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It offers design concepts, specifications, and practice, as well as the various types of bridges. The text includes over 2, tables, charts, illustrations, and photos. The book covers new, innovative and traditional methods and practices; explores rehabilitation, retrofit, and maintenance; and examines seismic design and building materials. The second book, Superstructure Design, contains 19 chapters, and covers information on how to design all types of bridges.

Skriv anmeldelse. Betal med gavekort her. Om Bridge Engineering Handbook Over experts, 14 countries, and 89 chapters are represented in the second edition of the Bridge Engineering Handbook. ARKs anbefalinger. Design rotations can be calculated as follows: 1. Elastomeric and Fabric Pad Bearings: The AASHTO LRFD specifications stipulate that the maximum service limit state rotation for bearings that do not have the potential to achieve hard contact between metal components shall be taken as the sum of unfactored dead and live load rotations plus an allowance for uncertainties of radians.

If a bearing is subject to rotation in opposing directions due to different effects, then this allowance applies in each direction. HLMR Bearings: The AASHTO LRFD specifications stipulate that the maximum strength limit state rotation for bearings that are subject to potential hard contact between metal components shall be taken as the sum of all applicable factored load rotations plus an allowance of radians for fabrication and installation tolerances and an additional allowance of radians for uncertainties.

The rationale for this more stringent requirement is that metal or concrete elements are susceptible to damage under a single rotation that causes contact between hard elements. Such bearings include spherical, pot, steel pin, and some types of seismic isolation bearings. Disc bearings are less likely to experience metal-to-metal contact because they use an unconfined load element. Accordingly, they are designed for a maximum strength limit state rotation equal to the sum of the applicable strength load rotation plus an allowance of radians for uncertainties.

If a bearing is subject to rotation in opposing directions due to different effects, then this allowance applies in each direction Elastomeric Bearing Design Steel reinforced elastomeric bearings and fabric pad sliding bearings are generally designed by the bridge design engineer. These relatively simple bearings are easy to depict and fabrication procedures are relatively uniform and straightforward. The Method B provisions provide more relief in meeting rotational demands than Method A. The Method A design procedure is a carryover based upon more conservative interpretation of past theoretical analyses and empirical observations prior to research leading up to the publication of NCHRP Report Rotation Limits for Elastomeric Bearings Stanton Both Method A and Method B design procedures require determination of the optimal geometric parameters to achieve an appropriate balance of compressive, shear, and rotational stiffnesses and capacities.

Susceptibility of steel shims to delamination from adjacent elastomer is controlled by limiting total compressive stress. Assuring adequate shim thickness precludes yield and rupture of the steel shims. Excessive shear deformation is controlled and rotational flexibility is assured by providing adequate total elastomer height.

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Generally, total elastomer thickness shall be no less than twice the maximum anticipated lateral deformation. Overall bearing stability is controlled by limiting total bearing height relative to its plan dimensions. The most important design parameter for reinforced elastomeric bearings is the shape factor. The shape factor is defined as the plan area of the bearing divided by the area of the perimeter free to bulge plan perimeter multiplied by elastomeric layer thickness.

Axial, rotational, and shear loading generate shear strain in the constituent layers of a typical elastomeric bearing as shown in Figure Computationally, Method B imposes a limit on the sum of these shear strains. It distinguishes between static and cyclic components of shear strain by applying an amplification factor of 1. Both the Method A and Method B design procedures limit translational movement to one-half the total height of the constituent elastomeric material composing the bearing. Translational capacity can be increased by incorporating an additional low-friction sliding interface.

In this case, a portion of the translational movement is accommodated by shear deformation in the elastomeric layers. Movement exceeding the slip load displacement of the low-friction interface is accommodated by sliding. Mathematical spreadsheets have been developed to evaluate these tedious calculations. Although constituent elastomer has historically been specified by durometer hardness, shear modulus is the most important physical property of the elastomer for purposes of bearing design.

Research has concluded that shear modulus may vary significantly among compounds of the same hardness. Accordingly, shear modulus shall preferably be specified without reference to durometer hardness. Constituent elastomeric layers and steel shims shall be fabricated in standard thicknesses. For overall bearing heights less than about 5 in. For overall bearing heights greater than 5 in. For this reason, compressive service dead and live loads should be specified in the project plans or specifications.

This allowance applies to rotation in each opposing direction. Unlike many HLMR bearing types, elastomeric bearings cannot be easily installed with an imposed offset to accommodate actual temperature at installation in addition to any anticipated long-term movements such as creep and shrinkage. For practical reasons, girders are rarely set atop elastomeric bearings at the mean of the expected overall temperature range. Rarely are girders subsequently lifted to relieve imposed vertical load to allow the bearings to replumb themselves at the mean temperature. This percentage may be reduced in instances in which girders are originally set or reset at the average of the design temperature range.

