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Bridge Insight : New Development in Long Span Arch Bridges
The application of Pre-Stressed Concrete(PSC) is used to offset the occurrence of tensile stresses in concrete, which is weak in tension, by applying an external force(Compressive Force) to the concrete beforehand.
Fig. Concept of prestressed concrete
PSC uses high-strength steel and concrete in comparison to RC(Reinforced Concrete). Furthermore, since it is designed without cracks, it has good durability and watertightness, and has outstanding resistance to impact load and repeated loads compared to RC. In addition, since the shear surface of concrete can be effectively used, due to the assumption that there are no cracks, the second moment of the cross-section is large, causing the deflection due to live loads to be small.
The Prestressing method is classified by its purpose and method.
A case in which the tendon is located within the concrete structure. An important feature of internal prestressing is that, due to the flexible arrangements of sheath tubes, it allows designers to apply desired tensile forces to the structure. However, after its application, it is difficult to replace the Tendons. Furthermore, if Grouting is preformed, it is difficult to check whether or not it was performed correctly. The concept of internal prestressing is being used in most Prestressed concrete structures.
Fig. Concept of internal prestressing
A case in which the tendon is outside the concrete structure. An important feature of external prestressing is maintenance because the external tendon can be inspected and replaced with ease. Furthermore, when existing structures require reinforcement, tension members can be easily installed. Since the sheath tube is not arranged inside the concrete structure, the concrete cross-section can be planned thinner. Moreover, it allows designers to freely plan concrete sections, allowing a more economical design by reducing the weight of the structure.
Fig. Concept of external prestressing
Pre-tensioning is a method of introducing prestress to the concrete structure through the bond between concrete and tendons. Firstly, tension is applied to the Tendon before casting concrete. Then the concrete is cast, and after it hardens, the tension in the Tendon is gradually released, transferring prestress to the concrete member. Tensioning is possible for one girder or several girders depending on the length of the prestressing bed.
Fig. Individual mold method & Long line method
Fig. Individual mold method & Long line method
The advantages and disadvantages of pre-tensioning are as follows.
1. Members of the same shape and dimensions can be manufactured in large quantities.
2. Additional members such as sheath tubes and anchorage devices are not required
3. Factory manufacturing is possible, making the quality of the product highly reliable.
4. Not suitable for large members because it is difficult to arrange the prestressing tendon in a curve.
5. A certain amount of prestress is not transferred at the end of the members so the design requires attention.
A. One end of the tendon is temporarily enclosed against some abutment while the other end is pulled by using a jack, tensioning the tendon.
Fig. Pre-tensioning method 1
B. Concrete is poured into the formwork and cured.
Fig. Pre-tensioning method 2
C. When concrete hardens and reaches sufficient strength, the anchorage is slowly released, transferring prestress.
Fig. Pre-tensioning method 3
Post-tensioning is a method of introducing prestress to the concrete structure by anchoring the Tendon on both sides of the concrete member. The general process of the post-tensioning is:
1. When casting the concrete, a sheath pipe must be previously installed in order to place the tendons inside the concrete member.
2. Once the concrete is cast and hardened, the tendons are placed inside the concrete member through the sheath pipe.
3. One side is anchored while the other end is pulled by using a jack, tensioning the tendon.
4. Anchor the other side to transfer the tensioning force to the concrete member.
There are two types of Post-tensioning method. The first one is Unbonded post-tensioning. The tendon of this type consists of a plastic tube, steel strands coated a grease. This type allows for installing tendons individually. And also this type is able to avoid installing sheaths and grouting work. The other is Bonded post-tensioning. The tendon of this type consists of a sheath(duct), strands, and grouting concrete. The prestressing force of this type is applied to a concrete member after the concrete that is poured inside of the sheath is hardened. This type allows applying larger prestressing force to the concrete member than the unbonded post-tensioning.
