Optimized Sections for High-Strength Concrete Bridge Girders--Effect of Deck Concrete Strength
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Analyses to evaluate the effect of using high performance concrete in bridge decks on the cost per unit area were performed using a computer program called BRIDGE.
The computer program BRIDGE was written as part of a previous investigation for the Optimized Sections for Precast, Prestressed Bridge Girders and was later revised.(6, 7) The required input of BRIDGE consists of girder span, spacing, and cross section; concrete and strand characteristics; and relative costs of materials. The program determines deck thickness and deck reinforcement, the required number of prestressing strands, and the cost index per unit surface area of bridge deck. It also provides section properties, moments, stress levels, and deflections. Comparisons are made based on relative costs for simply supported spans. A complete description of BRIDGE is given in reference 6.
The following variables were used in the analyses using BRIDGE:
The complete combination of variables is defined in tables 1 and 2. It is recognized that the use of a deck concrete strength of 69 MPa (10,000 psi) in combination with a girder concrete strength of 41 MPa (6,000 psi) is unlikely to occur. However, the complete combination of variables has been included for comparison purposes.
Table 1. Task 1 variables (SI units). Girder Section Girder Strength (MPa) Deck Strength (MPa) Girder Concrete Premium Deck Concrete Premium BT-72 41 28, 41, 55, 69 No No BT-72 55 28, 41, 55, 69 No No BT-72 69 28, 41, 55, 69 No No BT-72 83 28, 41, 55, 69 No No BT-72 41 28, 41, 55, 69 No Yes BT-72 55 28, 41, 55, 69 Yes Yes BT-72 69 28, 41, 55, 69 Yes Yes BT-72 83 28, 41, 55, 69 Yes Yes FL BT-72 41 28, 41, 55, 69 No No FL BT-72 83 28, 41, 55, 69 No No FL BT-72 41 28, 41, 55, 69 No Yes FL BT-72 83 28, 41, 55, 69 Yes Yes Table 2. Task 1 variables (English units). Girder Section Girder Strength (psi) Deck Strength (ksi) Girder Concrete Premium Deck Concrete Premium BT-72 6,000 4, 6, 8, 10 No No BT-72 8,000 4, 6, 8, 10 No No BT-72 10,000 4, 6, 8, 10 No No BT-72 12,000 4, 6, 8, 10 No No BT-72 6,000 4, 6, 8, 10 No Yes BT-72 8,000 4, 6, 8, 10 Yes Yes BT-72 10,000 4, 6, 8, 10 Yes Yes BT-72 12,000 4, 6, 8, 10 Yes Yes FL BT-72 6,000 4, 6, 8, 10 No No FL BT-72 12,000 4, 6, 8, 10 No No FL BT-72 6,000 4, 6, 8, 10 No Yes FL BT-72 12,000 4, 6, 8, 10 Yes YesThe following default assumptions in BRIDGE were used:
It is recognized that shipping lengths, girder weights, lateral stability of girders, prestressing bed capacities that exist today, and plant capabilities to produce high-strength concretes could limit
the type of girders that can be produced. However, these limitations were not used as a means to restrict potential applications. The intent of the project was to look beyond current production capabilities.
The computer program BRIDGE determines cast-in-place deck thickness and reinforcement from design aids prepared by the Washington State Department of Transportation. (15) Designs aids were based on AASHTO and ACI guidelines.(16, 17) For effective slab spans less than 2.1 m (7 ft), the design aids use a slab thickness of 175 mm (7 inches). However, for this project the FHWA requested that the minimum slab thickness be increased to 190 mm (7 1/2 inches). Slab reinforcement was then determined based on the new minimum slab thickness. Results of the design are shown in table 3 with the SI equivalents provided in table 4. These data as English units were stored within BRIDGE.
