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63-551: The Roseville Bridge , is a pre-stressed concrete box girder road bridge that carries Warringah Road, part of the A38 across Middle Harbour , located adjacent to the suburb of Roseville , in Sydney , New South Wales , Australia . The bridge is one of two crossings of Middle Harbour, the other being the Spit Bridge . The suburbs east of Middle Harbour grew rapidly in the years following

126-400: A = m 1 g − T {\displaystyle m_{1}a=m_{1}g-T} . In an extensible string, Hooke's law applies. String-like objects in relativistic theories, such as the strings used in some models of interactions between quarks , or those used in the modern string theory , also possess tension. These strings are analyzed in terms of their world sheet , and

189-467: A corrosion -inhibiting grease , usually lithium based. Anchorages at each end of the tendon transfer the tensioning force to the concrete, and are required to reliably perform this role for the life of the structure. Unbonded post-tensioning can take the form of: For individual strand tendons, no additional tendon ducting is used and no post-stressing grouting operation is required, unlike for bonded post-tensioning. Permanent corrosion protection of

252-412: A net force is present in the system. Tension in a string is a non-negative vector quantity . Zero tension is slack. A string or rope is often idealized as one dimension, having fixed length but being massless with zero cross section . If there are no bends in the string, as occur with vibrations or pulleys , then tension is a constant along the string, equal to the magnitude of the forces applied by

315-508: A broad range of structural, aesthetic and economic requirements. Significant among these include: a minimum number of (intrusive) supporting walls or columns; low structural thickness (depth), allowing space for services, or for additional floors in high-rise construction; fast construction cycles, especially for multi-storey buildings; and a low cost-per-unit-area, to maximise the building owner's return on investment. The prestressing of concrete allows "load-balancing" forces to be introduced into

378-682: A cost of A$ 1.64 million, the bridge was designed by the Department of Main Roads, with architects Fowell, Mansfield & Maclurcan being design consultants on the project; the primary contractor was John Holland (Constructions) Pty Ltd . The bridge is 377 metres (1,237 ft) long has a clearance of 17.4 metres (57 ft) from the water below. However, the adjacent Pipe Bridge has a clearance of only 11 metres (36 ft). This limitation, combined with only 1.5 metres (4 ft 11 in) depth of water, make it out of reach for most cruising vessels. Along with

441-488: A frictionless pulley. There are two forces acting on the body A: its weight ( w 1 = m 1 g {\displaystyle w_{1}=m_{1}g} ) pulling down, and the tension T {\displaystyle T} in the string pulling up. Therefore, the net force F 1 {\displaystyle F_{1}} on body A is w 1 − T {\displaystyle w_{1}-T} , so m 1

504-705: A net force somewhere in the system. In this case, negative acceleration would indicate that | m g | > | T | {\displaystyle |mg|>|T|} . ∑ F → = T → − m g → ≠ 0 {\displaystyle \sum {\vec {F}}={\vec {T}}-m{\vec {g}}\neq 0} In another example, suppose that two bodies A and B having masses m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} , respectively, are connected with each other by an inextensible string over

567-454: A net force when an unbalanced force is exerted on it, in other words the sum of all forces is not zero. Acceleration and net force always exist together. ∑ F → ≠ 0 {\displaystyle \sum {\vec {F}}\neq 0} For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards (positive acceleration) therefore there exists

630-582: A planned manner so that the stresses resulting from the imposed loads are counteracted to the desired degree. Prestressed concrete is used in a wide range of building and civil structures where its improved performance can allow for longer spans , reduced structural thicknesses, and material savings compared with simple reinforced concrete . Typical applications include high-rise buildings , residential concrete slabs , foundation systems , bridge and dam structures, silos and tanks , industrial pavements and nuclear containment structures . First used in

693-609: A proof-loaded, redundant and monitorable pressure-containment system. Nuclear reactor and containment vessels will commonly employ separate sets of post-tensioned tendons curved horizontally or vertically to completely envelop the reactor core. Blast containment walls, such as for liquid natural gas (LNG) tanks, will normally utilize layers of horizontally-curved hoop tendons for containment in combination with vertically looped tendons for axial wall pre-stressing. Heavily loaded concrete ground-slabs and pavements can be sensitive to cracking and subsequent traffic-driven deterioration. As

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756-419: A protective sleeve or duct which is either cast into the concrete structure or placed adjacent to it. At each end of a tendon is an anchorage assembly firmly fixed to the surrounding concrete. Once the concrete has been cast and set, the tendons are tensioned ("stressed") by pulling the tendon ends through the anchorages while pressing against the concrete. The large forces required to tension the tendons result in

