it is found that there is approximately 10% reduction in 1st midspan with overhang action ,and 5% in 2nd bearing.but in 3rd midspan and 4th bearing overhang action would bring about little increase in bending moment. Due to the overhang action,the gap of bending moment in 1st midspan and 3rd midspan is reduced by 25%. Conclusion The reduction on bending moment caused by overhang action has the maximum impact on the 1st midspan of the structure(about 10%),and the impact decreases in the following spans.Due to the overhang load,there would be little increase in some spans of the structure.

Reference Tianjian Ji and Adrian Bell Seeing and Touching Structural Concepts. from http://www.structuralconcepts.org accessed on 30/10/2011 The calculation by : Structural Mechanism Solver for Windows version 2.0 Copyright 1997-2004, ISBN 7-89493-637-5 Professor Yuan Si Structural Mechanics solve research group Department of Civil Engineering, Tsinghua University


2.11 Stress Concentration in Daily Life Jingting Huang 1. Introduction Generally we talking about stress distribution, we prefer to have a more uniformly stressed member which can carry more loads before failure. But if we want to make the structure fail more easily and quickly, then we need to find a way to increase local stress. The following examples show such approach by using a structural concept called ―Stress Concentration‖. 2.Concept For a given external or internal force, the smaller the area of the member resisting the force, the higher the stress. So a reduction in area, for instance, caused by a crack, results in a localized increase in stress. This is so called ―Stress Concentration‖. 2. Practical Examples

(a) food packaging with semicircle hole

(b) tear from other edge

(c) tear from hole Figure 1

The above figure 1 shows a very common phenomenon in our daily life. There is a small semicircle hole on the edge of food packaging. Without this hole, we have to use a much larger force to open it. Conversely, it is very easy for us to open from the hole.


Figure 2 Figure 2 illustrates a way to break a corn cob. When we try to break the corn cob directly, we use great force but still can not do it. Alternatively, it is much easier for us to break off by cutting a notch on the surface of the corn cob.

Figure3 Figure 3 indicates a all welded steel ship suffered severe fracture when a crack ran from welded joint in the deck through the hull. Stress concentration theory is used in all of the three examples.


4.Theory As is well known, the stress distribution equation: F  F  force   stress A

A  area

Under the same force: A    ; A    The discrepancy of area is explained to exist because of the presence of small flaws or cracks found either on the surface or within the material. These flaws cause the stress surrounding the flaw to be amplified sharply by the abrupt reduction of area. As for tensile member, when one of them has no crack, the internal force lines are uniform, as shown in figure 4(a).When one of them is with a round hole, the internal force lines are denser around the hole, producing the stress concentration. But this kind of stress concentration is local. When it is a little distance away from the hole, the stress and lines tend to be even, as shown in figure 4(b).

(a)

(b) Figure 4

Combined with figure 1 (c), the stress distribution is approximately like figure 5 shown below. This is why we always see a semicircle hole on the edge of food packaging and we can open it easily.

Figure 5


5.Conclusion The whole point of my study is to show that when a structure with small flaws or cracks, the stress will be concentrated around the crack tip or flaw, developing the concept of stress concentration. People can design different geometry to minimize or maximize the stress concentration. 6References [1]Ji T and Bell AJ.(2008). Seeing and Touching Structural Concepts. University of Manchester. [Online] www.structuralconcepts.org [2] http://en.wikipedia.org/wiki/Stress_concentration [3]Professor John Yates. Lecture of Introduction to Structural Integrity.


2.12 Mechanical analysis of the kitchen knife Jinglong Ye Description Kitchen knife is an indispensable tool which is widely used in our daily life. When it was designed, four points should be considered: they are pressure, force decomposition, friction and the material of kitchen knife. First two elements will be discussed particularly because they are related to the mechanical aspect..

Figure 1 kitchen knife

Explanation To assuming that a person is cutting meat using two kitchen knifes respectively. The two kitchen knifes are with the same mass, size and smooth. At the same time, the person uses the same power to the kitchen knifes. The only difference between the two kitchen knifes is they have different sharpness. It will be seen that the one with thinner blade will effect more pronounced deformation of meat which means that the person using the kitchen knife with thinner blade will be more efficient and convenient.