Table 3. Deck design (15)(English units). Effective Slab Span (ft) Slab Thickness (inches) Slab Reinforcement* Bar Size Spacing (inches) 1 to 3 inclusive 7 1/2 No. 5 11.0 3 to 4 inclusive 7 1/2 No. 5 9.5 4 to 5 inclusive 7 1/2 No. 5 8.5 5 to 6 inclusive 7 1/2 No. 5 7.0 6 to 7 inclusive 7 1/2 No. 6 9.0 7 to 8 inclusive 7 1/2 No. 6 8.0 8 to 9 inclusive 8 No. 6 8.0 9 to 10 inclusive 8 1/2 No. 6 8.0 10 to 11 inclusive 8 3/4 No. 6 7.5 11 to 12 inclusive 9 No. 7 10.0 12 to 13 inclusive 9 1/2 No. 7 10.0 13 to 14 inclusive 9 3/4 No. 7 9.5 14 to 15 inclusive 10 No. 7 9.5 15 to 16 inclusive 10 1/2 No. 7 9.5* Reinforcement shown is for each of top and bottom layers.
Table 4. Deck design (15) (SI units). Effective Slab Span (m) Slab Thickness (mm) Slab Reinforcement* Bar Size Spacing (mm) 0.3 to 0.9 inclusive 190 15 M 280 0.9 to 1.2 inclusive 190 15 M 240 1.2 to 1.5 inclusive 190 15 M 215 1.5 to 1.8 inclusive 190 15 M 180 1.8 to 2.1 inclusive 190 20 M 230 2.1 to 2.4 inclusive 190 20 M 205 2.4 to 2.7 inclusive 200 20 M 215 2.7 to 3.0 inclusive 215 20 M 215 3.0 to 3.4 inclusive 225 20 M 200 3.4 to 3.7 inclusive 230 20 M 195 3.7 to 4.0 inclusive 240 20 M 195 4.0 to 4.3 inclusive 250 20 M 190 4.3 to 4.6 inclusive 255 20 M 190 4.6 to 4.9 inclusive 265 20 M 190* Reinforcement shown is for each of top and bottom layers.
Relative Costs
The material weight for girder concrete, deck concrete, strands, reinforcing steel, and epoxy-coated reinforcing steel is also calculated by BRIDGE. The relative cost of materials is then determined as the product of material weight and relative unit cost. The summation of the relative cost of materials is then divided by deck area to give the cost index per unit area. In the previous investigation, analyses were made to determine the effect of the premium cost for higher-strength girder concretes on the cost per unit area. (6) Based on a limited survey of industry, the ratios in table 5 were assumed for the premium cost for higher-strength concrete used in the girders.
Table 5. Ratios for high-strength concrete. Concrete Strength Minimum Ratio Intermediate Ratio Maximum Ratio 41 MPa (6,000 psi) 1.00 1.00 1.00 55 MPa (8,000 psi) 1.00 1.05 1.10 69 MPa (10,000 psi) 1.00 1.13 1.25 83 MPa (12,000 psi) 1.00 1.25 1.50For the current investigation, the premium costs for higher-strength concrete in the girders were assumed to be those shown as intermediate ratio.
In the previous investigation, the deck concrete strength was assumed to be 28 MPa (4,000 psi) and the relative cost of the deck concrete was the same as that of the 41-MPa (6,000-psi) girder concrete. (6)
To investigate the costs of using high-strength concrete in bridge decks, it was necessary to determine the relative in-place costs for different strength concretes. Analyses of the data in the
previous report indicated that the cost based on materials alone for a 69-MPa (10,000-psi) concrete would be about 72 percent higher than that of a 28-MPa (4,000-psi) concrete. (6) On the assumption that the labor to deliver and place the concretes will be only slightly dependent on concrete strength, the relative premium costs of higher-strength concrete in place will be lower than these numbers. In-place costs for high-strength concrete have been published by ACI Committee 363 and these data are shown in table 6. (1)
Table 6. In-place costs as per ACI Committee 363. Strength $/yd3 $/m3 Relative Cost 48 MPa (7,000 psi) 80 105 1.00 62 MPa (9,000 psi) 85 111 1.06 76 MPa (11,000 psi) 104 136 1.30Based on these data, it was decided to use two sets of ratios for premium costs of high-strength concrete in the decks to determine the sensitivity of the cost index per unit area to the premium costs. The selected ratios are in table 7.
Table 7. Selected ratios for cost index per unit area to premium costs. Deck Concrete Strength No Premium Ratio* Premium Ratio* 28 MPa (4,000 psi) 1.00 1.00 41 MPa (6,000 psi) 1.00 1.05 55 MPa (8,000 psi) 1.00 1.13 69 MPa (10,000 psi) 1.00 1.25* Costs are relative to 41-MPa (6,000-psi) girder concrete.
