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With the Federal Highway Administration-mandated implementation of the LRFD specifications, many state departments of transportation (DOTs) have already started implementing LRFD specifications as developed by the AASHTO. Many aspects of the LRFD specifications are being investigated by DOTs and researchers in order for seamless implementation for design and analysis purposes. This paper presents the investigation on several design aspects of post-tensioned box girder bridges designed by LRFD Specifications using conventional or High-Strength Concrete (HSC). A computer spreadsheet application was specifically developed for this investigation. It is capable of analysis, design, and cost evaluation of the superstructure for a cast-in-place post-tensioned box girder bridge. Optimal design of a post-tensioned box girder is achievable by correct selection of design variables. Cost evaluation of superstructures with different geometrical and material configurations has led to the development of optimum design charts for these types of superstructures. Variables used to develop these charts include, among others, span length, section depth, web spacing, tendon profile, and concrete strength. It was observed that HSC enables the achievement of significantly longer span lengths and/or longer web spacing that is not achievable when using normal strength concrete.

American Association of State Highway and Transportation Officials (AASHTO) standard specification [

This new specification resulted in design procedures significantly different compared to the earlier methods. The new LRFD specification is based on a probability-based approach in which load and resistance factors are based on a specific level of structural failure [

In the present work, a detailed investigation was performed on different aspects of cast-in-place (CIP) post-tensioned box girder bridges. These include a general comparison of the two design specifications, utilization of post-tensioned high-strength concrete and cost based design optimization of the prestressed box girder bridges. A comprehensive spreadsheet was developed which enables the user to input almost every necessary design parameter and perform the analysis, design, and cost estimate of a post-tensioned box girder bridge superstructure according to both AASHTO standard and LRFD specifications. A copy of the program is obtainable by contacting the authors.

Different design parameters were studied for the comparison of the newer LRFD and the older standard AASHTO specifications. These include live load bending moment and shear force envelopes, service and factored bending and shear envelopes, bending capacity, moment and shear distribution factors, prestressing losses, designed number of prestressing strands, and superstructure cost.

LRFD HL-93 live load is by itself significantly heavier than the standard HS-20 loading, but this difference will partly offset by the introduction of completely new live load distribution methods, service, and ultimate load factors. Figure

Comparison of moment envelopes due to only distributed live load plus impact for 180 ft single-span box girder with eight webs spaced at 9 ft.

When the combined effect of live and dead loads is considered, two different service load combinations (service I and service II) are used in LRFD method when allowable compressive and tensile stresses need to be checked in prestressed concrete members. Figure

standard specification service

LRFD service I

LRFD service III

Comparison of moment envelopes for 180 ft single-span box girder with eight webs spaced at 9 ft.

Service load conditions

Due to factored loads (strength I was considered for LRFD and LFD)

This is because live loads are much smaller than dead loads in a concrete bridge, and the distribution factor is smaller for LRFD. These will significantly offset the effect of the large LRFD HL-93 live load. The ultimate moment envelope combinations for standard design and LRFD specifications were also compared, and the results are shown in Figure

standard specification LFD combination:

LRFD load combination:

According to formulas shown above, standard design method gives higher-load factors and smaller-distribution factors as compared to LRFD. These will significantly offset the effect of higher LRFD HL-93 live load.

In case of the live load shears, it is seen that LRFD gives a significantly higher shear force (up to 180% of those for the standard specification) as shown in Figure

Comparison of shear force envelopes for 180 ft single-span box girder with 8 webs spaced at 9 ft.

Due to distributed live load plus impact

Due to factored load

Live load distribution is one of the most important factors for a bridge design and the evaluation of existing bridges, and it has been the basis for design for several decades. The standard design specifications and LRFD specifications contain simplified methods to compute the live load effects. The new specification considers several structural properties of the bridge deck such as girder spacing, number of cells, and span length, and the examples are shown in (

Live load distribution is one of the most important factors for a bridge design bridge and for the evaluation of existing bridges, and has been the basis for design for several decades. The standard design specifications and LRFD specifications contain simplified methods to compute the live load effects. Extensive research work has been conducted for the live load distribution factors and for simplifying the equations [

Barr et al. [

A comparison of the distribution factors variation with span length can be seen in Figure

Moment distribution factors for a box girder (seven cells spaced at 9 ft) for standard and LRFD specifications.