Fig. Concept of Post-tensioning
The advantages and disadvantages of post-tensioning are as follows:
1. The tendons can be curved, which makes it suitable for large structures.
2. The structure itself is used as a support, so tension bands are not required.
3. Tensioning is possible at the construction site.
4. Unbonded post-tensioning tendons can be re-tensioned.
5. Unbonded PSC members have low fracture strength and wider crack width.
6. Special tensioning method and anchoring device required.
A. After placing a sheath to contain the tendons inside the formwork, concrete is poured and cured.
Fig. Post-tensioning method 1
B. When concrete reaches sufficient strength, One end is fixed while a jack is installed at the other end of the tendon. The tendon is then pulled, tensioning the tendons. Once tensioning is completed, the tendons are fixed to the concrete with an anchoring device.
Fig. Post-tensioning method 2
A Girder is one of a superstructure. It mainly supports structures located above it. For instance, girder bridges support the deck slabs on which vehicles and people pass. Loads due to structures, vehicles, passengers, and etc. are transferred to the substructure through the girder and then to the ground.
Various types of girders (I, U, Box, and T) are possible. Generally, due to the pre-tensioned characteristics, the shape of the Tendon profile is often straight. It is often used for composite girder bridges where the slabs and girders are combined.
Fig. Pre-tensioned PSC girders
Just like the pre-tensioned girders, there are various types of girders such as I, U, T, and Box. The characteristics of post-tensioned are that the shape of the Tendon profile can be varied and the anchorage is located at the end of the girder.
Fig. Post-tensioned PSC girders
Precast (Prestressed) concrete is used in various types of bridges where concrete is used such as Precast beam bridges, In situ balanced cantilever bridges, Precast segmental cantilever bridges, Incrementally launched bridges, Concrete arch foot bridges, Cable stayed bridges, etc., depending on the required length of the bridge.
a) Precast beam composite bridge
b) In situ balanced cantilever bridge
c) Precast segemtal cantilever bridge
d) Incrementally launched bridge
e) Arch bridge with PSC girder
Fig. Prestressed Concrete Bridges
f) Cable stayed bridge
Among the many prestressed concrete bridges, the most commonly used bridge type is the one using precast beams. This particular bridge has several precast PSC beams supporting the upper slab so that vehicles and pedestrians can pass over it. The bridge can be composed of 1 span or multi span with 20~40m per span. Depending on the shape and construction method of the beam, the length of one span can be as long as 50m.
Fig. Prestressed concrete bridge & cross-section 1
Fig. Prestressed concrete bridge & Cross-section 2
A member made out of more than one material is called a composite member. In bridges, girders and the slabs are combined and used as superstructures. These are called Composite Girders. The basis of Composite members is to assume full convergence. The strain is matched as shown in the figure below.
Fig. Composite action
There are various composite girders according to the shape of the girder. Concrete materials are used for Slabs while both steel and concrete materials are used for Girders.
a) Composite steel I girder
b) Composite steel tub girder
c) Composite PSC I girder
Fig. Composite girders
PSC girders are arranged in various ways according to the planar shape of the bridge. For curved shapes, two types are possible. Since each of the two types has its respective advantages and disadvantages, it must be selected taking into consideration design and economic conditions.
c) Curved – type1
Fig. Plan view of girder arrangement
There are three main types of concrete decks used in the presetressed concrete bridges: In Situ concrete deck, Full depth Precast deck, and Partial depth precast deck.
The In situ concrete deck is a universal type of concrete deck that has been widely used since ancient times. Compared to other types of decks, construction is flexible for cross-sectional shape and bridge geometrical shape. In addition, if the construction management is carried out smoothly, sufficient strength can be obtained, and there are certain advantages of combining the girder supports with the concrete deck. However, since the installation of the formwork is essential and the concrete curing period is required, there are certain disadvantages, including longer construction periods and labor-intensive work.