For precast prestressed concrete girder bridges, the maximum design thermal movement shall be added to shrinkage, long-term creep, and posttensioning movements to determine the total bearing height required. The material properties of most elastomers vary with temperature. Both natural rubber and neoprene stiffen and become brittle at colder temperatures.

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Therefore, it is important that the type of elastomer be considered explicitly in specifying the bearing and determining the resulting lateral forces that will be transferred to substructure elements. A higher grade number corresponds to greater resistance against stiffening under sustained cold conditions. Special compounding and curing are needed to provide this resistance and thus increase the cost of the constituent bearing. Determination of the minimum grade required depends upon the more critical of 1 the year low temperature and 2 the maximum number of consecutive days in which the temperature does not rise above 32 F 0 C.

The intent of specifying a minimum grade is to limit the forces transferred to the substructure to 1. Thus, all three HLMR bearing types may be allowed on most projects. Each bearing manufacturer has unique fabricating methods, personnel, and procedures that allow it to fabricate a bearing most economically. For these reasons, these bearing types are generally depicted schematically in contract drawings. Depicting the bearings schematically with specified loads, movements, and rotations provides each manufacturer the flexibility to innovatively achieve optimal economy subject to the limitations imposed by the contract drawings and specifications.

This generally requires a preliminary design to be performed by the bridge designer or bearing manufacturer. Diameter of a HLMR bearing is governed primarily by load magnitude and material properties of the flexible load bearing element. The height of a pot bearing or disc bearing is governed primarily by the rotational demand and flexibility of the deformable bearing element. The height of a spherical bearing depends upon the radius of the curved surface, the diameter of the bearing, and the total rotational capacity required.

Accessory elements of the bearing, such as masonry plates, sole plates, anchor rods, and any appurtenance for horizontal force transfer should be designed and detailed on the contract drawings by the bridge designer. Notes should be included on the plans allowing the bearing manufacturer to make minor adjustments to the dimensions of sole plates, masonry plates, and anchor rods.

The HLMR bearing manufacturer is generally required to submit shop drawings and detailed structural design calculations for review and approval by the bridge design engineer. HLMR bearings incorporating sliding interfaces require inspection and long-term maintenance. It is important that these bearings be designed and detailed to allow future removal and replacement of sliding interface elements. By limiting the jacking height, this work can be performed under live load and without damaging expansion joint components.

HLMR bearings must be designed, detailed, fabricated, and installed to provide a continuous load path through the bearing from the superstructure to the substructure. The load path must account for all vertical and horizontal service, strength, and extreme limit state loads. The importance of providing positive connections as part of a continuous load path cannot be overemphasized. The spherical bearing shown in Figure 1. The upper sole plate was embedded in the concrete superstructure.

Because uplift had not been anticipated in the design of this Seattle bridge, the lower sole plate was designed to fit loosely in a recess in the bottom of the upper sole plate. During the Nisqually Earthquake, the upper and lower sole plates of this bearing separated, causing the lower sole plate to dislodge and displace. A masonry plate connects the bottom of the bearing to the top of the supporting structural elements below. A sole plate connects the top of the bearing to the superstructure above Masonry Plates Masonry plates help to more uniformly distribute loads from a bearing to supporting concrete substructure elements below.

Additionally, they provide platforms to facilitate maintenance and repairs of bearings. Analysis shows that a steel masonry plate will deform under concentrated bearing loads Stanton This potential deformation, which tends to cause a dishing effect because of the relatively flexible. The masonry plate supporting a HLMR bearing is generally supported either on a thin preformed elastomeric pad or directly atop a grout pad that is poured after the superstructure girders have been erected.

Each of these two methods has associated advantages and disadvantages. Fully threaded anchor rods can be either cast into the concrete or drilled and grouted into place. An anchor plate can be either bolted or welded to the bottom of the anchor rod to augment uplift capacity in the concrete.

If no uplift capacity is required, a swedged rod may be substituted for a threaded one. The swedged rod may be terminated just below the top of the masonry plate and the void filled with a flexible sealant. A grout pad poured underneath the masonry plate after girder erection can provide the contractor more flexibility in leveling and adjusting the horizontal position of the bearing. A variation of this method incorporating postgrouted hollow steel pipes can be used to substantially increase uplift capacity of the anchor rods and provide some additional anchor rod adjustability.

