Limitations of Pre-stressing | Pre-stressed Concrete

Limitation of pre-stressing

• More complicated design.
• Small margin of error.
• Pre-stress need skilled technology & labour hence it is not common in reinforced concrete members.
• The use of high strength material is costly.
• There is additional cost in auxiliary equipments (cranes etc).
• There is need for quality control & inspection.

Advantages of Pre-Stressing | Pre-Stressed Concrete

Advantages of Pre-stressing:

The pre-stressing of concrete has several advantages compared to traditional reinforced concrete (RC) without pre-stressing. Following are the advantages of the pre-stressed concrete member over an equivalent RC member.

(1) Section remains un-cracked under service load

1. while it is un-cracked will cause reduction of steel corrosion ultimately increases the durability.
2. Full section is utilized (mean higher amount of inertia) >Higher stiffness > less deflection (improved serviceability).
3. Increase in shear capacity.
4. Suitable for use in pressure vessels & liquid retaining structures.
5. Improved performance under dynamic & fatigue loading.

 (2)  Higher span to depth ratio

1. Larger spans are possible with pre-stressing (bridges. buildings with column free spaces).
2. For the same span less depth is required compared to RC members (reduction in self weight).
3. More aesthetic appeal due to slender section
4. More economical section because of smaller sections & less weight.

 (3) Suitable for pre-cast construction

1. Rapid construction
2. Better quality control
3. Reduced maintenance
4. Suitable for repetitive construction
5. Multiple use of form work
6. Availability of standard shapes

Important Definitions | Bridge Engineering | Khyberacademy.blogspot.com

SOME IMPORTANT DEFINITIONS:

Load: It is the effect of acceleration, including that due to gravity, imposed deformation or volumetric change.

Nominal Load: An arbitrary selected design load level.

Load Factor: A coefficient expressing the probability of variations in the nominal load for the expected service life of the bridge.

Permanent Loads: Loads or Forces which are, or assumed to be, constant upon completion of construction.

Force Effect: A deformation or a stress resultant, i.e. thrust, shear, torque/moment, caused by applied loads, imposed deformation or volumetric changes.

LIMIT STATES

“A limit state is a condition beyond which a structural system or structural component cease to full-fill the function for which it is designed”.

Bridges are designed for specified limit states to achieve the objectives of constructibility, safety and serviceability.

Generally the limit states that are considered in bridge design are;

1. Service limit state
2. Fatigue and fracture limit state
3. Strength limit state
4. Extreme Event limit state

Service Limit State

This limit state refers to restrictions on stress, deflections and crack widths of bridge component that occur under regular service conditions, There are three limit conditions given in the table to cover different design situations.

Service I: This service limit state refers to load combination relating to the normal operational use of the bridge with 90 km/h wind.

Service II: This service limit state refers to the load combination relating to steel structures and is intended to control yielding and slip of slip critical connections.

Service III: This service limit state refers to the load combination relating only to tension in pre-stressed concrete structures with the objective of crack control.

Fatigue and Fracture Limit State
This limit state refers to restrictions on range caused by a design truck. The restrictions depend upon the stress range excursions expected to occur during the design life of the bridge.

This limit state is used to limit cracks growth under repetitive loads and to prevent fracture due to cumulative stress effects in steel elements, component, and connections.

For the fatigue and fracture limit state, Ф = 1.0

Since, the only load that causes a large number of repetitive cycles is the vehicular live load; it is the only load effect that has a non-zero load factor.

Strength Limit State

This limit state refers to providing sufficient strength or resistance to satisfy the inequality

                                                       ФRn ≥ η ∑ γi Qi

This limit state include the evaluation of resistance factor to bending, shear, torsion, and axial load.

The statically determined resistance factor Ф will be less than 1.0 and will have values for different materials and strength limit states.

Strength-I: This strength limit is the basic load combination relating to the normal vehicular use of the bridge

without wind.

Strength-II: This strength limit is the basic load combination relating to the use of the bridge by permit vehicles without wind.

Strength-III: This strength limit is the basic load combination relating to the use of the bridge exposed

to wind velocity exceeding 90 km/h.

Strength-IV: This strength limit is the basic load combination relating to very high dead load/live load force effect ratios.

Strength-V: This strength limit is the basic load combination relating to the normal vehicular use of the bridge with wind of 90 km/h velocity. It differs from the Strength-III limit state by the presence of the live load on the bridge, wind on the live load and reduced wind on the structures.

Extreme Event Limit State

This load effect refers to the structural survival of a bridge during a major earthquake or floods or when collided by a vessel, vehicle, or ice flow. These loads are specified to be applied separately, as the probability of these events occurring simultaneously is very low.

Extreme Event-I: This extreme event limit state is the load combination relating to earthquake. This limit state also includes water load and friction.

Extreme Event-II: This extreme event limit state is the load, to ice load, collision by vessels, vehicles and to certain hydraulics events with reduced live loads.