First, we know that the kitchen knife is able to cut into the meat because the kitchen knife pressure to the meat is bigger than the maximum pressure which the surface of meat can withstand. The one of the reasons is because of the pressure which is defined as an effect that occurs when a force is applied on a surface. It is undeniable that the kitchen knife with thinner blade has the smaller contact area. According to the formula for the pressure (P = F / A where: F is the normal force here is the force from the person, A is the area of the surface on contact here is the contact area between blade and the meat), if the normal force is the same, the bigger pressure will occur when the contact area is smaller (see Fig.1 below).

Second is about force decomposition. The figure 2 shows the stress analysis diagram of the kitchen knife. Figure.2 shows the longitudinal section of the kitchen knife which is a triangular; meanwhile, we add a force F in the back of the kitchen knife which will cause two forces N to push the both sides of the object. We assume that the longitudinal section is an isosceles triangle; the width of the kitchen knife back is D and the side length of the kitchen knife is L.

Back of the kitchen knife

Kitchen knife blade Fig.2 Stress analysis of the kitchen knife


From the similar triangles: N/F=L/D Hence: N = (LF) / D If the angle triangle is Ɵ, there sin (Ɵ/2) = (D/2) / L Hence: D / L = 2sin (Ɵ/2) From above, we can get that N = F / 2sin (Ɵ/2)

Conclusion When F is constant, the smaller Ɵ leads to bigger N. In other words, the thinner the blade is, the easier the kitchen knife can cut into food. The bigger pressure will occur when the contact area is smaller. It is also easier to cut food

Reference Tianjian J., Adrian B. 2011 Seeing and Touching Structural Concepts, [online], [Accessed 22 Oct 2011]. Available from: http://www.mace.manchester.ac.uk/project/teaching/civil/structuralconcepts/ People‘s Education Press. 2011 Mechanical Problems in Life, [online]. [Accessed 22 Oct 2011], Available from: http://www.pep.com.cn/gzwl/jszx/jxyj/jfxf/201101/t20110105_1003246.htm


2.13 CENTRE OF MASS TO PREVENT SWAY OF TALL BUILDINGS Mohammed Shabbir Bhagat Taipei 101 was the world‘s tallest building till 2010 before Burj Khalifa was built. Taipei 101 is special in many ways. It is built in a seismic zone with a big fault 200 meters away from the site. In order to prevent collapse of structure due to earthquake, engineers had to design a flexible structure. However being tallest building ever built during its time of construction, it also had to be designed for wind forces to prevent damage from sway, which meant the building had to be rigid to prevent any structural damage. The engineers had to design a rigid as well as flexible structure.

Fig 1: Sway Action Stabilization

In order to overcome this problem engineers came with a simple solution to prevent the building from sway using the concept of tuned mass dampers which eventually satisfied the principle of centre of mass and preventing the building from sway. The building has a huge steel ball pendulum weighing 730 ton from 88th to 92nd floor as in Fig 1. When the wind sways the building in one direction, the centre of gravity of the building is shifted towards the direction of sway and the building is subjected to topple due to action of gravity. However, the 730 ton steel ball swings in the opposite direction ensuring the centre of mass of the building is maintained and makes the building stable. Therefore the effectiveness of tuned mass dampers directly depends on the mass of the damper.


A simple demonstration video shows the effect of building stabilization from sway. A horizontal push is applied to a empty box and sway action is noticed and then in second instance push is applied with a coffee mug inside the box acting like a suspended pendulum where the basic concept of centre of mass is used to stabilize the building

The following video clips show the entire demonstration. http://www.youtube.com/watch?v=qQhcQ27JMLo http://www.youtube.com/watch?v=qICqqxd7t04

Fig 2: Tuned Mass Damper

Also to be noted is the centre of mass of the building is slightly lowered by placing 730 ton steel ball from the 92nd floor up to 88th floor making it more stable because the lower the centre of mass of a body the more stable is the structure. Reference www.structuralconcepts.org http://www.popularmechanics.com/technology/gadgets/news/1612252 http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_CenterMass.xml


2.14 BIRDS ARE STABLE EVEN ON ONE FOOT Parham Mohajerani Introduction: The term stability is one of the most important steps in structural designing process. While the designers focus on each member, during designing process, they consider stability in each parts of the structure. Broadly speaking, structural engineers define stability as the power of recover equilibrium. A question appears here is that ‗Does the Nature in equilibrium?‘. Birds are part of our nature and they can stand on one foot. Not only they can stand on one foot, but also they can sleep on one foot. How do they keep their stability even on one foot?