Several methods have been used successfully to temporarily support the masonry plate until the grout is poured. The two most commonly used methods are 1. Shim Packs Multiple stacks of steel shim plates are placed atop the concrete supporting surface to temporarily support the load on the masonry plate before grouting. Engineering judgment must be used in selecting the number and plan size of the shims, taking grout flowability, load distribution, and shim pack height adjustability into consideration.

To enhance uplift resistance, steel anchor rods are sometimes installed in hollow steel pipes embedded into the concrete. The steel pipes have plates welded to their bottoms through which the anchor rods are bolted. Grouting is accomplished using grout tubes that extend to the bottom of the pipes. Once all pipes are fully grouted around the anchor rods, the space between the top of the concrete support surface and the underside of the masonry plate is grouted. Steel studs are welded to the underside of the masonry plate to coincide with voided core locations.

With the girders erected and temporary shims installed between the top of the concrete surface and the underside of the masonry plate, the voided cores are fully grouted. Once the first stage grout has attained strength, the steel shims are removed, the masonry plate is dammed, and grout is placed between the top of the concrete support surface and the underside of the masonry plate.

The use of anchor rod leveling nuts, without shim packs, to level a masonry plate prior to grout placement is not recommended. The absence of shim packs results in the application of point loads at anchor rod locations. Similar consideration must be given to the sizing and number of shim plates as it relates to potential dishing of the masonry plate under load Sole Plates For concrete bridge superstructures, headed steel studs are typically welded to the top of the sole plate and embedded into the superstructure.

In steel bridge superstructures, sole plates may be bolted or welded to I-shaped plate girder bottom flanges. Sole plate assemblies should be bolted to the bottom flange of steel box girder bridges because welded connections would require overhead welding, which may be difficult to perform because of limited access. Welding of sole plates to steel I-shaped girders allows for greater adjustment during installation and is generally more economical.

Damage associated with removal of the weld as required for future. For these welded connections, it is recommended that the sole plate extend transversely beyond the edge of the bottom flange by at least 1 in. Welds for sole plate connections should be longitudinal to the girder axis.

The transverse joints should be sealed with an approved caulking material. The longitudinal welds are made in the horizontal position, which is the position most likely to achieve a quality fillet weld. Transverse welds would require overhead welding, which may be difficult to perform because of limited clearance.

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Caulking is installed along the transverse seams following longitudinal welding to prevent corrosion between the sole plate and the bottom flange. Bolting of sole plates to steel I-shaped girders is also used. Bolting typically requires minimal paint repair, as opposed to welding, and simplifies removal of a bearing for future maintenance and replacement needs.

Oversized holes allow for minor field adjustments of the bearing during installation. In some instances, an upper and lower sole plate may be used to simplify the bolted connection to a steel girder or to account for grade effects. The upper uniform thickness sole plate is bolted to the bottom flange while the lower tapered sole plate is welded to the upper sole plate. For a concrete bridge, the lower sole plate may be drilled and the embedded upper sole plate tapped for bolting together. The spherical bearing depicted in Figure 1. Flatness of the steel mating surfaces may be a concern when bolting a sole plate to a steel girder bottom flange.

In lieu of specifying a tighter flatness tolerance on the girder bottom flange, epoxy bedding can be used between the sole plate and the girder bottom flange. Silicone grease is used as a bond breaker on one of the surfaces in order to allow removal of the sole plate for servicing the bearing during the life of the bridge. The bridge design engineer is typically responsible for checking and approving these design calculations and shop drawings.

This review shall assure that the calculations confirm the structural adequacy of all components of the bearing, a continuous load path is provided for all vertically and horizontally imposed loads, and each bearing is detailed to permit the inspection and replacement of components subject to wear. The approved shop drawings should note that all HLMR bearings shall be marked prior to shipping. These marks shall be permanent and in a readily visible location on the bearing. They shall note the position of the bearing and the direction ahead on station.

Numerous field problems have occurred when bearings were not so marked. This is particularly true for minimally beveled sole plates. It is not always apparent which orientation a bearing must take prior to imposition of the dead load rotation. Bearing replacement operations generally require lifting of superstructure elements using hydraulic jacks. Anticipated lifting loads should be stipulated on the contract drawings. Limitations on lift height should also be specified. Considerations should be given to lift height as it relates to adjacent expansion joint components and adjoining sections of safety railing.

Superstructure stresses induced by nonuniform lifting are limited by imposing restrictions on differential lift height between adjacent jacks. Many factors may contribute to this phenomenon, including friction in the hydraulic jack system and underestimation of superstructure dead loads. In planning a bearing replacement project, the designer should verify from manufacturers literature that appropriate hydraulic jacks are available to operate within the space limitations imposed by a particular design situation.