819-620: A railway bridge constructed 1946 in the UK . By the 1960s, prestressed concrete largely superseded reinforced concrete bridges in the UK, with box girders being the dominant form. In short-span bridges of around 10 to 40 metres (30 to 130 ft), prestressing is commonly employed in the form of precast pre-tensioned girders or planks. Medium-length structures of around 40 to 200 metres (150 to 650 ft), typically use precast-segmental, in-situ balanced-cantilever and incrementally-launched designs . For

882-508: A result, prestressed concrete is regularly used in such structures as its pre-compression provides the concrete with the ability to resist the crack-inducing tensile stresses generated by in-service loading. This crack-resistance also allows individual slab sections to be constructed in larger pours than for conventionally reinforced concrete, resulting in wider joint spacings, reduced jointing costs and less long-term joint maintenance issues. Initial works have also been successfully conducted on

945-532: A significant permanent compression being applied to the concrete once the tendon is "locked-off" at the anchorage. The method of locking the tendon-ends to the anchorage is dependent upon the tendon composition, with the most common systems being "button-head" anchoring (for wire tendons), split-wedge anchoring (for strand tendons), and threaded anchoring (for bar tendons). Tendon encapsulation systems are constructed from plastic or galvanised steel materials, and are classified into two main types: those where

1008-503: A single tendon duct, with the exception of bars which are mostly used unbundled. This bundling makes for more efficient tendon installation and grouting processes, since each complete tendon requires only one set of end-anchorages and one grouting operation. Ducting is fabricated from a durable and corrosion-resistant material such as plastic (e.g., polyethylene ) or galvanised steel, and can be either round or rectangular/oval in cross-section. The tendon sizes used are highly dependent upon

1071-429: A string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". 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

1134-560: A string with tension, T , at a constant velocity . The system has a constant velocity and is therefore in equilibrium because the tension in the string, which is pulling up on the object, is equal to the weight force , mg ("m" is mass, "g" is the acceleration caused by the gravity of Earth ), which is pulling down on the object. ∑ F → = T → + m g → = 0 {\displaystyle \sum {\vec {F}}={\vec {T}}+m{\vec {g}}=0} A system has

1197-413: A string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object. In terms of force, it is the opposite of compression . Tension might also be described as the action-reaction pair of forces acting at each end of an object. At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing,

1260-592: Is a highly versatile construction material as a result of it being an almost ideal combination of its two main constituents: high-strength steel, pre-stretched to allow its full strength to be easily realised; and modern concrete, pre-compressed to minimise cracking under tensile forces. Its wide range of application is reflected in its incorporation into the major design codes covering most areas of structural and civil engineering, including buildings, bridges, dams, foundations, pavements, piles, stadiums, silos, and tanks. Building structures are typically required to satisfy

1323-418: Is fed into a greasing chamber and then passed to an extrusion unit where molten plastic forms a continuous outer coating. Finished strands can be cut-to-length and fitted with "dead-end" anchor assemblies as required for the project. Both bonded and unbonded post-tensioning technologies are widely used around the world, and the choice of system is often dictated by regional preferences, contractor experience, or

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1386-452: Is located on the western side of the bridge. On 8 March 2022, torrential rain and inadequate drainage led to the bridge being dubbed the new "Roseville Aqueduct" with images showing floating cars and water fall edge. An original bridge across Middle Harbour at Roseville was built jointly by the Willoughby , Ku-ring-gai and Warringah councils; with fifty percent of the funding provided by

1449-423: Is most commonly used for the fabrication of structural beams , floor slabs , hollow-core slabs, balconies , lintels , driven piles , water tanks and concrete pipes . Post-tensioned concrete is a variant of prestressed concrete where the tendons are tensioned after the surrounding concrete structure has been cast. The tendons are not placed in direct contact with the concrete, but are encapsulated within

1512-429: Is produced by the tensioning of high-strength "tendons" located within or adjacent to the concrete and is done to improve the performance of the concrete in service. Tendons may consist of single wires , multi-wire strands or threaded bars that are most commonly made from high-tensile steels , carbon fiber or aramid fiber . The essence of prestressed concrete is that once the initial compression has been applied,

1575-465: Is the force constant per unit length [units force per area], σ ( x ) {\displaystyle \sigma (x)} is the ...., τ ( x ) {\displaystyle \tau (x)} is the ...., and ω 2 {\displaystyle \omega ^{2}} are the eigenvalues for resonances of transverse displacement ρ ( x ) {\displaystyle \rho (x)} on