a. In situ concrete slab
Initially, Full depth Precast deck (hereinafter referred to as Precast deck) was developed in order to provide rapid construction of any damages that occurred to existing bridge concrete decks. Furthermore, it is used to minimize on-site work and shorten the construction time for newly constructed bridges. The use of Precast deck can reduce the construction time of the site by omitting on-site work such as the installation of formwork. Additionally, since it is manufactured at a factory, the quality of the concrete deck can be improved. However, if the geometrical shape of the bridge is uneven, the Precast deck is difficult to adapt to. Moreover, the production cost is relatively high, and proper planning for transportation and installation is necessary according to site conditions. Precast deck has joints due to its characteristics. Therefore, various construction methods are being studied so that sufficient strength can be manifested at the joint.
b. Precast slab
Partial depth precast deck has a characteristic that the structure itself acts as a formwork during construction and as a concrete deck after construction. The full depth precast deck has a disadvantage because it is difficult to adjust the height of the concrete deck for superelevation of the bridge and camber. Partial depth precast deck can compensate for this problem because in situ concrete can be poured on the deck panel. Furthermore, since precast concrete is used and formwork and scaffolding required for in situ concrete are not required, work efficiency can be expected to improve. Therefore, the partial depth precast deck has all the advantages of an in situ concrete deck and a full depth precast deck. Due to the nature of precast concrete, consideration should be given to joints and cracks.
c. Half-precast slab (fig. Plan view of girder arrangement)
The shear connector is installed on the girder and integrated with the concrete deck so that girder and the concrete deck work together. It is mainly installed by embedding the shear connector in the concrete girder. As for the forms of the shear connectors have been proposed and studied in consideration of the binding capacity of girders and concrete decks, and the work efficiency of construction workers.
(Fig. Plan view of girder arrangement)
b) Hooker rebars
The construction of the PSC Beam Bridge is performed in the following order
1) construction of piers and abutments,
2) beam installation
3) construction of the upper deck of the beam.
There are two construction methods for PSC Beam installment: The mobile crane method and launching gantry crane method. The mobile crane construction method is used when there are no significant restrictions on the construction environment, allowing for a smooth supply of PSC Beams, and it is characterized as a simple process of installing PSC Beams on piers.
Fig. Mobile crane
a.PSC girder transported to site using a trailer.
b. Lifting and installment of PSC girder using mobile cranes.
(Fig. Construction sequences)
The Launching Gantry Crane method is divided into the shuttle method, the one way method, and the side feeding method according to the supply method of the PSC Beam. Even in conditions where it is difficult to supply PSC Beams, such as supplying to downtown areas or floating cities, the Launching Gantry Crane construction method enables the construction of PSC Beam bridges in such rough conditions by supplying the material to the construction site through trailers. Girder Bridges can be applied in locations where construction conditions are unfavorable such as mountainous terrains, high piers located at an ocean, busy downtown areas with uncontrollable traffic, and railroad crossing bridges. When a sea bridge is constructed, it is possible to preserve the river ecology by not installing a road or a railroad. For theoretical application, the planar and longitudinal alignments must be considered in advance to fit equipment specifications when planning for bridge construction.
Fig. Launching Gantry Crane shuttle/one way method
a. PSC girder is lifted and the Launching crane with the girder moves over the gap to the next pier.
b. PSC girder installed
c. Launching crane moves back and supplies another PSC girder
Fig. Launching gantry crane side feeding method
a. PSC girder is transported to site and Launching crane moves over the gap to the next pier.
b. PSC is lifted and installed.
c. Launching crane moves to the next pier
(Fig. Construction sequences)
The PSC Spliced Girder method is when girder bridges are used for long-span bridges. It is a construction method where the manufacturing of the girders is divided into segments at the pier heads and at the span (side span, middle span), and connects the point where the bending moment is minimal. The construction method is as follows: after the pre-built members are transported and constructed on site, a Bent is installed between the pier head and the span.
Fig. Construction procedure and characteristics of the PSC spliced girder method.
a. Installment of pre-fabricated segment member at a pier head
b. Installment of pre-fabricated segment member at a span.
c. To be continuity of PSC girder, bents are installed at the connection points of girder.