BEHAVIOR OF BRIDGE SUPER STRUCTURE

The typical bridge superstructure consists of the deck slab placed on girders spaced at a certain interval and placed parallel to the direction of traffic flow. The centre to centre spacing of the girders and the slab thickness are of main concern in predicting the response of the bridge under vehicle loads.

Load Transfer Path

The vehicle moves over the deck slab, which distributes the load to the girders, and the girders in turn transfer the load to abutments.

Distribution Factor

The fraction of load transferred to each girder is called the distribution factor for that girder. The distribution factor is a function of proximity of the load to the girder and relative stiffness of deck and girder. In general, the girder near to the load will support greater fraction of the load hence having a greater distribution factor, while the girder away from the load will support a smaller fraction of load and thus having a smaller distribution factor.

Effect of High Relative Stiffness

The relative stiffness of girder and deck plays an important role in distributing the load to the girders. A relatively thin slab, resulting in a higher relative stiffness of girder to deck will not distribute the load evenly to all girders. The demand on the girders will be highly localized, i.e., the closest girder will support a significant fraction of load, resulting in higher deflections. Such a system utilizes the structural system inefficiently. It reduces the amount of concrete in the deck, thereby saving some cost and reducing the self weight of deck, but on the other hand, induces a higher live load demand on the critical girder.

Note that this not only increase demand on the deck but also on the critical girder, while other  girders are contributing less to support the load. This demonstrates inefficient utilization of structural system.

Effect Of Low Relative Stiffness

The relatively thick slab results in a low relative stiffness of girder to deck and will distribute the load more evenly to all girders. The demand on the girders will be more uniform, I.e. all girders will support almost same fraction of load, resulting in lower deflections. Such a system utilizes the structural capacity efficiently. Although, it increases the amount of concrete in the deck, thereby increasing cost of concrete and increasing self weight of deck, but on the other hand, requires a lighter girder section due to reduced distribution of live load demand on the critical girder. Note that this not only decreases demand on the deck but also on the critical girder, while other girders are also contributing equally to support the load. This demonstrates efficient utilization.

CATEGORIZATION OF BRIDGES ACCORDING TO MATERIAL OF  CONSTRUCTION

1.  Steel bridges
2. Concrete bridges
3. Hybrid bridges
4. Wood bridges
5. Stone / Brick bridges

CATEGORIZATION OF BRIDGES ACCORDING TO SPAN

1.Small Span Bridges (Up to 15m)

• Culvert bridges
• Slab bridges
• T-Beam bridges
• Wood Beam bridges
• Pre-cast concrete Box Beam bridges
• Pre-cast concrete I-Beam bridges
• Rolled steel Beam bridge

2.Medium Span Bridges (Up to 50m)

• Pre-cast concrete Box Beam bridges
• Pre-cast concrete I-Beam bridges
• Composite Rolled Steel Beam bridges
• Composite Steel Plate Girder bridges
• Cast in RCC Box Girder bridge
• Cast in Place Post-Tensioned Concrete Box Girder
• Composite Steel Box Girder

3.Large Span Bridges (50m to 150m)

• Composite Steel Plate Girder bridges
• Cast in place Post-Tensioned Concrete Box Girder
• Post Tensioned Concrete Segmental Construction
• Concrete Arch and Steel Arch

4.Extra Large (Long) Span Bridges (Over 150m)

• Cable Stayed bridges
• Suspension bridges

Cable Stayed Bridge

Substructure – Abutments | Bridge Engineering

SUBSTRUCTURE TYPES
 
The type of foundation generally depends on the soil loading or waterway conditions. Early in the development of a bridge, geotechnical information may not be available and the project foundation engineer may have to rely on existing soils information from a nearby structure to determine the most practical foundation type.
Typical Foundation types are:

1. Drilled Shafts (wet or dry conditions)
2. Steel H Piling
3. Pipe Piling (closed or open end)
4. Spread Footing

Field splices for steel H piles, plate dimensions, and weld symbols. Permissible field splices for pipe piles. Details of the splices, plates, and sizes of welds should be shown on the plans.
The type of bridge bearing selected can have large force impacts on substructure when stiff substructures are used. It is very important to select a bearing/substructure system that is functional and economical. Sometimes the process can become quite iterative.

1. PIERS
Piers can be multiple or single column bents. If the structure is not too wide, A single column bent may be used to reduce the clutter underneath the bridge. Single columns usually rest on a pile cap footing or drilled shaft.
The bents of many structures have multiple round columns with a rectangular pier cap. The columns usually rest on single drilled shafts or a pile cap footing. For very short bents on stream crossings, a line of piling many be extended into the pier cap and encased in concrete to form a curtain wall.

2. ABUTMENTS

There are two basic types of abutments, open end and closed end (or retaining). Each has several subtypes. Open end abutments are located near the top of the approaching roadway embankment. Closed end abutments retain the soil so that an embankment does not exist under the bridge. The type of abutment used is based on economic considerations.