Concept title: Stability If the structure and its members can satisfy all equilibrium equations, the result is a stable structure. However, engineers should check support constraints conditions to avoid geometrically instability. This concept derived from this fact that the components of external forces in x, y and z direction, which act on structure, should balance each other.to reach this balance, all of the equations, which mentioned below, should be satisfied. ∑Fx=0 ∑Fy=0 ∑Mx=0 ∑My=0

∑Fz=0 ∑Mz=0

Analysis Details: The first step is drawing free-body diagram of flamingo‘s body structure.as it is shown in figure (1), the joint at the middle of flamingo‘s foot is not mentioned and assume that it is a rigid body. This assumption is true, because flamingos are able to lock intertarsal joint (foot middle joint). Thus, the joint at the middle, acts like rigid connection. The solution of equations of equilibrium shows that there is not any bending moment and horizontal load at flamingo‘s body structure.


Bending moment is disappeared, because the weight force direction pass the point of support.as a result, all equations are satisfied and structure is stable. Equilibrium equations for 2D flamingo,s body structure :



∑Fx=0

●∑Fy=0 Ay-W=0 » Ay=W

● ∑Mx=0

(figure 1- flamingo free body diagram) Flamingo‘s weigth force direction in both elevations(figure (2),(3)) pass the support center and remove all bending moments effects from body structure.

(Figure 2-Vertical section)

(Figure 3- Elevation)


Other birds ,also,try to move their center of mass to top of their foot when they want to stand on one foot.figure(4)

(Figure 4 – birds stability)

Conclusion: Flamingos and some other birds are stable even on one foot and stability concept, which is one of the most dominant structural concepts, proves this fact.


2.15 The concepts of equilibrium and the application in fish tank Xi Du

Introduction This project aims to understand the concept of equilibrium, and apply the method to a real case.

Definition: When the sum of all reactions and moments acting on an object at any direction equals zero, the structure can reach a static balance status. This is so called equilibrium. ΣF=0 ΣM=0 Moment is equal to load times distance. And the unit is KNm. M=F*L Examples: A glass fish tank is put on the edge of table (as shown in Figure 1). The fish tank is in the perfect balance status.

Figure 1: Glass fish tank, 2011 (http://www.patent-cn.com/tag/%E5%AE%B6%E5%B1%85) In order to the analyse the forces and moment act on the fish tank. The fish tank is assumed to be an ‗L‘ shape section. The diagrammatic sketch of tank is shown in Figure 2.


Figure 2: Analysis of fish tank The hollow ‗L‘ section stand for the empty fish tank. The two red lines mean the x-axis and yaxis. The tank has been cut into 3 small rectangular sections by these two red lines. They are Section A, Section B and Section C as shown in Figure 2. The yellow dot means the mass centre of empty fish tank. The water tank is rest on the table. The tank is only subject to two forces: self weight of tank W and a reaction force R from the table. The tipping point is on the y-axis. Since the reaction force of the table is upward, it will cause an anticlockwise force moment. To the theory of equilibrium, the force moment from the fish tank should be clockwise. The direction of the force gravity is downward; hence the mass centre of the tank should be on the right side of y-axis. Step 1: Fill water into the fish tank slowly. The mass centre starts to move closer to the y-axis.. The height of water H is rising. The weight of water in Section A defined as Wa.

Define the weight of the fish tank is Wt, the distance between the centre of the tank and y-axis is x. L1 and L2 mean the distance between y-axis to the left and right edge of the tank. Symbol h stands for the height of Section A. The moment caused by reaction force of the table (Mr) can vary to satisfy the equilibrium theory. The value of Mr≥0 In the situation H≤h, to satisfy the equilibrium formula (1), the condition formula (2) below should be guaranteed: Wt•x = Wa•L1/2 + Mr (H≤h) (1) Wt•x ≥ Wa•L1/2 (H≤h) (2) In this formula, the only variable is Wa, which is defined by H. When the water level H equals h, the critical case happens. The structural analysis is shown in Figure 3. In this case, Section A is fully filled by water.