(Fig. Construction sequences)
PSC Beams are supported on the piers. There are three different methods for supporting the PSC Beams:
1) Simply supported & discontinuous slab
2) Continuous beam & continuous slab
3) Simply supported & continuous slab. Each method is shown below.
Fig. Schematic diagram of simply supported & discontinuous slab
Movement joints between the upper slabs with PSC girders are installed to be continuous. Each PSC girder is supported by bearing plates.
Advantages & Disadvantages
- Structural analysis is simple due to support conditions
- Maintenance needs frequently due to problems with the movement joints. Movement joints between the upper slabs with PSC girders are installed to be continuous. Each PSC girder is supported by bearing plates.
Fig. Schematic diagram of continuous beam & continuous Slab
The upper slab is continuous and the PSC girders are simply supported by each bearing plate.
Advantages & Disadvantages
- Structural analysis is simple due to support conditions
- Continuous upper slab provides good drivability.
Simply Supported & Continuous Slab
Fig. Schematic diagram of simply supported & continuous slab
Both the upper slab and the PSC girder are continuous.
Advantages & Disadvantages
- Continuous upper slab provide good drivability.
- - The girder is continuous and interpreted as a statically indeterminate structure providing outstanding structural performance. Compared to the simply supported beam, the moment and deflection are small.
- It can be considered an uneconomical design because tendons must be bent along the change of the bending moment.
The PSC girder Bridge is completed by constructing the concrete deck on the top of PSC girders. There two methods of constructing concrete deck:
1) Cast-in-place method and 2) Precast method. Each method can be selected according to the site conditions; each shown below.
- The most commonly used construction method.
- Formworks and scaffolding systems required.
Fig. Schematic diagram formwork method
- Unable to check cracks or deterioration occurred on the lower part of the Deck.
- Expensive and poor aesthetics due to rust.
Fig. Schematic diagram of steel form-deck
- Fast Construction
- No formwork required.
- Difficult to transport and install for high piers
- Its regular geometry makes it difficult to changes in superelevation, camber, and etc..
- Measures to prevent cracking of joints are required.
Fig. Schematic diagram of full depth precast slab
- A construction method that complements the disadvantages of cast-in-place and existing pre-cast construction methods.
- After precast construction, the superstructure is constructed by reinforcement work and on-site casting
- Adaptable to changes in superelevation and camber through cast-in-place method
Fig. Schematic diagram of half depth precast slab
One of the tasks designers must perform in the design of PSC girders is global structural modeling/analysis. Global structural modeling refers to the process of numerical analysis of design loads, geometry of structures (linearity and boundary conditions), stiffness (cross-sectional shape), tendon profile, and construction methods. Afterwards, the structural analysis is completed by reviewing the safety and usability according to the design criteria using the cross-sectional forces obtained from the subsequent analysis results. Bridges consist of a superstructure and a substructure. If large displacements occur in the substructure and does not affect the superstructure, modelling and structural analysis of the substructure and superstructure may be carried out respectively.
Fig. Analysis model of prestressed concrete bridges
The plane grillage model is one of the proposed modeling methods for structural analysis of composite bridges. It is also actively applied in practice as the most common and easy method for interpreting bridge concrete deck structure. Any form of support condition can be freely expressed, as it can be constrained in any direction at each node. Furthermore, since there are no application restrictions depending on the type of bridge deck, the plane grillage model can be applied to skew bridges, curved bridges, or irregular bridge structures. The grillage spacing can be determined according to the designer’s experience. As a general modelling method, the main girders in the longitudinal direction are modeled as 1D beam elements. In the lateral direction, the slab is modeled as a 1D beam element, and if there are diaphragms/cross beams, the same is modeled as a 1D element.