Open end abutments may be backwall, integral and semi-integral, or spill-through type. The backwall type is generally supported on piles or drilled shafts which extend through the embankment. The spill-through abutment is a common type used in New Mexico. The fill extends from the bottom of the cap beam and is allowed to spill through the open spaces between the columns.

Closed end abutments can be mechanically stabilized earth (MSE), double T, or conventionally reinforced retaining walls. The MSE wall is not a true closed type abutment because it is not load bearing and is used with an open type abutment. The recommended minimum offsets required for an MSE abutment. The earthwork requirements for both open and closed type abutments.

Since the abutments and the bridge settle with the MSE wall and the approach embankment, smooth riding bridges can be obtained. This same settlement of the abutments can however be problematic if it is large or if the abutment is part of a continuous multi-span bridge. Use of this type of abutment should therefore be carefully considered and discussed with both the State Bridge Engineer and the Foundation Engineer before design is begun.

Types of Abutment

INFLUENCE FUNCTIONS | Bridge Engineering

A function that represents the load effect (force or displacement) at a point in the structure as a unit action moves along a path or over surface.

 Influence Function:

• Superposition of all the load effects yields

• Action    A = P1* η (x1)+P2* η (x2)+--- +Pn*η (xn) = ΣPi*η (xi) = ΣPi*ηi (5.1)

• Linear behavior is a necessary condition for application of Equation 5.1, that is, the influence coefficients must be based on a linear relationship between the applied unit action and the load effect.

• For statically determinate structures, this relationship typically hold true except for cases of large deformation where consideration of deformed geometry must be considered in the equilibrium formulation.

• The unit action load effect relationship in the statically indeterminate structures is a function of the relative stiffness of the elements. If stiffness changes are due to load application from either material non linearity and/or  geometric non linearity (large deflections), then the principle of superposition cannot be applied. In such cases, the use of influence functions is not appropriate and the loads must be applied sequentially as expected in the real structure. 

• The analysis of a structure subjected to numerous load placements can be labour intensive and algebraically complex. The unit action must be considered at numerous locations requiring several analyses.

• The Muller-Breslau Principle allows the analyst to study one load case to generate the entire influence function.

• Because the function has the same characteristics whether generated by traversing a unit action or by the Muller-Breslau Principle, many of the complicating features are similar.

• The development of the Muller-Breslau Principle requires the application of Betti’s Theorem. This important energy theorem is prerequisite to the understanding of the Muller-Breslau Principle.  

• Consider  two force systems P and Q associated with displacements p and q applied to a structure that behaves linear elastically.

• Application of the Q-q system to the structure and equating the work performed by gradually applied forces to the internal strain energy yields

•   ½ * Σ Qi * qi = UQq                                                                                 

•  where UQq is the strain energy stored in the beam when the loads Q are applied quasi-statically through displacement q.

• Now apply the forces of the second system P with the Q forces remaining in place. Note that the forces Q are now at the full value and move through displacement p due to force P. The work performed by all the forces is

•   ½ * Σ Qi * qi + ½ * Σ Qi * pi + ½ * Σ Pi * pi =Ufinal                               

• where Ufinal is the associated internal strain energy due to all forces applied in the order prescribed.

• Use the same force systems to apply the forces in the reverse order, that is, P first and then Q. The work performed by all forces is

•   ½ * Σ Pi * pi + ½ * Σ Pi * qi + ½ * Σ Qi * qi =Ufinal   

• If the structure behaves linear elastically, then the final displaced shape and internal strain energy are independent of the order of load application. Therefore, equating  Ufinal in Equations 5.5 and 5.6 yields

•    Σ Qi * pi  = Σ Pi * qi 

• In a narrative format, the Betti’s Theorem  states

• The product of the forces of the first system times the corresponding displacements due to the second force systems is equal to the forces of the second force system times the corresponding displacements of the first system.

• Although the derivation is performed with reference to a beam, the method is generally applicable to any linear elastic structural system.  

•  An influence function for an action may be established by removing the constraint associated with the action and imposing a unit displacement. The displacement at every point in the structure is the influence function. In other words, the structure’s displaced shape is the influence function.

• The sense of the displacements that define the influence function must be considered. For concentrated or distributed forces, the translation collinear with the direction of the action is used as the influence ordinate or function. If the applied action is a couple, then the rotation is the associated influence function. 

• One of the most useful applications of the Muller-Breslau Principle is in the development of qualitative influence functions. Because most displaced shapes due to applied loads may be intuitively generated in an approximate manner, the influence functions may be determined in a similar fashion.

• Although exact ordinates and/or functions require more involved methods, a function can be estimated by simply releasing the appropriate restraint, inducing the unit displacement, and sketching the displaced shape.

• This technique is extremely useful in determining an approximate influence function that in turn aids the engineer in the placement of loads for the critical effect.