For precast prestressed concrete girders, this process is somewhat complicated by the need to track camber rotations at various stages under different loading conditions. In general, two times are most likely to be critical: 1 after girders are set but immediately before the slab is cast, at which time some of the prestressing has been lost and 2 after the bridge is constructed and live load is applied, at which time all prestressing losses have occurred. Both cases should be checked.

For each instance, the radian tolerance needs to be applied in the most critical direction, positive or negative.

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A condensed version of one of these examples has been adapted to the following example Given A single span precast prestressed concrete girder bridge near Minneapolis, Minnesota, has a total length of ft. The abutments are not skewed. Each girder end is supported on a in. These layers are reinforced with five steel plates having a yield stress of 36 ksi MPa.

Assume that one end of the bridge is fixed against movement. The contract documents specify the shear modulus of the elastomer at 73 F With the exception of checking the bearing against slippage, the critical extreme range value of psi 0. For the purpose of determining resulting displacements imposed upon each bearing, a sequence of nine movement phenomena are considered and included in this problem.

These movements are: transfer of prestressing following girder casting, girder self-weight, creep and shrinkage occurring before each girder is erected on bearings, creep and shrinkage occurring after each girder is erected on the bearings, weight of slab on each girder, differential shrinkage of the slab after it is placed, uniform thermal expansion and contraction, lane live load, and truck live load.

Because they occur prior to the girders being set onto the elastomeric bearings, the uniform shortening movements associated with the first three phenomena do not induce corresponding shear deformations in the bearings. However, because the bottom of the girder does not have a sloped recess to accommodate anticipated end rotations, all phenomena, with the exception of uniform thermal expansion and contraction, induce rotation in the bearings.

Nonthermal related longitudinal movements at the top of the bearing at the free end of the bridge have been calculated as follows, with negative numbers denoting movement toward midspan:. It should be noted that the horizontal displacements reported earlier result from a combination of two effects: 1 change in the length of the concrete girder at its centroid and 2 end rotation of the girder about its centroid.

For instance, creep and shrinkage of the girder following erection causes it to uniformly shorten and to deflect upward and rotate about its ends. The end rotation causes the bottom of the girder at the bearing to shift inward toward midspan , augmenting the shortening effect. Similarly, differential shrinkage of the slab causes the girder to uniformly shorten and to deflect downward and rotate about its ends.

In this case, the end rotation causes the bottom of the girder at the bearing to shift outward away from midspan , reducing the uniform shortening effect. The longitudinal bearing movements listed earlier include both of these effects. Determine the design thermal movement Check the adequacy of the bearing to accommodate maximum horizontal displacement, using the AASHTO LRFD Method B design procedure Calculate shape factor of the bearing Check service load combination Check condition immediately before deck placement Evaluate stability of the bearing Determine required thickness of steel reinforcement Determine low temperature requirements for the constituent elastomer Calculate approximate instantaneous dead load, the long-term dead load, and the live load compressive deformation of the bearings Consider hydrostatic stress.

These maps show T MaxDesign as F Note that movement associated with superimposed dead load is not specified in this provision. This movement can be either expansion or contraction. Uniform temperature change does not produce girder end rotation augmenting this movement. Step 2: Check adequacy of the bearing to accommodate maximum horizontal displacement As noted earlier, for the purpose of calculating the shear deformation in each bearing, the design thermal movement is added to all creep, shrinkage, and posttensioning effects that occur after the girders are set on the bearings.

Shear strain due to axial cyclic load is taken similarly. The thermal displacement range during the short interval between when the girders are erected and the slab is poured is deemed to be negligible. Step 6: Evaluate stability of the bearing Per LRFD Article , bearings shall be investigated for instability at the service limit state load combination.

First, consider stability in the longitudinal direction. Next, consider stability in the transverse direction. Zone D is associated with a year low temperature of 45 F LRFD Table requires a Grade 4 elastomer for bridges located in Zone D unless special force provisions are incorporated into the design. When special force provisions are incorporated into the design, a Grade 3 elastomer is permissible.

In summary, LRFD Article allows three options: Option 1: Specify a Grade 4 elastomer and determine the shear force transmitted by the bearing in accordance with LRFD Article Option 2: Specify a Grade 3 elastomer and provide a low-friction sliding surface, in which case the shear force transmitted by the bearing shall be assumed as twice that computed in accordance with LRFD Article Option 3: Specify a Grade 3 elastomer without providing a low-friction sliding surface, in which case the shear force transmitted by the bearing shall be assumed as four times that computed in accordance with LRFD Article Step 9: Calculate approximate instantaneous dead, long-term dead, and live load compressive deformation of the bearing Limiting instantaneous live load deflections is important to ensure that deck expansion joints are not damaged.