1638-459: Is the most popular structural material for bridges, and prestressed concrete is frequently adopted. When investigated in the 1940s for use on heavy-duty bridges, the advantages of this type of bridge over more traditional designs was that it is quicker to install, more economical and longer-lasting with the bridge being less lively. One of the first bridges built in this way is the Adam Viaduct ,

1701-486: Is the protection afforded to the end-anchorage assemblies of unbonded tendons or cable-stay systems, as the anchorages of both of these are required to retain the prestressing forces. Failure of any of these components can result in the release of prestressing forces, or the physical rupture of stressing tendons. Modern prestressing systems deliver long-term durability by addressing the following areas: Several durability-related events are listed below: Prestressed concrete

1764-417: Is undertaken for three main purposes: to protect the tendons against corrosion ; to permanently "lock-in" the tendon pre-tension, thereby removing the long-term reliance upon the end-anchorage systems; and to improve certain structural behaviors of the final concrete structure. Bonded post-tensioning characteristically uses tendons each comprising bundles of elements (e.g., strands or wires) placed inside

1827-563: The NSW Government . It was built of reinforced concrete by unemployed returned servicemen and opened on 20 September 1924. It was claimed to be the longest bridge of that type in NSW although the bridge across the Hawkesbury River at North Richmond was longer. It was claimed to be the first bridge supported on reinforced concrete piles. This low-level two-lane bridge was located downstream of

1890-798: The Burnt Bridge Creek Deviation, which is the only part of the Warringah Expressway built on the Northern Beaches by the Labor Wran government, there are today only two other major roads to these areas: Mona Vale Road, and Spit Road which crosses Middle Harbour downstream from Roseville Bridge using the Spit Bridge. The road carries three lanes of traffic towards Roseville, and three lanes of traffic towards Frenchs Forest . A grade-separated shared pedestrian footpath and cycleway

1953-405: The application, ranging from building works typically using between 2 and 6 strands per tendon, to specialized dam works using up to 91 strands per tendon. Fabrication of bonded tendons is generally undertaken on-site, commencing with the fitting of end-anchorages to formwork , placing the tendon ducting to the required curvature profiles, and reeving (or threading) the strands or wires through

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2016-444: The authorities of building codes or standards, but rather exist to promote the understanding and development of prestressed concrete design, codes and best practices. Rules and requirements for the detailing of reinforcement and prestressing tendons are specified by individual national codes and standards such as: Tension (physics) Tension is the pulling or stretching force transmitted axially along an object such as

2079-468: The availability of alternative systems. Either one is capable of delivering code-compliant, durable structures meeting the structural strength and serviceability requirements of the designer. The benefits that bonded post-tensioning can offer over unbonded systems are: The benefits that unbonded post-tensioning can offer over bonded systems are: Long-term durability is an essential requirement for prestressed concrete given its widespread use. Research on

2142-641: The bridge, a significant upgrade of the approach roads was completed, which became the six-lane Warringah Road. This upgraded section of road is approximately 2 kilometres (1.2 mi) long. Today Roseville Bridge is part of a major thoroughfare from the Pacific Highway at Roseville to the Northern Beaches and suburbs east of Middle Harbour. Due to the halt of the construction of the Warringah Expressway across Middle Harbour to Wakehurst Parkway and

2205-433: The concrete volume (internal prestressing) or wholly outside of it (external prestressing). While pre-tensioned concrete uses tendons directly bonded to the concrete, post-tensioned concrete can use either bonded or unbonded tendons. Pre-tensioned concrete is a variant of prestressed concrete where the tendons are tensioned prior to the concrete being cast. The concrete bonds to the tendons as it cures , following which

2268-404: The concrete wall to form a series of hoops, spaced vertically up the structure. When tensioned, these tendons exert both axial (compressive) and radial (inward) forces onto the structure, which can directly oppose the subsequent storage loadings. If the magnitude of the prestress is designed to always exceed the tensile stresses produced by the loadings, a permanent residual compression will exist in

2331-589: The current bridge, and connected Babbage Road to what is today called Healey Way, which is the entrance to Davidson Park within Garigal National Park . The first bridge replaced an earlier ferry service consisting of rowing boats across the narrowest section of water. The 1924 bridge survived the opening of the new bridge, and provided pedestrian access only, until it was demolished in 1974, along with Roseville Baths. Almost nothing remains from these structures. Pre-stressed concrete This compression

2394-964: The design and construction of prestressed concrete structures. In the United States, such organizations include the Post-Tensioning Institute (PTI) and the Precast/Prestressed Concrete Institute (PCI). Similar bodies include the Canadian Precast/Prestressed Concrete Institute (CPCI), the UK's Post-Tensioning Association, the Post Tensioning Institute of Australia and the South African Post Tensioning Association. Europe has similar country-based associations and institutions. These organizations are not

