Segmental concrete bridge pdf

English Pages [] Year The leading structural concrete design reference for over two decades—updated to reflect the latest ACI code A go. This book provides an up-to-date survey of durability issues, with a particular focus on specification and design, and h. The book is about bridging the huge gaps between what engineers know, what they do and why things go wrong. Actually, there is a great is usually done while the segments are stockpiled deal of grouted high strength post-tensioning rein- awaiting erection.

These ure at ultimate load is, of course, determined on specifications are presented in Appendix Section the basis of a cracked section, and there is, in this A. Selection of the span arrangement and other 3. The material presented in this chapter deals primarily with those aspects of precast segmental bridge design that differ from or require more de- tailed consideration than conventional types of 3. Back- In selecting the span arrangement for a precast ground information on the fundamentals of analy- segmental bridge, it is necessary to consider the sis of continuous prestressed concrete structures method of construction.

When cantilever con- may be obtained from References 2, 4, 5 and 18, struction is used, the segments are erected in bal- Appendix Section A.

If the end span is to other applicable specifications for railway or selected as 65 to 70 percent of the interior span as rapid transit structures. Additional specifications in Fig. State Highway and Transportation Officials to To provide a transition between span lengths Ll provide specific coverage of precast segmental and L2, for example at the transition between bridges are presented in Appendix Section A.

As suggested by the specifications in Appendix A. Notation is generally explained as it is used in the text. In addition, notation is presented in Appendix Section A. The method of erection, Fig. When end spans are only 50 percent of the length of interior spans, as in Fig.

Abutment details that may be used to accom- plish this are shown in Fig. Here, the webs of the main box girder deck are cantilevered under the expansion joint into slots in the main abut- ment wall. It is de- sirable to keep the number of joints to a minimum to reduce maintenance costs and improve riding quality. This may be accomplished by use of piers which permit longitudinal volume changes of the superstructure for example the Chillon Viaduct shown in Fig. In very long structures, intermediate expan- sion joints become necessary.

Location of these joints near the dead load contraflexure point, as WEB - shown in Fig. A conven- tional bearing is provided at the front abutment wall in Fig. Design information on these bearings is available from suppliers. Pier details should be developed with consider- Heavy pier reactions during erection, or tem- ation given to the need to provide stability to the porary prestressing of the pier segment to the pier, cantilevers during construction.

Some details that may require use of temporary bearing pads of steel have been used to accomplish this are discussed or concrete. Details of this type are shown in Sec- and illustrated in Section 4. The use of four bearings at piers as shown in Fig. The Bear 3. During erection, the moments over the piers increase with the addition of each pair of segments, as illustrated in Fig.

The additional moment 3. However, the European specifi- 3. These moments are resisted by post-tension- cations for design of neoprene bearings are con- ing tendons in the top slab which may be anchored siderably less restrictive than U. The use of build-outs makes it cast segmental bridges during erection are modi- possible to place the segments and stress the ten- fied by thechange in statical system due to coupling dons in two separate operations, but tends to com- cantilevers and the post-tensioning used to connect plicate the process of manufacturing the segments.

Subse- The amount of post-tensioning required to main- quent to casting the closure joint and stressing tain zero tensile stress in the top slab under the of the continuity tendons, the influence of con- erection moments including weight of any erec- crete creep modifies both the cantilever and con- tion equipment is readily calculated from the tinuity moments as will be illustrated in the fol- simple formula: lowing sections.

Restraint of creep deforma- top fibers, in. This occurs in the case of support settle- The concrete area in the bottom slab at the pier ments. The and elastic deformations is linear. The ratio is stress f,, is calculated as: called the creep factor 6. A more detailed procedure for evaluation of 8 is presented in Section 3. The elastic deflection is 6 and the angle of rotation at the ends of the cantilevers is Q as shown in Fig.

For a uni- formly distributed load q applied when the con- 0 37I42? Using the relationships for II and p: Substituting in the above, noting that 2!?

This illustrates the fact that moment redistributions due to creep following a change in the statical system tend to approach the moment distribution that relates to the statical system obtained after the change. Cl Fig. The moment M,, if acting in the cantilever, causes rotation at 6 defined aso. The magnitude of fl may be calculated as: The restraint moment M, produces both elastic and creep deformations. From these relations and the fact that there is no net increase in disconti- nuity after the joint is closed we may write the general compatibility of angular deformation expression : Fig.