Analyses were performed for both the no premium ratio and the premium ratio.
The computer program BRIDGE determines the deck thickness and reinforcement based on a design aid prepared by the Washington State Department of Transportation. (15) The design aid is based on AASHTO and ACI guidelines and uses a concrete compressive strength at 28 days of 28 MPa (4,000 psi).(16, 17) The design aid is based on the distribution of loads and design of concrete slabs given in the AASHTO Standard Specifications for main reinforcement perpendicular to traffic. (16) Discussions with several bridge engineers indicated that many States use design aids similar to the one incorporated into BRIDGE.
In the AASHTO design of concrete slabs, deck thickness and reinforcement are calculated to resist the bending moments caused by the dead load of the slab and the live load moment for the selected concentrated wheel load. In flexural design for under-reinforced sections, the concrete compressive strength has little effect on the flexural strength of the section. Consequently, the use of high-strength concrete in the deck will not impact the flexural strength of the deck. Based on this design approach, the deck thickness and the amount of reinforcement required to resist a given bending moment will not decrease as higher-strength concretes are used. Therefore, no revision was made to the design aid for use with higher-strength concretes in the decks. In addition, a minimum slab thickness of 190 mm (7.5 inches) was requested by FHWA. This controlled the deck thickness for effective span lengths up to 2.4 m (8 ft). Thus the use of higher-strength concrete in bridge decks will not reduce the thickness of the deck or the weight of the superstructure. In fact, the higher-strength concretes in the deck will slightly increase the dead load of the superstructure because of the higher density of the higher-strength concretes.
The computer program BRIDGE was used to perform cost efficiency analyses for various strengths of concrete in the girders and bridge decks. A sample cost chart for a BT-72 is shown in Figure 3. The figure shows the cost index per unit surface area of the bridge deck versus span length for various girder spacings. The "optimum cost curve" is obtained where the end points of each individual cost curve are joined as shown by the dashed line in Figure 3. This optimum cost curve indicates the least cost index for a particular span and varies as a function of girder spacing (see Figure 3). As reported in previous investigations, for a given span, the cost index per unit area of a bridge deck decreases as girder spacing increases.(6,7) In all optimum cost curves used in this report, the girder spacing is allowed to vary to obtain the optimum cost.
Optimum cost curves are generated for a constant girder and deck concrete strength. The cost chart in Figure 3 is for girder concrete strength at 28 days of 41 MPa (6,000 psi) and a 28-day concrete strength for the deck of 28 MPa (4,000 psi). Additional optimum cost curves can be generated for other deck concrete strengths for the same girder cross section and the same girder concrete strength. Figure 4 is a plot of the optimum cost curves for a BT-72 with a girder concrete strength of 41 MPa (6,000 psi) and deck concrete strengths of 28, 41, 55, and 69 MPa (4,000, 6,000, 8,000, and 10,000 psi, respectively). The data in figure 4 are based on the assumption that there is no cost premium for the higher-strength concrete. This figure illustrates that, at the shorter span lengths, there are no cost advantages or disadvantages in using the higher-strength concrete in the bridge deck. However, at the longer span lengths a slight advantage is achieved in a reduction in cost for the same span length. Alternatively, the ability to achieve a slightly longer span length is obtained. For the same girder cross section, these advantages occur because of the higher moment of inertia of the composite cross section that is achieved with the higher-strength concretes in the deck. In addition, the increase in the moment of inertia of the composite section will result in less live load deflection.
Figure 3. Cost chart for a BT-72, 41 MPa.
Figure 4. Optimum cost curves for a BT-72, 41 MPa.
A comparison of optimum cost curves for a BT-72 girder with a girder concrete strength of 83 MPa (12,000 psi) and deck concrete strengths of 28, 41, 55, and 69 MPa (4,000, 6,000, 8,000, and 10,000 psi, respectively) and no cost premium is shown in figure 5. In this combination, there are no real cost advantages or disadvantages with the use of the higher-strength concrete in the deck. Similar data for a BT-72 girder with concrete strengths of 55 MPa (8,000 psi) and 69 MPa (10,000 psi) and no cost premium are shown in figures 6 and 7, respectively.