2457-413: The ducting. Following concreting and tensioning, the ducts are pressure-grouted and the tendon stressing-ends sealed against corrosion . Unbonded post-tensioning differs from bonded post-tensioning by allowing the tendons permanent freedom of longitudinal movement relative to the concrete. This is most commonly achieved by encasing each individual tendon element within a plastic sheathing filled with

2520-426: The durability performance of in-service prestressed structures has been undertaken since the 1960s, and anti-corrosion technologies for tendon protection have been continually improved since the earliest systems were developed. The durability of prestressed concrete is principally determined by the level of corrosion protection provided to any high-strength steel elements within the prestressing tendons. Also critical

2583-399: The end-anchoring of the tendons is released, and the tendon tension forces are transferred to the concrete as compression by static friction . Pre-tensioning is a common prefabrication technique, where the resulting concrete element is manufactured off-site from the final structure location and transported to site once cured. It requires strong, stable end-anchorage points between which

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2646-409: The ends of the string. By Newton's third law , these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are massless and frictionless . A vibrating string vibrates with a set of frequencies that depend on

2709-432: The force per cross-sectional area rather than the force alone, so stress = axial force / cross sectional area is more useful for engineering purposes than tension. Stress is a 3x3 matrix called a tensor , and the σ 11 {\displaystyle \sigma _{11}} element of the stress tensor is tensile force per area, or compression force per area, denoted as a negative number for this element, if

2772-451: The form of post-tensioned anchors drilled into the dam's concrete structure and/or the underlying rock strata. Such anchors typically comprise tendons of high-tensile bundled steel strands or individual threaded bars. Tendons are grouted to the concrete or rock at their far (internal) end, and have a significant "de-bonded" free-length at their external end which allows the tendon to stretch during tensioning. Tendons may be full-length bonded to

2835-404: The late nineteenth century, prestressed concrete has developed beyond pre-tensioning to include post-tensioning , which occurs after the concrete is cast. Tensioning systems may be classed as either monostrand , where each tendon's strand or wire is stressed individually, or multi-strand , where all strands or wires in a tendon are stressed simultaneously. Tendons may be located either within

2898-432: The longest bridges, prestressed concrete deck structures often form an integral part of cable-stayed designs . Concrete dams have used prestressing to counter uplift and increase their overall stability since the mid-1930s. Prestressing is also frequently retro-fitted as part of dam remediation works, such as for structural strengthening, or when raising crest or spillway heights. Most commonly, dam prestressing takes

2961-602: The opening of the inaugural Roseville Bridge. On 2 April 1966, the Liberal Premier Robin Askin , the local Member for Collaroy , officially opened the new six-lane, high-level bridge, in a ceremony attended by several hundred people, including Pat Morton (Minister for Local Government and Highways), Milton Morris (Minister for Transport), Dick Healey (Member for Wakehurst), Harry Jago (Member for Gordon), and J. A. L. Shaw (Commissioner for Main Roads). Built at

3024-537: The restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length. Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units ). The ends of

3087-413: The resulting material has the characteristics of high-strength concrete when subject to any subsequent compression forces and of ductile high-strength steel when subject to tension forces . This can result in improved structural capacity and/or serviceability compared with conventionally reinforced concrete in many situations. In a prestressed concrete member, the internal stresses are introduced in

3150-416: The rod is being compressed rather than elongated. Thus, one can obtain a scalar analogous to tension by taking the trace of the stress tensor. A system is in equilibrium when the sum of all forces is zero. ∑ F → = 0 {\displaystyle \sum {\vec {F}}=0} For example, consider a system consisting of an object that is being lowered vertically by

3213-553: The strands is provided by the combined layers of grease, plastic sheathing, and surrounding concrete. Where strands are bundled to form a single unbonded tendon, an enveloping duct of plastic or galvanised steel is used and its interior free-spaces grouted after stressing. In this way, additional corrosion protection is provided via the grease, plastic sheathing, grout, external sheathing, and surrounding concrete layers. Individually greased-and-sheathed tendons are usually fabricated off-site by an extrusion process. The bare steel strand

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3276-408: The string's tension. These frequencies can be derived from Newton's laws of motion . Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string. If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a net force on that segment of

3339-409: The string, with solutions that include the various harmonics on a stringed instrument . Tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or truss member. In this context, tension is analogous to negative pressure . A rod under tension elongates . The amount of elongation and the load that will cause failure both depend on