In Fig. The deflection resulting from the load P in the time interval dt increases by 6d ,. The level of support B does not change between Figs. The increase in the support reaction X, induces both elastic by dX, and creep by X,d , deformations. Since there is no further deflection after Fig. Applying an axial force 3. This graph illustrates the reduction of loads d is added to the value of f.

The value of The variation of d with time is shown in Fig. This indicates 3. In general, the creep reduction scissa. By comparison of Figs. The ordinate shows the factor of develop- hth of the structural element in combination with ment of and the abscissa the time t, in days. In the relative humidity of the atmosphere. These contrast to delayed elasticity, ed, the time scale factors are represented by pc2.

The value of f, in Fig. Such corrections may be f, can be calculated. Theoretical time and real time are also equivalent when loading takes place im- Fig. The average concrete thickness is 0. A three-week erection period starts four weeks after production of the last segment.

The structure is made continuous by casting a midspan splice one week after completion of segment 0. The delayed elasticity that occurs during the week after erection normally the case for precast segmental bridges. The average age of the 3 The effects of dead load, cantilever pre- stress, continuity prestress, and other loadings that may cause moment redistribution are treated separately.

The general procedure is as follows the step numbers below do not necessarily relate to the diagram numbers shown in the various exam- Casting of midspan ples : splice completed at joints B and F.

Step 1. Bending moments are determined during Bending moments the erection phase. Bending mo- if the structure had been erected in one ments continuous structure: single step. The difference between the moments of k-ft. This dif- K-ft. The diagram obtained in Step 3 is multi- obtained by multiplication plied by the factor l-e- and the 6- II.

Bending moments of Steps 1 and 4 are only Dead load mo- added in order to find the moment dis- ments at infin- tribution at infinity. Comparing the examples in Figs. In ft. Construction Procedure close joints B ft. Erect cantilevers Fig. P P work,close j o i n t s B and F and re- Figs. Concrete splice at D post-tensioning depends on the construction se- Fig. C, result of Step 2. Difference be- tween diagrams 5 Fig. Example 2 Creep bending moments, ob- tained by multi- plication of dia- gram 7 with factor Construction Procedure 1 -e here chosen to be 0.

Dead load bending ft. A- Creep Moments Creep bending obtained by multi- moments obtained 4- 1 plication of 3 by 4 by multiplication I O. Tendons tion by stressing Ft are stressed in of tendons F2. Ft and F2, ob- tained by addition of 3 and 6. In this case, the effect of creep is independent of the construction sequence since the stressing of the Fig. The change in overall length of structure Section 3.

The response of the structure differential effects on a simply supported box to these loads is elastic. The superimposed dead girder bridge, Fig. The distribution of moments. For purposes of analysis, the deformation verse post-tensioning in deck slabs is considered in of the box section may be considered to be pre- Sections 3. Concrete stresses in the top slab will be: 3.

For illustrative pur- Under the loading condition in Fig. The restraint moments M,, shown in Fig. Proceeding with the first step in the analysis, the superstructure is considered to be cut over each support, and a constant equivalent thermal moment, M, is applied over the full length of all girders as shown in Fig. M causes equal 1 ft. In 1 in. The total slope at support 2 resulting from the constant temperature moment From these calculations it is seen that a tempera- M acting on simple spans l-2 and may be cal- ture increase in the top slab with respect to the re- culated using moment-area or slope-deflection mainder of the cross section causes very small compressive stresses when the superstructure is techniques as: simply supported.

For the three span structure shown in Fig. The continuous superstructure is considered to be cut over the supports into three simply sup- Setting the slope due to the temperature moment ported spans as illustrated in Fig. Further, A A A A I a the stress is less than 50 percent of the modulus 1 2 3 4 5 6 of rupture of the concrete so temperature stresses would not be expected to cause cracking in the superstructure.

The moments M, and M2 cause a change in sup- , port reactions. The weight of the girder is 3. Therefore, the change in dead load reactions due to the tempera- Fig. The compressive stress of 0. While this is a significant to provide data on the magnitude of shear lag stress, the magnitude is much less than the 25 to effects. The computer model assumed rigid dia- 40 percent stress increase for temperature and phragms at the pier and at abutments. A :: E 0 :: Fig. The analyses were performed using a computer program, MUPDlt8 , which is based on the folded plate method using elasticity theory.