As discussed earlier, the LRFD live load (HL-93) is by itself significantly greater than the one compared to the standard specification live loading (HS20). For the design of prestressed members, it is considered in LRFD only 80% of the live load plus impact in its service III load combination (also refer to Figure

Comparison in box girder (seven cells spaced at 9 ft) for different span length.

Required number of strands

Final prestress losses

Moment capacities

Apart from the new formulation for prestressing loss due to elastic shortening in LRFD-C5.9.5.2.3b [

Moment capacities were calculated in accordance with both standard specification and LRFD. The same formulation of standard specification for rectangular sections is used in LRFD. Other parameters mentioned previously have minor effects and the resulting moment capacities are very close as shown in Figure

Superstructure cost for post-tensioned cast-in-place concrete box girder was calculated based on the cost estimates of similar recent projects in Arizona. Similar span-to-depth ratios, web and bottom slab thickness, and reinforcements were used for both methods. Differences in design parameters appeared to be the number of strands and deck reinforcements. The LRFD introduces two design methods for deck reinforcement, and the traditional method in this paper was used with slightly lower steel reinforcement. Among two methods, the total cost in standard specification is slightly lower when using LRFD (Figure

Superstructure cost, $/ft^{2} for a box girder (seven cells spaced at 9 ft).

Web spacing

distribution factor (DF) is directly dependent on a value of S for both methods, and as it is seen in Figure

top slab (deck) thickness and reinforcement are both dependent on web spacing;

superstructure weight is depending on the number of webs and top slab thickness;

prestressing steel area and superstructure cost are dependent on web spacing.

Distribution factors for box girder (150 ft span, 100 ft width, and varying web spaces).

In the study of the effect of web spacing on other parameters, a box girder with 45.7 m (150 ft) span length and constant width of 30.5 m (100 ft) was considered. The web spacing varied from 1.83 to 5.18 m (6 to 17 ft). For each case, deck thickness, deck reinforcement, and prestressing strands were designed.

The optimum web spacing for the box girder was considered to be the spacing for which the superstructure cost is minimized. Superstructure cost was determined based on the cost estimates of recent similar project in Arizona. In the design process, all design constraints such as the maximum number of tendons and the maximum number of strands per tendon were considered. Any other design limitations set by the respective specifications were also considered as a constraint. Web and bottom slab thicknesses were assumed to be 30.5 cm (12 in.) and 15.2 cm (6 in.), respectively, for all design cases. The primary variable is web spacing, which will affect top slab depth, top slab steel, overall weight, prestressing steel, and shear reinforcement. As seen in Figures

Superstructure cost and optimum web spacing.

Span of 150 ft and width of 100 ft

Span of 180 ft and width of 100 ft

The advantage of high-strength/high-performance concrete (HSC/HPC) has been well documented during the past 25 years. Most of the researches in this area address the importance of HPC/HSC to improve the concrete durability, physical properties (strength, creep, shrinkage, etc.) and concrete strength capacity when used as a structural member [

The required amount of prestressing steel depends on the compressive and tensile strength of concrete. The allowable compressive stress is directly dependent on concrete strength,

Effect of concrete strength for the span of 180 ft and 8 webs spaced at 10 ft: (a) on designed number of strands, (b) on moment capacity, (c) on final prestressing loss, and (d) on cracking moment.

Bending capacity of a flexural member is not sensitive to the concrete compressive strength. It is mainly dependent on the effective depth and the amount of steel used in the section. For the strength range from 24 to 35 MPa (3.5 to 5 ksi), some increase in moment capacity can be seen (Figure

Furthermore, the number of strands was kept constant, and the effect of concrete strength was observed. A change of concrete strength from 35 to 70 MPa (5 to10 ksi) will increase the moment capacity of the box section by only 4%, which is still insignificant. The reason is that by increasing the concrete strength, the depth of compressive zone will slightly decrease to make the same compressive force (equal to the steel tensile force). As a result, we cannot solely rely on the concrete strength to improve the bending capacity of the section.