Steel reinforced elastomeric bearings exhibit nonlinear compressive load-deflection behavior. Compressive stiffness of an elastomeric layer substantially increases with increasing shape factor. The total compressive deformation of an elastomeric bearing is equal to the sum of the compressive deformation of all its constituent elastomeric layers. LRFD commentary allows an assumed linear relationship between compressive stress and compressive strain. Specifically, compressive strain can be estimated as.

This will result in the largest compressive deformation. Step Consider hydrostatic stress The bearing has no externally bonded steel plates. Therefore, hydrostatic stress is not a consideration. Step Evaluate the need for providing anchorage against slippage The traditional anchorage check contained in previous editions of AASHTO design codes has been to compare the maximum horizontal force induced in the elastomeric bearing versus the incipient force required to cause the bearing to slip.

This check was generally performed using service loads and assumed a friction coefficient of 0. The maximum shear displacement of the bearings occurs at the extreme low temperature in the absence of live loading. LRFD Article further requires that the superstructure and substructure be designed to transmit, at the strength and extreme limit states, the horizontal forces induced by sliding friction or shear deformation of flexible bearing elements.

Article of the current LRFD specifications requires a check of rotation versus axial strain for bearings without externally bonded steel plates. The service live load without impact is kips kn. The horizontal strength limit state load is kips kn. The allowable compressive stress for the polyether urethane material constituting the disc is 5.

For the polyether urethane used in this bearing, E may be taken as 10 ksi The disc element is sandwiched by upper and lower bearing plates having a yield strength of 50 ksi MPa. The 95 ksi MPa yield strength shear resisting pin is threaded 12 threads per inch into the lower bearing plate and bears against a hole in the upper bearing plate. A longitudinally guided disc bearing differs from the fixed disc bearing depicted in Figure 1. The maximum strength limit state rotation for the bearing is rads.

Step 2: Determine the required diameter of the polyether urethane disc tpi. The polyether urethane disc is essentially an annular ring with a steel shear-resisting pin in the center. The outer edge of the disc is V-shaped as depicted in Figure The V-shape accommodates bulging under load. Each leg of the V forms a 30 angle with the vertical. Establish a practical manufacturing diameter of the top and bottom bearing surfaces of the disk, accounting for the V -shaped notch. Dbase 1. Use 18 in. A disc 2. This article further proscribes lift off of component elements of the disc bearing, effectively imposing limits on allowable service limit state rotation.

Calculate the instantaneous compressive deformation of the disk under total service load and compare with the allowable deformation. D disc Step 4: Determine minimum engagement length and check combined flexure and shear on the shear-resisting pin The required diameter of the steel shear-resisting pin has already been determined in Step 1. The pin is threaded into the lower bearing plate and bears against a hole in the upper bearing plate.

The minimum engagement length of the pin against each bearing plate is determined by checking against the allowable bearing force. The maximum bending moment in the pin is calculated from the required engagement length and the compressed height of the disc under dead load. Check combined flexure and shear. Edge contact stress for all loads at the service limit state is further limited to 5. Edge contact stress is evaluated by calculating the moment induced in the polyether urethane disc element due to the maximum service limit state rotation.

This moment is transferred through the PTFE by contact stresses. The upper and lower bearing plates, sole plate, masonry plate, and bolted connections need to be designed to transfer all loads between the superstructure and the substructure. As part of a continuous load path, the bearing plates need to be designed of sufficient thickness to transfer to the sole and masonry plates the same horizontal loads imposed upon the steel shear-resisting pins. Stainless steel sliding surfaces need to be detailed to provide sufficient travel distance to accommodate all anticipated movements.

Clearances must be adequate to accommodate unrestrained service limit state movements. Additionally, guide bars need to be designed and detailed to accommodate the transfer of transverse loads between the sole plate and the upper bearing block. As noted earlier, it is important that bearings be designed and detailed to allow for the inspection, maintenance, and future removal and replacement of all sliding interface elements. Lehman, D. Roeder, R. Larson, K. Prepared for the Washington State Transportation Commission. Stanton, J. Roeder, P. Mackenzie-Helnwein, C.

White, C. Kuester, B. Roeder, T. Although piers are traditionally designed to carry vertical loads, these days it is common for designers to take into account the high lateral loads caused by seismic events. Even in some low-seismic areas, designers are paying more attention to the ductility aspect of the design. Piers are predominately constructed with reinforced concrete.