Figure 3: Most critical case Define the thickness of fish tank is b. The following equation can be obtained: Wt•x ≥ ρw•b•h•L1

(3)

Step 2: Keep filling water to the tank, the water level in Section B and C will rise up. Since L2 is larger than L1, the area of Section C is larger than Section B. It can contain much more water than Section B. To the tipping point, the force moment of Section B (Mb) is anticlockwise and that of Section C (Mc) is clockwise. Mc is larger than Mb, therefore the increasing of H (when H>h) will be favorable to resisting the overturning. So the most critical case is as Figure 3 shows.

Summary: The project shows that, when the moment of empty tank greater or at least equal to moment of water in the Section A, the whole tank could be reach to equilibrium. In the project, the concept of equilibrium is proved by the most critical case of water tank. When the sum of force and moment in any point is zero, the object is rest.

Reference: [1] Concepts of Equilibrium, access from: http://en.wikipedia.org/wiki/Equilibrium on 30/10/2011. [2] Glass fish tank, (2011). access from http://www.patentcn.com/2011/10/06/56814.s html#more-56814 on 27/10/2011


2.16 HOW THE LONDON EYE WORKS Yu Junlong Concepts: 1. Rotational stiffness (the connection of hub and cable) 2. Pre-stress in cable Structure: The London Eye

The London Eye is an excellent example of a frame structure. Its wheel part comprises a triangular truss with one inner chord and two outer chords. The behavior of London Eye can be considered using two major concepts: rotational stiffness (the connection of hub and cable) and pre-stress in cable.

Figure1 the model of London Eye (Debra Ronca 2008)

Point one: Rotational stiffness (the connection of hub and cable) Sixty-four cables run from the hub to the inner

inner chord

chord and they point to the center of the circle, because they keep the rim at a constant distance from the hub (Figure2). Other sixteen

cable

cables then join the outer chord with the edge of hub but they are tangent to the hub circle, which can increase the rotational stiffness of

Figure 2


structure (Figure3). The hub, which gets

outer chord

power from hydraulic motors, turns the wheel, and under the circumstance, the sixteen cables

hub

are in tension rather than in bending. One

cable

advantage of this is that tension member should just be designed to resist the axial load and the whole area of the section can be utilized.

Figure 3

Hence, a little material is needed to keep high rotational stiffness and stability of structure.

Figure4 the detail of hub (Rosie Rogers 2011)

Point two: Pre-stress in cable Many observation wheels in the past suffered from cable slack during rotation, which will result in fatigue in the cable connection. In order to avoid this, cables of London Eye are pre-stressed at first. As is known to all, cable is equipped with good tension ability. It can be subject to high tension force but cannot bear compression force. Even a little compression force will make the cable bend, like a spring, and it will become a vulnerable member actually. In view of this characteristic, the cables are pre-stressed in tension in advance in order to keep in tension force even under negative pressure load. With this method, the cables always work by tension and what the difference is that the tension force in bottom cables are higher and in top cables are lower.


Figure5 the detail of pre-stressed cable (Paul Frocchi 2011)

Reference: [1] A. P. Mann. Building the British Airways London Eye [J]. Proceedings of the ICE - Civil Engineering, 2011, Volume 144, Issue 2, pages 60-72. [2] Debra Ronca. [Accessed: 28 Oct 2011]. Available from: http://adventure.howstuffworks.com/london-eye1.htm.


2.17 Wire-spoke Wheel Mohammad Morniman Bin Jonhimran Wheel is one of the oldest technologies that still in use with many applications today. From one generation to the next generations, wheel had a drastic change in terms of size, material used and its application in daily life. Wooden-spoke wheel were invented in 500BC as shown in figure 1.0. The spoke is made from thick-rigid wood and will not buckle when the compressive loads are applied to it. In a wooden spoke wheel, the force exerted from the ground is transferred to the hub by compressing the bottom spoke.