Longitudinal force distributions obtained from these computer analyses were plotted at vari- Fig. Results are given at several sec- analyses and the forces at the same points found tions along the span which are deemed important. The forces may be ex- tions close to the center support; and sections pressed in terms of stresses by dividing by the slab where concentrated live loads act.

A careful study of Tables 3. In the following, the loading conditions shown in Fig. Loadings 5 and 6 for brevity. Comparing force ratios of structure A with those 3 and 4, respectively.

The combination of four of structure B, they are seen to be very similar. C with those of structure D. This indicates the Since the major interest in this investigation was force ratios are essentially independent of varia- the ratio of the peak longitudinal forces from the tion in depth for a given span within the span MUPDI analysis to the forces at the same points depth ratio range between 20 and Results are given at 2. LOAD 1. For a given structure, considering the dominant forces for any of the loadings, the force ratios are highest at the center support and drop off rapidly a few feet away.

Note that nearly all force ratios are less than 1. The dead load longitudinal force variation across the section of structure f3 at 6 ft. The force ratios in the midspan positive moment regions are much smaller. The force ratios are primarily a function of shear lag, which in turn is a func- tion of the magnitude of the shear, which is greatest at the center support.

The forces can be expressed in terms of stresses at the various points by dividing by the web or slab thickness, respectively. For the important dead load case 1, the force ratios at the center support ranged from 1. For structures A and B, some high values of force Fig.

When com- pared to small initial values of N, from beam analysis, the values of N, from MUPDI gave large force ratios, even though the numerical force increase was not large. For dominant forces in the top slab, the force ratios for the prestress load case ranged from 1. As seen in the key to load cases shown in Fig. The shear lag effect from the prestressing counteracts the shear lag due to dead load and live load.

The use of 5. An important finding from the computer analy- sis was the very limited length of structure in which significant shear lag effects were found to Fig. As illustrated in Section 3. Thus, force ratios for from the center of the support.

In most designs, these loadings reflect not only the effect of this would mean that shear lag effects are only shear lag, but also of eccentric loading.

As significant within the pier section. The computer mentioned earlier, live load forces are much analyses also show the most significant effects on smaller than dead load forces.

For load cases 3 the short span ft. At tude and length of structure affected in conjunc- the sections where the concentrated live loads tion with the specification requirement of zero acted near midspan the force ratios ranged tensile stress in the top slab under full service from 1. Thus, force ratios For shorter span structures ft. Force ratios at the center support shear lag might be considered in the pier segment ranged from 1.

At the sections where the the magnitude of the shear lag effect. OO to 1. Therefore, the combination of negative moment tendons and positive moment continuity tendons will usually provide more than adequate longitudinal moment capacity to meet the load factor requirements under loading conditions which produce maximum moments in the continuous structure.

Additional tendons may be re- quired in the top slab at midspan to assure continu- ity between the top slab negative moment tendons. This check is important to avoid the possibility that a negative moment hinge might form in an unloaded span before the sections in the loaded b span have reached their ultimate capacity.

Curve a shows the required moment capacity under full loading of all spans. Curve b shows the required moment capacity under loading of the central span only.

Note that negative moment ca- pacity is required at the center of the unloaded spans under the partial loading. The ultimate moment capacity of the structure is indicated be- Fig. Inter- P P mediate diaphrams are generally not required, and the design method presented in the following sec- Id tions does not include consideration of them. Con- sider the corners of the box girder supported as shown in Fig.

The analysis reduces then to simple case of a frame. This analysis is carried out and transverse moments, shear and axial forces are calculated.

Also the support reactions R,, Ra, Ra, and R4 are evaluated. Non-symmetrical loading as indicated in Fig. These forces are shown in the load P. For a subsequent analysis of the box shown, since they must be at right angles to the lon- girder by forces RI , R2, RB, and R,,, these loads gitudinal shear forces in top slab and bottom slab are rearranged in symmetrical and antisymmetrical caused by the rate of change of longitudinal components as shown in Fig.