Steel, to a lesser degree, is also used for piers. Steel tubes filled with concrete, known as composite columns, have been used in some recent projects in China and other countries. This chapter deals only with piers or columns for conventional highway bridges, such as grade separations, overcrossings, overheads, underpasses, and simple river crossings. Reinforced concrete columns will be discussed in detail, whereas steel and composite columns will be discussed briefly.

Substructures for arch, suspension, segmental, cable-stayed, and movable bridges are excluded from this chapter. Chapter 3 discusses the substructures for some of these special types of bridges. However, from time to time, it is also used particularly for a solid wall in order to distinguish it from columns or bents. From a structural point of view, a column is a member that resists the lateral force mainly by flexure action, whereas a pier is a member that resists the lateral force mainly by a shear mechanism.

A pier consisting of multiple columns is often called the bent. There are several ways of defining pier types. One is by its structural connectivity to the superstructure: monolithic or cantilevered. Another is by its sectional shape: solid or hollow; round, octagonal, hexagonal, or rectangular. It can also be distinguished by its framing configuration: single- or multiple-column bent; hammerhead or pier wall.

Figure 2. The smooth monolithic construction not only creates an esthetically appealing structure but also provides an integral system to resist the seismic forces. Esthetics is also a very important factor of selection because modern highway bridges are.

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Often times, pier types are mandated by government agencies or owners. Many state Departments of Transportation in the United States have their own standard column shapes. Solid wall piers, as shown in Figures 2. These features lend themselves well for providing minimal resistance to water flows. They are used to support steel girder or precast prestressed concrete girder superstructures.

They are esthetically appealing and generally occupy less space, thereby providing more room for the traffic underneath. Standards for the use of hammerhead piers are often maintained by individual transportation department. A bent consists of a cap beam and supporting columns forming a frame. Bents, as shown in Figure 2. The columns can be either circular or polygonal in cross section. They are by far the most popular forms of piers in the modern highway systems. An obvious advantage of this type of pier is that they occupy a minimal amount of space.

Widening an existing bridge in some instances may require pile extensions because space limitation precludes the use of other types of foundations. Selection of proper pier type depends on many factors. First, it depends on the type of superstructure. For example, steel girder superstructures are normally supported by cantilevered piers, whereas the cast-in-place concrete superstructures are normally supported by monolithic bents.

Second, it depends on the locations of bridges. Pier walls are preferred on river crossings, where debris is a concern and hydraulics dictates. Column bents are typically used in street crossings and highway separations. Multiple pile extension bents are commonly used on slab bridges. Last, the height of piers also dictates the type of selection of piers.

The taller piers often require hollow cross sections in order to reduce the weight of the substructure. This then reduces the load demands on the costly foundations. Table 2. TABLE 2. Some of the loads and forces to be resisted by piers include the following: Dead loads Live loads and impact from the superstructure Wind loads on the structure and the live loads Centrifugal force from the live loads Longitudinal force from live loads Drag forces due to the friction at bearings Stream flow pressure Ice pressure Earthquake forces Thermal and shrinkage forces Ship impact forces Force due to prestressing of superstructure Forces due to differential settlement of foundations The effect of temperature changes and shrinkage of the superstructure needs to be considered when the superstructure is rigidly connected with the supports.

Where expansion bearings are used, forces caused by temperature changes are limited to the frictional resistance of the bearings. In the following, however, two load cases, live loads and thermal forces, are discussed in detail because they are two of the most common loads on the piers but are often applied incorrectly in the design Live Loads Bridge live loads are the loads specified or approved by the contracting agencies and owners.

There are other special loading conditions peculiar to the type or location of the bridge structure, which should be specified in the contracting documents. Live load reactions obtained from the design of individual member of the superstructure should not be used directly for substructure design. These reactions are based on maximum conditions for one beam and make no allowance for the distribution of live loads across the roadway. Using these maximum loadings would result in a pier design with an unrealistically severe loading condition and uneconomical sections.

For substructure design, the maximum reaction of design traffic lane using either the standard truck load or standard lane load or a combination of both should be used. A design tandem combined with the design lane load. A design truck with variable axial spacing combined with the design lane load. Ninety percent of two design trucks spaced a minimum The distance between the kn 32 kip axle should be fixed at 4. Each state transportation agency may add one more load condition that considers its own permit loads and their combination.

For the calculation of the actual beam reactions on the piers, the maximum lane reaction can be applied within the design traffic lanes as wheel loads and then distributed to the beams, assuming the. Wheel loads can be positioned anywhere within the design traffic lane with a minimum distance between lane boundary and wheel load of 0. For integral bent cap, the bent should be modeled as a frame. The calculated reactions due to the wheel load should be applied to the beam element of this frame.