Figure 1.0 Wooden-spoke wheel [1.0] The wire-spoke wheel invented in the late 18th century to replace the wooden spoke wheel as shown in figure 1.1. By using the wire-spoke wheel, the weight is greatly reduced and also improves the durability compared to the wooden-spoke wheel. Wires are rigid material, however it is not rigid enough to carry the compression load alone exerted from the ground. In order for the wire-spoke wheel to work properly, the wire must be pre-tensioned. By tensioning the wires, buckling under compression load can be resisted. The pre-tension of the wire spoke is designed to such extent that there will always be a residual tension in the spoke. Therefore, when compression load is applied at the bottom spoke, instead of gaining compression load, the bottom spoke lose some of its tension force.

Figure 1.1 Wire-spoke wheel [1.1]


The wire spoke wheel has a similar concept with prestressed concrete. Wires in the wire-spoke wheel act as compression members and design by pre-tension in order to be able to resist the compression load. In prestressed concrete beam, the steel member acts as a tension member. The steel is pre-tensioned and designed in such a way that the concrete can take some tension force due to the weakness in tension of the concrete. When prestressed concrete beam is loaded vertically, instead of gaining tensile force for the concrete, it loses some of its compression force.

REFERENCES [1.1] http://www.amishwares.com/site/1504461/product/189-SCW [1.2] http://nbwuyi.en.made-in-china.com/offer/yemQbOFZyuWk/Sell-Harley-21-Wire-SpokeFront-Wheel-Wide-Glide-Dual-Disc.html [1.3] The Bicycle Wheel, Third Edition, Jobst Brandt [1.4] History of wheel,en.wikipedia.org/wiki/wheel


2.18 Wind, Roof and a Aircraft Waqar Ahmad Farooqui In tropical region during heavy storm roof of houses often get damaged. Many a times if there is sheeting on the roof, the sheeting flies away if it is not properly fixed.

Figure 2 (Loss of corrugated metal Figure 1 (Roof of a school in a sheet) village flew away during a storm) The answer to this phenomenon lies in Bernoulli's principle. The theorem states that increase in speed of fluid occurs simultaneously with the decrease in pressure or a decrease in fluid pressure energy. In other words energy in a fluid is constant. Air is a fluid and the same applies to it also. Design guides for wind analysis often give an upward lift on the roof. There is similarity between this phenomenon and flying of an airplane. Both uses same principle Hence if velocity, V is higher Pressure, P has to be lower Consider a roof as shown in figure 3. During a storm, air velocity is more above the roof (outside) and lesser below the roof (inside). Hence the pressure above the roof is lesser whereas the pressure below the roof is higher. This means that pressure exerted by the air on roof surface is higher below than the pressure above the roof surface (fig 4). This difference in the air pressure creates an outward force. Moreover from this argument it is obvious that the openings in the house will have a significant role in the calculation of the wind load on the roof. Design codes talk about coefficient of external pressure and coefficient of internal pressure. The latter depends upon the openings in the building. Outside higher wind Outside lower pressure velocity Wind Implies Inside higher Inside lower wind pressure velocity Figure 3 Figure 4

The case of an Aircraft

Low Pressure

High Pressure Figure 5 Cross-section of an aircraft wing

Figure 6


In an air craft wing surface area of upper part is more than surface area of lower part hence air velocity above wing increases. Air velocity in lower part of the wing is lower hence due to this an upward pressure acts lifting the wings thereby lifting the aircraft.

An experiment Blowing air on one side of a strip of papers causes the paper to bend to the side on which air is blown. By blowing air, velocity on the upper surface increases, this results in decrease in pressure on the upper surface. Hence the paper moves up.

The paper is hanging down, no air is blown

References  

www.ndindia.nic.in – Figure 2 www.web.mit.edu – Figure 5,6

The paper lifts up when air is blown over the top surface


2.19 To Reduce Bending Moments Fariborz Mohebipour Domabi Leaning backward while pulling something could end in more effiecient performance while standing straight may waste energy and risk of toppling will be increased. Below figures shows the concept.

Such a concept has been applied to the construction of El Alamillo bridge. As illustrated in the below figure, a pylon inclines away from the river and supports this long span. Instead of employing back stays to counterbalance the tension, weight of the pylon has been used to reduce moment at joint A.