Fig. Grillage model of prestressed concrete bridges
The combined model is a slab modeled as plate/shell elements, and girders and cross beams modeled as beam elements. In the slab, which is the upper deck of the bridge, out of plane bending deformations are dominant, so it is appropriate to use plate/shell elements. Plate/shell elements have quadrilateral or triangular shape and have compression, tensile, and shear stiffness in the planar direction, and flexural and shear stiffness in the thickness direction. It is desirable to use tetrahedron elements as much as possible for plate/shell elements, particularly in areas where stress changes are severe or areas requiring exact results. Theoretically, when the overall behavior of the plate is dominated by the out-of-plane flexural deformation, it is appropriate to use a thin plate, and when the effect of the out-of-plane shear deformation is considered, it is appropriate to use a thick plate. However, when it is difficult to choose even when the above are considered, they can be chosen in a simpler way. If the ratio of the length and thickness of the longest span on the plane of the model exceeds 10, a thin plate can be used, and if the ratio is less than 10, a thick plate can be used.
Fig. Combined model of prestressed concrete bridges
The behaviors of pre-stressed concrete structures depend on the effective pre-stress. When a pre-stressed concrete structure is analyzed, the change of tensions in pre-stressing tendons must be accurately calculated for a load history through every construction stage. Tension losses in Pre-Stressed (PS) tendons occur due to many different factors including the tensioning method.
In the case of pre-tensioning, tension losses are attributed to shrinkage and tendon relaxation before tensioning and elastic shortening, creep, shrinkage, tendon relaxation, loading and temperature after tensioning.
In the case of post-tensioning, tension losses are attributed to frictions between tendons and sheaths, anchorage slip, creep, shrinkage, tendon relaxation, loading and temperature.
Depending on the structural analysis program, there are various ways to apply the prestressing force to the model. Here are the most typical methods:
Directly inputting member loads and eccentricity to the element.
Applying prestressing force to the element by creating a tendon profile and inputting the prestressing force.
In case of a detailed analysis, prestressing force is applied by modeling a tendon profile as a truss in a 3D solid element.
Fig. Finite element models contain tendon profiles
When a prestressed force is applied to the member, the primary force and the secondary force can be observed. The primary force is the member force generated on the structure by the load acting on the structure. The secondary force is a member force generated by the restraint in deformation when deformation occurs in a structure due to a load. If the following prestressed concrete girder, for example, is classified as primary and secondary forces, 1) the following bending moment diagram (BMD) case occurs due to the prestressing forces. Looking at the bending moment diagram of the following case, it can be seen that there may be some deformation upward in the center of the girder. However, due to the boundary conditions in the center of the girder, the deformation is restrained, which results in a secondary force, and 2) the same BMD as the following case can be obtained. This phenomenon can be easily found in the statically indeterminate structure of the prestressing force. If a secondary force occurs, it must be considered as it changes the cross-sectional force generated in the structure.
Fig. Primary & secondary forces
The loss of prestress occurs due to various reasons. The loss contains the instantaneous loss and the time dependent loss.
Instantaneous Loss refers to the loss of prestressing force that occurs immediately when prestressing force is introduced into the tendon. The causes of Instantaneous loss include: Elastic shortening, Anchorage slip, and friction & wobble.
Elastic shortening refers to the loss caused by elastic deformation of the structure when a prestressing force is introduced into the concrete structure. If the prestressing force is introduced only once, the loss due to the elastic shortening is not considered. In the case of the pre-tensioning method, it is regarded as a loss that occurs at the moment when a tensile force is tensioned and before being used as a structural member, and it is not considered in the structural analysis. In the case of the post-tensioning method, the prestressing force is measured simultaneously with the elastic shortening of the concrete member, so it is not considered in the structural analysis. However, if a tendon group is tensioned gradually into a structure including multiple tendons, the loss must be considered because the prestressing force introduced in the tendons in the previous stage cause deformation.
a) Single tendon & pre-tensioning method
b) Tendons & post-tensioning method
(Fig. Prestressed Concrete Bridges)
The loss of prestressing force due to anchorage slip appears in the prestressed concrete structure where the post-tensioning method was applied. Frictional force is generated as much as the slipped length, which causes a loss in prestressing force and is mainly limited to the area close to the stressing anchorage, and the further away from the stressing anchorage, the less it is affected. In particular, a relatively large slip occurs when a wedge, one of the tendons fixing devices, is used. There are values allowed according to the design criteria, but in general, a slip length of about 2~3mm does not have a big effect on long tendons, but for a short tendon, the effect of slip should be considered. Loss due to slip can be corrected by overstressing during tension work.