The design traffic lanes and the live load within the lanes should be arranged to produce beam reactions that result in maximum loads on the piers. Live load reactions shall be increased due to impact effect. Pier design should be checked against these forces. Design codes or specifications normally specify the design temperature range. Some codes even specify temperature distribution along the depth of the superstructure member.

After this point is determined, one can calculate the relative displacement of any point along the superstructure to this point by the distance to this point times the temperature range and times the coefficient of expansion. With known displacement at the top and known boundary conditions at the top and bottom, the forces on the pier due to the temperature change can be calculated by using the displacement times the stiffness of the pier. The determination of point of no movement is best demonstrated by the following example, which is adapted from Memo to Designers issued by California Department of Transportation Caltrans Example 2.

The size of the column is 1. Other assumptions are listed in the calculations. The calculation is done through a table. A pier as a structure component is subjected to combined forces of axial, bending, and shear.


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For a reinforced concrete pier, the bending strength is axial force dependent. The shear strength is also affected by bending and axial loads. In current design practice, the bridge designers are paying increasing attention to the adverse effects of earthquake. Therefore, ductility consideration has become a very important factor for bridge design. Failure due to scouring is also a common cause of failure of bridges. In order to prevent this type of failure, the bridge designers need to work closely with the hydraulic engineers to determine adequate depths of cover for the foundations and provide proper protection measures Slenderness and Second-Order Effect The design of compression members must be based on forces and moments determined from an analysis of the structure.

Small deflection theory is usually adequate for the analysis of beam-type members. For compression members, however, the second-order effects must be considered. According to AASHTO LRFD AASHTO , the second-order effect is defined as follows: The presence of compressive axial forces amplify both out-of-straightness of a component and the deformation due to nontangential loads acting thereon, therefore increasing the eccentricity of the axial force with respect to the centerline of the component.

The synergistic effect of this interaction is the apparent softening of the component, i. To accurately assess this effect, a properly formulated large deflection nonlinear analysis can be performed. However, it is impractical to expect the practicing engineers to perform this type of sophisticated analysis on regular bases. Super str. Columns fixed top and bottom 3. Abutment footing will a force equal to D. Whether a member can be considered slender is dependent on the magnitude of the member s slenderness ratio. However, a lower value of K may be used if further analysis demonstrated that a lower value is warranted.

L u is defined as the clear distance between slabs, girders, or other members that is capable of providing lateral support for the compression member. Any detailed analysis should consider the influence of axial loads and variable moment of inertia on member stiffness and forces and the effects of the duration of the loads. It is an approximation of the effects of creep, so that when larger moments are induced by loads sustained over a long period of time, the creep deformation and associated curvature will also be increased Concrete Piers and Columns Combined Axial and Flexural Strength A critical aspect of the design of bridge piers is the design of compression members.

The following discussion provides an overview of some of the major criteria governing the design of compression members. Interaction diagrams are usually used as aids for the design of the compression members. Interaction diagrams for columns are usually created assuming a series of strain distributions and computing the corresponding values of P and M.

Once enough points have been computed, the results are plotted to produce an interaction diagram. In an actual design, though, a few points on the diagrams can be easily obtained and can define the diagram rather closely. At this condition, the section has the highest moment capacity. Generally, designers rely on computer programs based on equilibrium and strain compatibility to generate a moment axial interaction diagram.

For cases like noncircular members with biaxial flexure, an interaction surface is required to describe the behavior. In a day-to-day practice, such a surface has little value to designers. Rather, the design program normally gives out a series of lines, basically slices of the surface, at fixed interval, such as From these lines, one can see that below the balanced condition the moment capacity increases with the increase of axial load.

So, when designing a column, it is not enough to simply take a set of maximum axial load with maximum bending moments. The following combinations should to be evaluated: 1. M ux max, corresponding M uy and P u 2.


  1. Optimization of Discrete Time Systems: The Upper Boundary Approach.
  2. Bridge Engineering Handbook: Seismic Design.
  3. German Fighter Units: 1914-May 1917.
  4. Bridge Engineering Handbook: Seismic Design, Book by Wai-fah Chen (Hardcover) | vagutuxyvi.cf.
  5. Oil Paints.
  6. M uy max, corresponding M ux and P u 3. A set of M ux and M uy that gives largest M u combined and corresponding P u 4. However, in a seismic design, the shear is very important. In recent years, great effort has been put forth on the evaluation of shear strength of columns, especially on the interaction between shear and flexure in the plastic hinge zone. The concrete shear capacity component and the angle of inclination of diagonal compressive stresses are functions of the shear stress on the concrete and the strain in the reinforcement on the flexural tension side of the member.