3402-758: The string, causing an acceleration. This net force is a restoring force , and the motion of the string can include transverse waves that solve the equation central to Sturm–Liouville theory : − d d x [ τ ( x ) d ρ ( x ) d x ] + v ( x ) ρ ( x ) = ω 2 σ ( x ) ρ ( x ) {\displaystyle -{\frac {\mathrm {d} }{\mathrm {d} x}}{\bigg [}\tau (x){\frac {\mathrm {d} \rho (x)}{\mathrm {d} x}}{\bigg ]}+v(x)\rho (x)=\omega ^{2}\sigma (x)\rho (x)} where v ( x ) {\displaystyle v(x)}

3465-579: The structure to counter in-service loadings. This provides many benefits to building structures: Some notable building structures constructed from prestressed concrete include: Sydney Opera House and World Tower , Sydney; St George Wharf Tower , London; CN Tower , Toronto; Kai Tak Cruise Terminal and International Commerce Centre , Hong Kong; Ocean Heights 2 , Dubai; Eureka Tower , Melbourne; Torre Espacio , Madrid; Guoco Tower (Tanjong Pagar Centre), Singapore; Zagreb International Airport , Croatia; and Capital Gate , Abu Dhabi UAE. Concrete

3528-475: The surface of the tendons is critical to the pre-tensioning process, as it determines when the tendon anchorages can be safely released. Higher bond strength in early-age concrete will speed production and allow more economical fabrication. To promote this, pre-tensioned tendons are usually composed of isolated single wires or strands, which provides a greater surface area for bonding than bundled-strand tendons. Unlike those of post-tensioned concrete (see below),

3591-432: The surrounding concrete or rock once tensioned, or (more commonly) have strands permanently encapsulated in corrosion-inhibiting grease over the free-length to permit long-term load monitoring and re-stressability. Circular storage structures such as silos and tanks can use prestressing forces to directly resist the outward pressures generated by stored liquids or bulk-solids. Horizontally curved tendons are installed within

3654-546: The tendon element is subsequently bonded to the surrounding concrete by internal grouting of the duct after stressing ( bonded post-tensioning); and those where the tendon element is permanently de bonded from the surrounding concrete, usually by means of a greased sheath over the tendon strands ( unbonded post-tensioning). Casting the tendon ducts/sleeves into the concrete before any tensioning occurs allows them to be readily "profiled" to any desired shape including incorporating vertical and/or horizontal curvature . When

3717-418: The tendons are stretched. These anchorages form the ends of a "casting bed" which may be many times the length of the concrete element being fabricated. This allows multiple elements to be constructed end-to-end in the one pre-tensioning operation, allowing significant productivity benefits and economies of scale to be realized. The amount of bond (or adhesion ) achievable between the freshly set concrete and

3780-406: The tendons are tensioned, this profiling results in reaction forces being imparted onto the hardened concrete, and these can be beneficially used to counter any loadings subsequently applied to the structure. In bonded post-tensioning, tendons are permanently bonded to the surrounding concrete by the in situ grouting of their encapsulating ducting (after tendon tensioning). This grouting

3843-662: The tendons of pre-tensioned concrete elements generally form straight lines between end-anchorages. Where "profiled" or "harped" tendons are required, one or more intermediate deviators are located between the ends of the tendon to hold the tendon to the desired non-linear alignment during tensioning. Such deviators usually act against substantial forces, and hence require a robust casting-bed foundation system. Straight tendons are typically used in "linear" precast concrete elements, such as shallow beams, hollow-core slabs ; whereas profiled tendons are more commonly found in deeper precast bridge beams and girders. Pre-tensioned concrete

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3906-677: The use of precast prestressed concrete for road pavements, where the speed and quality of the construction has been noted as being beneficial for this technique. Some notable civil structures constructed using prestressed concrete include: Gateway Bridge , Brisbane Australia; Incheon Bridge , South Korea; Roseires Dam , Sudan; Wanapum Dam , Washington, US; LNG tanks , South Hook, Wales; Cement silos , Brevik Norway; Autobahn A73 bridge , Itz Valley, Germany; Ostankino Tower , Moscow, Russia; CN Tower , Toronto, Canada; and Ringhals nuclear reactor , Videbergshamn Sweden. Worldwide, many professional organizations exist to promote best practices in

3969-491: The wall concrete, assisting in maintaining a watertight crack-free structure. Prestressed concrete has been established as a reliable construction material for high-pressure containment structures such as nuclear reactor vessels and containment buildings, and petrochemical tank blast-containment walls. Using pre-stressing to place such structures into an initial state of bi-axial or tri-axial compression increases their resistance to concrete cracking and leakage, while providing

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