Not negligible, however, are the transverse may be calculated as illustrated in Fig. The axial forces which are: tension in webs, tension shear stress diagram over the bottom slab, maxi- in bottom slab, and compression in the top slab. The value Top and bottom slab axial forces are a conse- of T may be calculated as: quence of the rate of change of longitudinal shear as is shown in the following. The box girder shown Pbdz Pbz in Fig. Support and loading P are indicated. Shear forces T,, TZ, and T3 occur in top slab, where I is the moment of intertia of the half sec- web and bottom slab, respectively, in a section of tion shown.

This results in transverse The transverse axial force diagram caused by cen- moments M, and horizontal and vertical shear tral loading of 2P is as indicated in Fig. There The shortening or elongation of the individual are also horizontal and vertical displacements h members due to axial loads sets up transverse mo- and v.

These displacements h and v cannot occur with- out the resistance of the top slab and bottom slab h and webs v in the longitudinal direction. Deflection v of web AD will cause longitudinal 3. Because of compatability of strains, shown in Fig. In the transverse direction, transverse bending c. This illustrates that, as a result of transverse and torsional shear are induced. In the longitudinal direction, moments and are set up in the longitudinal direction of the box shear forces are set up acting in the planes girder.

The longitudinal forces act in the planes of of the bottom slab and top slab. Moment Fig. After having determined the basic consequences of transverse deformations, the box girder may be cut at the horizontal neutral axis. The lack of horizontal equilibrium is restored by the torsional shear forces. Assuming the concrete thickness d to be small with respect to box girder dimensions V and H, the shear forces t, are constant per unit length of web or slab.

The moment of inertia of the full section is 2. Web and slab thicknesses are 0. Consider the box supported at four corners as shown in Fig. This leads to:? The coefficient Y equals L for the Fig.

The central loading of Fig. Transverse moments are negligible. However, axial forces are developed 0. The transverse axial force is evaluated as: 1. B52 x 0. Solving the above equations: The loading of Fig. Resulting bending moment and axial force dia- grams are presented in Figs. Axial forces are obtained from: 1 for displacements h. From vertical equilibrium: Fig. Transverse axial tensile forces cannot be neglect- ed since they increase the required amount of rein- forcement.

These forces are particularly signifi- - OJ7 an cant in the bottom slab. Axial compressive forces reduce the required Fig. This is particularly sulting from example transverse analysis loading case of significant in the webs at the connection with the Fig. At these points, compressive forces are high and occur simultaneously with high moments. A solution for loading case d in Fig. Moment and axial force 4. Corner moments as given in Figs. At sections near the supports, the relatively and shears in deck slabs of precast segmental thin top slab may cool much more rapidly bridges requires consideration of the effect of con- than the thicker bottom slab.

This will centrated loads on variable depth plates which cause tensile stresses around the exterior of are integral parts of a tubular frame. Design of such the cross section. When the outer air on the influence surface and multiplying by the cools during the night, the temperature dif- magnitude of the wheel load to obtain the mo- ference between the interior and outer air ment per unit length for the point under considera- produces transverse flexural moments in the tion.

For interior span positive moments, the webs and slabs which cause tensile stresses influence surfaces are used to determine fixed end around the exterior of the cross section. The Fig. This ability of avoiding the use of thick concrete webs analysis may be accomplished by an extension of and slabs which are highly rigid with respect to the analytical procedures described in Section transverse flexure.

The flexural stiffness is, of 3. A detailed procedure to accomplish this analy- course, a function of both the thickness and length sis has been published. This factor becomes sis of single or multiple cell box girder sections more significant when the transverse temperature may be made by use of one of the available com- stresses are combined with the transverse tensile puter programs. The -joint between the web and bottom 3.

These tensile stresses and potential su lting reductions in concrete quantities cracks may be accommodated by use of a conser- and dead load moments and shears. The 2 Longer slab spans may be achieved which latter option has the advantage of providing a permits reduction in the number of webs much higher degree of assurance against cracking required in wide structures.

This reduces in the webs. This provides a more durable is sufficient to meet the load factor requirements. Tendon geometry used for the Kish- anchorage forces. The placement of the bar tendons in the center of the slab was selected in this case to Transversely post-tensioned deck slabs also nor- provide a means of support for the longitudinal mally have transverse and longitudinal nonpre- tendons.