    It is rather involved and hard to use. ACI Code has a set of simpler equations, but they do not address the shear strength in the plastic hinge zones. The procedure presented by Paulay and Priestley overcomes both of those shortcomings but does not include the effect of displacement ductility demand on the shear strength. The procedure adapted by California Department of Transportation Caltrans in its Seismic Design Criteria Caltrans addresses all these factors and is presented here. For members subjected to minor tension, totally ignoring the shear strength of concrete may be unnecessarily conservative.

    This multiplier should not be less than zero, where P c is negative for tension, where A g is gross section area of the column; A e is effective section area, can be taken as 0. In these equations, A v is the total area of shear reinforcement parallel to the applied shear force, A h the area of a single hoop, f yh the yield stress of horizontal reinforcement, D the diameter of a circular hoop, and s the spacing of horizontal reinforcement Ductility of Columns The AASHTO LRFD introduces the term of ductility and requires that a structural system of bridge shall be designed to ensure the development of significant and visible inelastic deformations before failure.

    The term ductility defines the ability of a structure and selected structural components to deform beyond elastic limits without excessive strength or stiffness degradation. This is a measure of the ability for a structure, or a component of a structure, to absorb energy. The goal of seismic design is to limit the estimated maximum ductility demand to the ductility capacity of the structure during a seismic event. For concrete columns, the confinement of concrete must be provided, and a good detailing practice must be followed to ensure a ductile column.

    The typical section of the structure is shown in Figure The concrete box girder is supported by a two-column bent and is subjected to HL loading. The columns are pinned at the bottom. Therefore, only the loads at the top of columns are given here. Provide 9 30 longitudinal reinforcement. The reinforcement ratio is 1. Following the procedure outlined in Section 2.

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    The nominal moment capacity of the section corresponding to the axial force of 1, Kip is 4, k-ft. Mu The analysis results with the comparison of applied moments to capacities are summarized in Table 2. Column lateral reinforcement is calculated for two cases: 1 for applied shear and 2 for confinement. Typically, the confinement requirement governs. Apply Equation 2. For seismic analysis, the unreduced seismic shear forces shall be compared with the shear forces due to plastic hinging of columns. The smaller shall be used.

    The plastic hinging analysis procedure is discussed elsewhere in this handbook and will not be repeated here. First, determine the lateral reinforcement by confinement. However, the axial force in right column is larger than that of the left column, the shear capacity will be larger. By observation, the shear will not govern. Final design: 4 ft 1. Nevertheless, they are viable solutions for some special occasions, for example, in space-restricted area. Steel pipes or tubes filled with concrete known as composite columns Figure 2.

    Steel at the perimeter of the cross section provides stiffness and triaxial confinement, and. The toughness and ductility of composite columns makes them the preferred column type for earthquake-resistant structures in Japan. In China, the composite columns were first used in Beijing subway stations as early as Over the years, the composite columns have been used extensively in building structures and bridges Cai and ; Zhong The design specifications of steel and composite columns are given in various codes.

    Wall thickness of steel or composite tubes shall satisfy the following: For circular tubes D t 2. Cai, S. Caltrans Seismic Design Criteria, Version 1. Louis, MO. Galambos, T. Paulay, T. White, D. Towers give to a bridge a characteristic identity, a unifying theme, a motif from which people can identify that particular bridge. Towers project a mnemonic bridge image that people can recall as their lasting impression of that bridge itself, making towers an important part of the overall esthetics. As examples of the powerful imagery of towers, contrast the elegant art deco towers of the Golden Gate Bridge Figure 3.

    Then compare these robust towers to those of the delicate towers of the Firth of Forth Suspension Bridge Figure 3. Both of these are self-anchored suspension bridges and have no heavy and bulky concrete anchorages visible at each end. Then compare the concrete quasi-diamond-shaped towers of the Glebe Island Bridge Figure 3. One can easily see that there is great diversity in bridge tower designs; the only requirement that these towers have in common is that they must resist the loads and forces of nature and be in equilibrium according to the three equations of statics.

    Towers surely do impact the appearance of bridges, for good or for bad. Courtesy of Charles Seim. Courtesy of T. Lin International. If they are well maintained, all these bridges could continue to serve for another years. These bridges are excellent examples of enduring structures; they serve as a reminder to bridge engineers that well-designed and well-maintained structures can last for years, or perhaps longer. Robust designs, durable materials, provisions for inspection and maintenance access, and a well-executed maintenance program will help to ensure long service lives.

    Both suspension and cable-stayed bridges are supported by abutments or piers at the point at which these structures transition to an approach roadway or to an approach structure.