Tensile Strength

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TENSILE STRUCTURES

description

It is a powr point presentation made for class seminar.

Transcript of Tensile Strength

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TENSILE STRUCTURES

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IndexAcknowledgementsTensionTensile StrengthSpider WebHistoryTypes Of Structures With Significant Tension MembersLinear StructuresThree Dimensional StructuresMembrane MaterialsCablesStructural FormsForm FindingHyperbolic ParaboloidPretensionMathematics Of CablesTransversely and Uniformly Loaded CablesCable with Central Point LoadGallery Of Well Known StructuresConclusionBibliography

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Acknowledgements

We would like to express our deepest appreciation for our coordinator Mr. Sandeep Mishra who has the substance of a genius, he continuously conveyed a spirit of adventure to our project. It is his patient help which inspired us when it seemed we had lost our will to carry on. Without his able guidance this project would not have seen the light of the day. Thank You.

With regards,Project Team.

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Tension

In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is a force, it is measured in Newton's (or sometimes pounds-force) and is always measured parallel to the string on which it applies. There are two basic possibilities for systems of objects held by strings. Either acceleration is zero and the system is therefore in equilibrium or there is acceleration and therefore a net force is present. Note that a string is assumed to have negligible mass.

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Tensile strength

Tensile strength (σUTS or SU ) is indicated by the maxima of a stress-strain curve and, in general, indicates when necking will occur. As it is an intensive property, its value does not depend on the size of the test specimen. It is, however, dependent on the preparation of the specimen and the temperature of the test environment and material.

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Tensile strength, along with elastic modulus and corrosion resistance, is an important parameter of engineering materials used in structures and mechanical devices. It is specified for materials such as alloys, composite materials, ceramics, plastics and wood.

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Alum

iniu

mGol

d

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Y (Gpa)Ultimate Strength (Mpa)

Y (Gpa)Yield Stress (Mpa)Ultimate Strength (Mpa)

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Spider WebA spider web or cobweb (from the obsolete word coppe, meaning "spider") is a device built by a spider out of proteinaceous spider silk extruded from its spinnerets.

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Spider silk Ultimate tensile strength : 1,000 MPa

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TYPES OF SPIDER WEB

Spiral orb web Tangle web Funnel web Tubular web Sheet web Dome or tent web

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Spiral orb web

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Tangle web

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Funnel web

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Tubular webs

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Sheet web

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Dome or tent web

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History

Tensile structures have long been used in tents, where the guy ropes provide pre-tension to the fabric and allow it to withstand loads.

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A Simple Paraboloid defined by a Minimum of Four Points with at Least One out of Plane

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Russian engineer Vladimir Shukhov was one of the first to develop practical calculations of stresses and deformations of tensile structures, shells and membranes. Shukhov designed eight tensile structures and thin-shell structures exhibition pavilions for the Nizhny Novgorod Fair of 1896, covering the area of 27,000 mts2.

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<< SHELL STRUCTURE

MEMBRANE STRUCTURE >>

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Types of structure with significant tension members

Linear structures Three-dimensional structures Surface-stressed structures

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Linear structures

Suspension bridges Draped cables Cable-stayed beams or trusses Cable trusses Straight tensioned cables

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SUSPENSION BRIDGE

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Three-dimensional structures

Bicycle wheel (can be used as a roof in a horizontal orientation) 3D cable trusses Tensegrity structures Tensairity structures

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Membrane materialsCommon materials for doubly-curved fabric structures are PTFE coated fibreglass and PVC coated polyester. These are woven materials with different strengths in different directions. The warp fibres (those fibres which are originally straight equivalent to the starting fibres on a loom) can carry greater load than the weft or fill fibres, which are woven between the warp fibres.HOME PREVIOUS NEXT

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Other structures make use of ETFE film, either as single layer or in cushion form (which can be inflated, to provide good insulation properties or for aesthetic effect—as on the Allianz Arena in Munich). ETFE cushions can also be etched with patterns in order to let different levels of light through when inflated to different levels. They are most often supported by a structural frame as they cannot derive their strength from double curvature

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Cables

Simple suspended bridge working entirely in tensionCables can be of mild steel, high strength steel (drawn carbon steel), stainless steel, polyester or aramid fibres. Structural cables are made of a series of small strands twisted or bound together to form a much larger cable. Steel cables are either spiral strand, where circular rods are twisted together and "glued" using a polymer, or locked coil strand, where individual interlocking steel strands form the cable (often with a spiral strand core).

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Spiral strand is slightly weaker than locked coil strand. Steel spiral strand cables have a Young's modulus, E of 150±10 kN/mm² (or 150±10 GPa) and come in sizes from 3 to 90 mm diameter. Spiral strand suffers from construction stretch, where the strands compact when the cable is loaded. This is normally removed by pre-stretching the cable and cycling the load up and down to 45% of the ultimate tensile load.Locked coil strand typically has a Young's Modulus of 160±10 kN/mm² and comes in sizes from 20 mm to 160 mm diameter.