It is worth noting here that by using higher concrete strength, in fact the compressive strain capacity of concrete will increase (approximately from 0.3% to 0.5%). This is a very good advantage, which provides more rotation capacity (and hence, ductility) for the section even though the moment capacity remains the same.

Among several prestress losses, only elastic shortening and anchor set are dependent on the concrete modulus of elasticity, which can be improved when using high-strength concrete. The effect of concrete strength is not currently considered on creep and shrinkage of concrete, which are the two most important time-dependent parameters. It should be mentioned that a higher concrete strength may significantly reduce their effects in prestressed members. Figure

The cracking moment depends on the tensile strength of concrete, which is in turn affected by compressive strength. An increase of 5% in cracking moment may be predicted for concrete strengths changing from 35 to 70 MPa (5 to 10 ksi) (see Figure

Superstructure cost will be affected by the use of high-strength concrete. For high-strength concreted the rate of cost increase is higher compared to conventional concrete (Figure ^{2} ($3/ft^{2}) of superstructure at a strength increment of 7 MPa (1 ksi). This cost increase may not be justified only for structural improvements. Considering the inherent durability improvements when using high-strength concrete, there will be significant long-term saving in the project. As it was also seen before, the superstructure cost for LRFD is slightly less than that of the standard specification. The main reason was found to be reduced deck steel calculated with LRFD.

Approximate superstructure cost versus concrete strength.

In the process of prestressed concrete design, the most beneficial effect of high-strength concrete would be its higher tensile strength when using LRFD service I and service III load combinations. In this part, all the parameters were keep constant except concrete strength and the span length. Figure

Design summary.

Span length, ft | Concrete strength, ksi | No. of strands |
---|---|---|

168 | 4 | 850 |

180 | 9 | 850 |

180 | 4 | 910 |

168 | 9 | 800 |

Span stretching by using higher concrete strength.

Conventionally, a span-to-depth ratio of 0.045 is used for simple span concrete box girders. Based on experiences, it seems that the use of this ratio will ensure the control of deflection. In this part of investigation, the superstructure costs were observed for different span-to-depth ratios. As it is seen in Figure

Effect of span-to-depth ratio on superstructure cost (150 ft span, eight webs spaced at 10 ft).

Single-span cast-in-place post-tensioned box girders were analyzed and designed according to standard and LRFD specification. The primary objective was to compare all design parameters using theses specifications and also to perform some detailed parametric studies subjects such as geometrical optimization of the box girder section and structural utilization of high strength concrete (HSC). Comparison reveals that despite significant increase in live loads, other design parameters (distribution factors, load factors, and design methods) are observed as following:

(1) The LRFD design needs slightly more (about 4%) prestressing steel as compared to the Standard Specification.

(2) Predicted shear carried by the concrete is significantly lower when using LRFD method. This will lead to a greater stirrup requirement.

(3) Final prestressing loss is about 7% more for LRFD method.

(4) Superstructure cost is slightly lower for LRFD due to introduction of new method of moment calculation in the deck slab.

(5) Cost analysis and comparison shows that when changing the girder spacing, there is always a minimum superstructure cost. The girder spacing associated with that minimum cost could be considered as the optimum spacing.

(6) The optimum web spacing can be based on minimum cost. It was found that for box girders with span lengths 46 to 55 m (150 to 180 ft), the optimum web spacing is 3.35 to 3.66 m (11 to 12 ft).

(7) Higher concrete strength provides great flexibility for designers to utilize the maximum service load capacity for the specific girder section. This advantage may result in larger span length, smaller number of strands, or wider web spacing for the same section.

(8) Using higher concrete strength will reduce final prestressing loss and the number of strands. Moment capacity is not sensitive to concrete strength, except for lower strengths (less than 31 MPa (4.5 ksi)).

(9) Anticipated cost increase for superstructure is about $32/m^{2} ($3/ft^{2}) for each 7 MPa (1 ksi) increase in concrete strength.

(10) Compared to the LRFD-recommended depth/span ratio of 0.045, it was observed that the slightly higher ratio of 0.05 is more cost effective.