If the tower was straight, moment at joint A was as follows : MA = ( pulling of cables ) * (distance a ) – ( dead load ) * 0 MA = ( pulling of cables ) * ( distance a ) But now that the tower is inclined, the dead load helps reduce moment at joint A as follows : MA = ( pulling of cables ) * (distance a ) – ( dead load ) * ( distance b ) The moment at joint A would be incredably reduced by using dead load to counterbalance forces. The tower can be simulated as a person who wants to pull cables, as illustrated in the following figure. If the simulated person leans backward, better performance could be achieved.

Reference: Mary Ann Sullivan (2005) http://www.bluffton.edu/~sullivanm/spain/seville/calatravabridge/bridge.html [accessed 31/10/2011]


2.20 Tensegrity Structures Theory An American engineer, Buckminster Fuller, developed a structural concept known as tensegrity (derived from tensional integrity). Tensegrity structures are typified by a continuous net of ties (tension-only members) supporting isolated struts (compression-only members).     

The structure is pre-stressed such that tensile/compressive elements always remain in tension/compression respectively, with or without external loading. The equilibrium position of the structure is maintained by the balance of tensile and compressive forces. Forces at connections will self-balance, reducing internal forces throughout the structure and providing relatively high rigidity. All structural elements are subjected to purely axial forces, thus the structure can only fail if individual elements yield/buckle respectively. No bending moments are present in structural elements, reducing material usage to a minimum (axial forces can be resisted efficiently, especially tension which is not prone to buckling).

Tensegrity can be observed in some existing structures, however, ―pure‖ tensegrity structures which obey all the above points tend to be restricted in form. Some modern form-finding techniques (based upon computational analysis) are applicable to tensegrity structures. Kenneth Snelson’s Sculptures Kenneth Snelson studied under Buckminster Fuller and his contemporary sculptures consist of purely tensile and compressive members arranged such that they form a perfect tensegrity structure. The engineering applications of his work include the design of a communications antenna positioned at the top of the Freedom Tower in New York. The illustration to the left shows his Needle Tower, built in 1968 and composed of aluminium tubes and stainless-steel cables. It is just over 18m tall and although the structure appears weak and flimsy, it can withstand severe storms. This demonstrates the efficiency of pure tensegrity structures. Such structures do have some disadvantages. Their form limits their practical applications to the likes of antenna structures. However, since the mass of the structure is inherently low and antennae are often heavy this can result in significant dynamic deformations.

Geodesic Domes


Geodesic domes were developed by Buckminster Fuller. These are not strictly tensegrity structures as the members are designed to withstand tensile and compressive forces and can be subject to either at any instant. However, they are extremely efficient as they do not allow bending stresses to propagate throughout the structure. They are often used to enclose large spaces with minimal material in the same way a truss may efficiently span large distances. Michael McDonough’s Bamboo Bridge The purpose of this bridge is to demonstrate the practical applications of bamboo as a high strength engineering material. It was designed by the architect Michael McDonough and is to be located in a rainforest in California. Bamboo is a strong construction material and this design promotes innovation. Bamboo is primarily used for the compressive elements which are supported by prestressed steel cables anchored at either end of the bridge. This effectively forms a tensegrity system which supports the bridge decking. The design is extremely efficient; it is predicted to support up to 60 times its own weight. Conclusions There may not be many practical applications for tensegrity at this moment in time. This is can be attributed to its recent development. Design techniques have not realised its potential but some computational form-finding techniques such as the dynamic relaxation or force density method used for cable/membrane structures can also be used to find tensegrity forms. It is a viable area of research and is likely to become more prominent in future structures, particularly lightweight structures such as membrane roofs. It can provide economic designs where the problem and innovation of the engineer allow for it. References 1) http://kennethsnelson.net/1970/needle-tower/ 2) http://www.wtc.com/about/freedom-tower 3) http://www.michaelmcdonough.com/projects/spec/bambridge.php4