While this increased the required amount stressed reinforcement in the top and bottom of of transverse post-tensioning by about 30 percent, the slab. This contributes to the flexural capacity this increase in cost was offset by reduction in of the slab in ultimate strength calculations and labor requirements for placement of the longitud- provides the necessary flexural capacity to permit inal tendons.

The tendon profile shown in Fig. The transverse post-tensioning is proportioned to One additional factor that must be considered limit the tensile stresses in the deck slabs to the when transverse post-tensioning of the deck slab design values.

Subsequently, the slab is checked is used is the effect of the transverse elastic short- I E Sor Qirder Symm. The lateral bend- ing of the webs sets up fixed end moments that 3.

An analysis of this effect on a cross sec- The development of segmental construction has tion of a post-tensioned box girder bridge cast-in- made it economical to build slender concrete place on falsework is shown in Fig. As a result, the magnitude For wide sections, such as this, relatively high of the deformations and deflections may be in- tensile stresses are generated by the slab short- creased to such an extent that they require more ening.

Even in narrower sections that might be attention and usually need adjustment during con- expected in a precast segmental bridge, this effect struction. The amount of deformation is further may be substantial and should be considered in increased by erection of a structure in free can- the design. These stresses become highest near piers tilever. The newly erected cantilever is 3.

This procedure by use bf the thinnest possible concrete sections is repeated for each additional span, however, with consistent with strength requirements and with different resulting deformations since these depend segment design recommendations presented in on the statical system in which the addition takes Chapter 2.

As mentioned above, total deformations are obtained by summing up the contributions of each intermediate phase of construction. Also, the changes occurring after completion of the structure are added. In the latter case, the influence of time de- pendent properties such as modulus of elasticity numerous times in the construction process. The of concrete, influence of creep, shrinkage, and analysis of deformations therefore implies the sum- relaxation losses on tendon forces, and differences mation of deformations in all successive inter- in the creep factors of individual segments can be mediate phases.

This is a tedious and complex, integrally entered into the calculations. In the case but, nonetheless unavoidable, aspect of the design of hand calculations, this is not feasible and sim- calculations. The following sections are based on the assump- tion of hand calculated deformations. It is com- 3. Steel relaxation varies significantly for different 1. Elastic deflection due to self weight. Elastic deflection due to initial cantilever and low relaxation materials are available relax- prestress.

Creep deformation of 1 and 2 for the dura- range of 25 percent of the values in Fig. For this reason, use of relaxation curves for the The deflected shape of the completed cantilever is specific material to be used is recommended. This time interval is different for each canti- The prestressing force used for the calculation is lever arm as illustrated by Fig. Creep deformations are obtained by multiplica- zyxwvu the total of initial tendon forces reduced only by friction losses and part of the steel relaxation tion of the elastic deformations by a creep factor.

After application of continuity prestress, Fig. The total elastic deformation is obtained by summation of the three 3. Creep deforma- Deformations in this phase are those from: tions are found by multiplying the elastic values by 1.

The weight of cast-in-place splices. The creep influence is limited to 2. Continuity prestress in the span considered. Continuity prestress in the adjacent spans. Creep deformation resulting from 2 and 3 respectively.

The remainder of the creep deforma- I- above. Elastic and creep deformation by prestress losses. Creep deformations by self weight, cantilever prestress and continuity prestress. Determination of the elastic deformation by lb superimposed dead load weight of topping, curbs, railings, etc.

The creep deformation is obtained by multiplication of the elastic value by ct, -t, , with t, being the time of application of the dead load. For the amount of deformation by prestress losses, a simplification is made. The total amount of the losses caused by creep, shrinkage and re- laxation is reduced by the part of the relaxation loss deducted in phase A.

Evaluation of the creep deformations in this phase can be restricted to those occurring system. With reference to Fig. After a few spans The total deformation is shown in Fig. Also, this rotation in- pleted structure. Addition of a new span, Fig. For this reason, it is easier The need for correction of deformations should to calculate the deformation due to secondary be investigated for all precast segmental bridges. The rotation of each forward rections during construction awkward and un- arm, however, must be determined just before desirable.

