Structural Concepts 2010│Page 2
Understanding
Structural Concepts
Understanding,
Developing,
Learning…
Structural Concepts 2010│Page 4
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
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
1.27 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
2.17 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
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.
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
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
The angle of the trailer when equilibrium is lost = Cos-1
((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 = Cos-1
((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.comhttp://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. 4
Contact stresses develop which induce a direct shearing in the bolt. The contact stress bis computed using the formula:
b b b A F
In our case F is equal the axial applied forceb P. The maximum contact stress is: br b F t d P min max _ *
where d and tminare the bolt diameter and the minimum thickness of the two parts connected by the bolt.
b r
F 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 nand the average shear stress b _avg is: v avg b F d P 2 _ * * 4
where F is the also obtained from laboratory tests. v (Simulescu I., 2004, Lectures in Mechanics of Materials)
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.
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 PHYSICAL MODEL Geometry and
loading Bending moment 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.
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 cross-section 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: STATIC EQUILIBRIUM
MODEL: 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).
a
F
L
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).
F*Cosa
C
L*Cosa
B
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‖.
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-del-mundo.html
1.10 The concept of equilibrium and centre of mass--tumbler
Li Chen
IntroductionThe 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 earthquake-resistant 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.
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.
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 = 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
1
2
K
f
M
Δ W Seismic Force Acceleration
FEM Theoretical analysis
So let us look at the proposed design which best meets these outlined criteria
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
non-conventional 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). 35m 19.42m B B 27m 27m 19.42m B-B plan section [A] [B] A A
A-A plan section
5m 5m
Each Floor height at 3.5m spacing’s
3.5m
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
Wall
Inclination
74.05
degrees
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
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.
Time/Freq
Mode set No. 1 2 3 4 5 6 7 8 9 10
CONV STRUC 2.379 3.3611 4.5131 7.1106 9.5321 9.9858 11.759 14.662 15.179 16.258
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)
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)
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,
Δ= wL³/8EI (1)
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
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.
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
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
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
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 we
do not applied the load at the each end of 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 (2nd edition). British Cement Association. ISBN: 0 7210 1586 7.
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.
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.
The Highest Point
The Lowest Point