Fig. Loss due to anchorage slip
In post-tensioning, frictions exist between the PS tendon and its sheathing. The pre-stressing force in the tendon decreases as it gets farther away from the jacking ends. The length effect and the curvature effect can be classified. The length effect, also known as the wobbling effect of the duct, depends on the length and stress of the tendon and refers to the friction stemming from imperfect linear alignment of the duct. The loss of pre-stress due to the curvature effect results from the intended curvature of the tendon in addition to the unintended wobble of the duct. Frictional coefficients, (/radian) per unit angle and k (/m) per unit length are expressed. If the coefficients for the materials used are unknown, the values suggested in the design criteria are used. However, if special tendons and sheaths are used, their coefficients must be obtained from the manufacturers.
Loss occurs over a long period of time after the prestressing force is introduced. The main causes are Creep & Shrinkage of concrete members and relaxation of tendons.
Creep refers to a phenomenon in which the strain increases gradually over time when a constant stress acting on a structure is applied. The modulus of elasticity of concrete increases with time. When stress is applied to concrete, deformation occurs immediately, and if this stress is not removed and continues to act upon the concrete, the deformation continues to increase over time due to creep. This change causes a loss of the prestressing force.
Drying of concrete causes shrinkage. Conversely, when concrete is cast in water, expansion occurs. Eventually, drying shrinkage causes a change in the volume of concrete, causing the tendon length to be relatively short, which causes a loss of prestressing force.
Steel exhibits creep when subjected to a stress of 50% or more of its tensile strength. It is said that the steel for prestressing is subjected to a stress of about 50~80% of the tensile strength in use. If the prestressing steel is strained between the two fixed points and left in a constant state of deformation, the stress gradually decreases with time due to creep. This phenomenon is called relaxation. The inherent relaxation of steel can be determined by measuring the loss of tensile force after tensioning the steel for a long period of time under conditions of constant temperature and length. At this time, the stress generated by the applied loads is called the initial stress. The calculation of relaxation is expressed as a percentage by diving the amount of reduced stress by the initial stress. In the prestressed concrete structure, the tendon is subjected to continuous tensile forces as shown above, resulting in relaxation. Therefore, relaxation in a prestressed concrete structure is one of the things that should be considered for loss and deformation of the prestressing force over time. The initial stress is needed to calculate the loss of the prestressing force due to relaxation. In prestressed concrete structures, the initial tension is reduced due to the effect of the creep and shrinkage of concrete, so the reduced relaxation should be used in consideration of the reduced tension.
In the pretension method, cracks occur due to the stress concentration at the concrete girder ends. To prevent this, partially unbonded tendons are used at both ends of the concrete girder. This is called debonding. Each country’s design standard specifies the unbonded length. In addition, sheath tubes are inserted to unbond the tendons partially.
Fig. Cracks at the end of a girder and debonding
In a pretensioned concrete member, it is the length required to transfer the effective prestressing force to the concrete member by bond. As shown in the figure below, the prestressing force is gradually introducing from the end of the member.
Fig. Transfer length of pretensioned concrete
Partially prestressed concrete allows some degree of cracking in the PSC member. This particular cracking behavior can be resolved by inserting reinforcing bars in the member. Furthermore, because there are less tendons inside the member and some degree of cracking is allowed, partially prestressed concrete is economical. However, overcoming crack control and fatigue loads are still challenges that must be addressed.
Fig. Partially prestressed concrete