In the casting yard, corrections are al- closure of the next span. Adjustments of alignment can be made during construction by use of stainless steel shims in the joints. The following procedure 3. Corrections 1. Elastic and creep deformation by superim- consist of those resulting from deformation, ro- posed dead load. Typical deflection curves are shown in Fig. The theoretical curve is approached by ,.

As indicated in Section 3. Although it is possible to make additional corrections during casting for forward and backward cantilever arms, it proves simpler to make such corrections by counter rotations. A similar rotation p occurs in the subsequent spans. The continuity prestress obviously affects not only the forward cantilever arm but also the re- 3. However, the resulting up and downward curves Part of a bridge is shown in Fig. The de- from this source are usually part of the deforma- flection X of span LM is the value calculated for tion corrections made in the form.

This also ap- the sum of elastic and creep deformations caused plies to the angle changes occurring at the splices. The camber Y of span MO and the rotation of the forward cantilever arm OP are those calculated for elastic and creep deformations caused by continuity prestress of span MO only. It is clear 3. After erection, the de- from a straight line.

With the procedure illustrated in Figs. After completion, addi- tional deformations will occur. These can be treated, if found to be of considerable magni- tude, similar to corrections of superimposed curvature as described in Section 3.

The corrections described are based on deforma- tion calculations. It is essential to check the re- sults of such calculations by field measurements. Such comparative measurements should always Fig. The correc- tion to obtain a straight axis, shown shaded in Fig. Drawing the deformation line a due to contin- 3. Reducing curve a by the free cantilever de- In some cases, hand calculations may be suffi- flection, resulting in curve b.

However, for more complex superstructures, the use of a computer program to Verification of this result is illustrated in Fig. Fur- 1. The correction is introduced with opposite ther, the calculation of deflections becomes sign in curve d. The free cantilever deflection is superimposed proximations are introduced, and a computer pro- in curve e.

In this cise estimate of time-related deflections. The situation the midspan splice is cast. Continuity prestress is added resulting in adapted specifically for use in design of precast curve g. Additional programs undoubt- 5. Deflection by continuity prestress of all ad- edly exist that could be used more or less directly jacent spans results in the final geometry h.

Box Sacramento, California i. The principle of the match-cast joint is that the 4. Each segment is cast against During design of a segmental structure, consider- its neighbor.

The sharpness of line of the assembled ation should be given to the formwork necessary construction depends mainly on the accuracy of to achieve economy and to obtain efficiency in the manufacture of the segments. It is generally preferable to use as few units as possible, consistent with economic ship- ping and erection. Match-cast joint members are cast 1. Proportioning the segments or parts of them, 4.

One or 3. Maintaining a constant web thickness in the more formwork units move along this line. The longitudinal direction. Maintaining a constant thickness of the top An example of this method is shown in Figs.

Keeping the dimensions of the connection Advantages-A long line is easy to set up and to between webs and the top flange constant. Bevelling corners to facilitate casting. After stripping the forms it is not 7. Avoiding interruptions of the surfaces of webs necessary to take away the segments immediately. The minimum length is 8. Using a repetitive pattern, if practical, for normally slightly more than half the length of the tendon and anchorage locations.

It must be con- 9. Minimizing the number of diaphragms and structed on a firm foundation which will not stiffeners. Avoiding dowels which have to pass through In case the structure is curved, the long line must the forms. Because Minimizing the number of blockouts. Curves in the vertical and horizontal direc- 4. After casting, the neighboring element is type of joint between elements.

Also designers will find this book useful in preparing the Project Specifications. Durability has become a key issue for state bridge officials as they determine the best design solutions for each unique situation. In California, segmental concrete bridge designs are used in a variety of situations that play to their strengths and offer high durability. Engineers at the Michigan Department of Transportation MDOT put a moratorium on designing concrete segmental bridges after a complex project in the s resulted in a major accident during construction.

When recently returning to retrofit this and another bridge they discovered the long-term durability that segmental bridges can offer—and they lifted the moratorium. Through the past four decades, the Texas Department of Transportation TxDOT has relied on segmental concrete bridge technology to resolve a variety of key design and construction challenges. Those began in the early s with the construction of the John F.

This causeway included the first precast concrete segmental bridge in the United States. Current News fib News. Contact Members Members Only Login. Publication Download