2.21 The Effect of Wind Loading on the Stability of High Rise Twisted Structures - ‘Infinity Tower’ Darwish Al Zaabi Background The infinity tower is located in Dubai, UAE and is to be completed this year, 2011. The tower is about 305 meters high with a twisting nature. It twists a full 90 degrees from the base to the top. This tower is the first of its nature. The residents can benefit from two views, one towards the marina and as the building ascends the view becomes towards the gulf. This is interesting as a series of incremental rotations occurs at each level. The tower consists of 75 stories which are cast on site reinforced concrete [1]. The tower received several awards and among them was the Best International High Rise Architecture [2]. The Design In order to generate the twist of the building, the columns slope in one direction and is offset over the column below it. So basically, the outer columns lean in or out in a direction such that they are perpendicular to the slab edge as they ascend from story to story. Because the building is twisted, the walls are shifted from level to level about 1.3 degrees about the center of the tower. However, the floor layout is repetitive in each level despite the fact that the building is twisted [1]. The design concept is very simple, as one of the engineers working on the project has mentioned. Mr. Wimer stated that: "Each floor is actually exactly the same so it is almost as though you stacked up a pile of books and you twisted each book slightly to get the twist", "If you drilled a hole through a stack of books and put a pole in it and rotated each book just slightly, you would be able to create the same spiral shape" [2].

Figure 1: The Infinity Tower [1]

Figure 2: Infinity Tower Rotation [1]


Wind Engineering For all high-rise buildings, wind is the main design issue. Wind forces could cause the building to sway laterally which is undesirable for such important buildings. Since the structure is of a twisting nature, it has the tendency to undergo additional horizontal twist movement under gravity loads. This could be resulted from the self weight of the cast in place concrete. Therefore, wind has to be carefully designed for in such a unique structure [1]. The Infinity tower is a unique structure. Because of the building twisting nature, the variation of the building shape over its height changes the frontal wind flow as building ascends causing to disrupt and disorganize the wind forces which are generated. This disruption will reduce the lateral motion of tower and reduce the wind forces acting on the structure [1].

Figure 3: Disorganization of the wind forces due to the twisting nature of the tower [1] The Infinity tower was compared to a similar building with a straight face, i.e. no twist, and was found that the twisting nature of the infinity tower reduced the wind excitation by 25%. In tall slender towers, the wind dynamic response is the main contributor to lateral sway motion, so the reduction of the wind excitation will result in a decrease in the towers peak lateral acceleration. Moreover, the wind forces are also reduced due to the twisting nature of the building but to a lesser amount than the sway accelerations. The wind forces are designed according to the wind response along with tower‘s resonant response [1]. Another important aspect to be noted is that cast in place concrete has been used as the primary material in the construction of this tower. This is because of its ideal mass and stiffness characteristics as well as it will contribute to the reduction of wind induced movement of the tower. Therefore, for the stability of the structure, a lateral resisting system has been used. The lateral resisting system of the tower consists of the reinforced concrete moment resisting perimeter frame along with the circular central core which are connected to reinforced concrete flat slabs to act as diaphragms [1]. This will provide stability and lateral load resistance.


Figure 4: Tower finite element model mode shapes [1] The effect of wind loading was performed in a lab through a wind tunnel testing. This was done to understand the wind forces acting on the building.

Figure 5: Pressure integration model [1] Conclusion The Infinity tower is not just architecturally unique but also serves a structural function. The tower twisted design has been benefited from in structural design. The reduction of the effect of wind loading in such structures is very important as wind design has always been the main concern in tall and slender structures. To sum up, engineers can benefit from ‗The Infinity‘ in their future designs. References [1] [2]

William F. Baker, Christopher D. Brown and Bradley S. Young. (2010). Structures Congress . Retrieved 10 28, 2011, from Infinity Tower, Dubai, UAE. Qabbani, B. A. (2011). Retrieved 10 29, 2011, from Infinity Towers give new twist to Dubai's skyline: http://www.thenational.ae/news/uae-news/infinity-towers-give-newtwist-to-dubais-skyline


This booklet is a collection of students’ coursework on, “Enhancing the understanding of structural concepts”, which is part of the module Research Methods in 2010-11 at The University of Manchester. The booklet forms a source of learning for the students themselves enabling them to learn from each other rather than from lecturers and textbooks.

It is hoped that students learn effectively and actively and this, in part, requires appropriate activities and/or stimulators being provided. Students were asked to study, Seeing and Touching Structural Concepts, at the website, www.structuralconcepts.org, where structural concepts are demonstrated by physical models and their applications are shown by practical examples. It was hoped that students could not only quickly revise a number of concepts they studied previously but could also gain an improved understanding of the structural concepts.

Understanding Structural Concepts

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