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Solid

Ste

el B

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Polyes

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ibre

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UTS

UTSMpaStrain at 50 % of UTS

Properties of individuals strands of different materials :

(ultimate tensile strength)

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Structural forms

Air-supported structures are a form of tensile structures where the fabric envelope is supported by pressurised air only.The majority of fabric structures derive their strength from their doubly-curved shape. By forcing the fabric to take on double-curvature, the fabric gains sufficient stiffness to withstand the loads it is subjected to (for example wind and snow loads). In order to induce an adequately doubly curved form it is most often necessary to pretension or prestress the fabric or its supporting structure.

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Form-findingThe behaviour of structures which depend upon prestress to attain their strength is non-linear, so anything other than a very simple cable has, until the 1990s, been very difficult to design. The most common way to design doubly curved fabric structures was to construct scale models of the final buildings in order to understand their behaviour and to conduct form-finding exercises. Such scale models often employed stocking material or tights, or soap film, as they behave in a very similar way to structural fabrics (they cannot carry shear).

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Soap films have uniform stress in every direction and require a closed boundary to form. They naturally form a minimal surface—the form with minimal area and embodying minimal energy. They are however very difficult to measure. For large films the self-weight of the film can seriously and adversely affect the form.For a membrane with curvature in two directions, the basic equation of

equilibrium is: w=(t1/R1)+(t2/R2)

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R1 and R2 are the principal radii of curvature for soap films or the directions of the warp and weft for fabrics t1 and t2 are the tensions in the relevant directions w is the load per square metre Lines of principal curvature have no twist and intersect other lines of principal curvature at right angles.A geodesic or geodetic line is usually the shortest line between two points on the surface. These lines are typically used when defining the cutting pattern seam-lines. This is due to their relative straightness after the planar cloths have been generated, resulting in lower cloth wastage and closer alignment with the fabric weave.In a pre-stressed but unloaded surface w = 0, so t1/R1= -(t2/R2) .In a soap film surface tensions are uniform in both directions, so R1 = −R2.

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It is now possible to use powerful non-linear numerical analysis programs (or finite element analysis to formfind and design fabric and cable structures. The programs must allow for large deflections.The final shape, or form, of a fabric structure depends upon:shape, or pattern, of the fabric the geometry of the supporting structure (such as masts, cables, ringbeams etc) the pretension applied to the fabric or its supporting structure

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Hyperbolic Paraboloid

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There are many different doubly-curved forms, many of which have special mathematical properties. The most basic doubly curved from is the saddle shape, which can be a hyperbolic paraboloid (not all saddle shapes are hyperbolic paraboloids). This is a double ruled surface and is often used in both in lightweight shell structures. True ruled surfaces are rarely found in tensile structures. Other forms are anticlastic saddles, various radial, conical tent forms and any combination of them.

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PretensionIt is tension artificially induced in the structural elements in addition to any self-weight or imposed loads they may carry. It is used to ensure that the normally very flexible structural elements remain stiff under all possible loads.A day to day example of pretension is a shelving unit supported by wires running from floor to ceiling. The wires hold the shelves in place because they are tensioned - if the wires were slack the system would not work.Pretension can be applied to a membrane by stretching it from its edges or by pretensioning cables which support it and hence changing its shape. The level of pretension applied determines the shape of a membrane structure.

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Simple mathematics of cables

Transversely and uniformly loaded cable

Cable with central point load

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Transversely and uniformly loaded cableFor a cable spanning between two supports the simplifying assumption can be made that it forms a circular arc (of radius R).

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The tension is also equal to : T =wR By equilibrium : The horizontal and vertical : H=wS2/8d , V=wS/2.By geometry : The length of the cable : L=2Rsin (S/2R)The tension in the cable : T=(H2+V2)1/2

By substitution : T=[(wS2/8d)2 + (wS/2)2]1/2

The tension is also equal to: T = wR The extension of the cable upon being loaded is (from Hooke's Law, where the axial stiffness, k, is equal to k=EA/L) : e = TL/EA where E is the Young's modulus of the cable and A is its cross-sectional area.If an initial pretension, T0 is added to the cable, the extension becomes:

[{L0(T-T0)}/EA]+L0 = {2Tsin-

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Cable with central point load

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By equilibrium : W=(4Td)/L, d+(WL)/4TBy geometry : L= (S2+4d2)1/2 = {S2+4(WL/2T)2}1/2

This gives the following relationship

L0+{L0(T-T0)}/EA = [S2+4[W[L0+{L0(T-T0)}/EA]/4T]]1/2

As before, plotting the left hand side and right hand side of the equation against the tension, T, will give the equilibrium tension for a given pretension, T0 and load, W.

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GALLERY OF WELL KNOWN STRUCTURES

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Conclusion

“Any person without invincible prejudice who had the same experience would come to the same broad

conclusion, viz., that things hitherto held impossible do actually occur”- Oliver Joseph Lodge

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Bibliography

www.google.com

www.wikipedia.org