Figure 8 shows a cost comparison for the BT-72 with girder compressive strengths of 41, 55, 69, and 83 MPa (6,000, 8,000, 10,000, and 12,000 psi, respectively) and deck concrete strengths of 28 and 69 MPa (4,000 and 10,000 psi, respectively). This figure illustrates the benefits and limitations of using higher-strength concrete with no cost premiums in precast, prestressed bridge girders. At shorter span lengths there are no benefits realized by using the higher-strength concretes. However, at longer span lengths, it is more economical to use the higher-strength concrete in the girders. The higher-strength concrete in the girders results in larger prestressing forces and, consequently, greater girder spacings for a given span length, thus reducing unit costs. These data have been confirmed in previous investigations.(6,7) For the very long span lengths, it is possible only to design for these lengths using the higher-strength concretes. Figure 8 also indicates another important point: the diminishing returns associated with the use of high-strength concrete, the primary cause of which is decreasing strand eccentricity. Once strands are placed within the web, the efficiency of the cross section begins to decrease rapidly. The incremental benefit of each succeeding strand decreases when sufficient room within the flange does not exist. Once additional prestressing force cannot be induced in the girder, the beneficial effects are limited to the increase in concrete tensile strength (which increases only as the square root of the compressive strength). (1)
Optimum cost curves for a FL BT-72 with girder concrete strengths of 41 and 83 MPa (6,000 and 12,000 psi, respectively) and varying deck concrete strengths are shown in figure 9. The data represent the cost index per unit area when there is no cost premium for the higher-strength concrete. This figure shows a pattern of results similar to that shown in figure 8 for the BT-72. In a previous investigation, the FL BT-72 was found to be more cost effective than the BT-72 for span lengths greater than 46 m (150 ft). These data show the same results.
It is reasonable to expect the payment of a premium for the use of high-strength concrete in bridge decks. This premium results from the increased cost of materials to be used in the concrete, the inexperience of bridge contractors in placing and finishing these concretes, and the necessity of proper curing procedures. Analyses were therefore made using the cost premiums indicated in table 8.
Table 8. Relative premium costs of high-strength concretes. Girder Deck Strength (MPa (psi)) Strength (MPa (psi)) Cost 28 (4,000) 41 (6,000) 55 (8,000) 69 (10,000) 41 (6,000) 1.00 1.00 1.05 1.13 1.25 55 (8,000) 1.05 1.00 1.05 1.13 1.25 69 (10,000) 1.13 1.00 1.05 1.13 1.25 83 (12,000) 1.25 1.00 1.05 1.13 1.25Optimum cost curves for a BT-72 with girder concrete strengths of 41, 55, 69, and 83 MPa (6,000, 8,000, 10,000, and 12,000 psi, respectively) and varying deck concrete strengths are shown in figures 10, 11, 12, and 13, respectively. Optimum cost curves for a FL BT-72 with girder concrete strength of 41 and 83 MPa (6,000 and 12,000 psi, respectively) are shown in figures 14 and 15, respectively. These figures indicate that at span lengths of 24 m (80 ft), increasing the deck concrete strength from 28 MPa to 69 MPa (4,000 to 10,000 psi) results in an increase in the cost per unit area of approximately 10 percent for both the Bulb-Tee and the Florida Bulb-Tee. At span lengths of 44.5 m (146 ft) the percentage of increase is approximately 8 percent for both strengths of girder concrete. At the maximum span lengths achievable with the BT-72 and the FL BT-72 with a girder concrete strength of 83 MPa (12,000 psi), the increase is approximately 5 percent.
Figure 5. Optimum cost curves for a BT-72, 83 MPa.
Figure 6. Optimum cost curves for a BT-72, 55 MPa.
Figure 7. Optimum cost curves for a BT-72, 69 MPa.
Figure 8. Comparison of optimum cost curves for a BT-72 with varying concrete strengths.
Figure 9. Comparison of optimum cost curves for a FL BT-72 with varying concrete strengths.
Figure 10. Optimum cost curves for a BT-72, 41 MPa with cost premium.
Figure 11. Optimum cost curves for a BT-72, 55 MPa with cost premium.
Figure 12. Optimum cost curves for a BT-72, 69 MPa with cost premium.
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Figure 13. Optimum cost curves for a BT-72, 83 MPa with cost premium.
Figure 14. Optimum cost curves for a FL BT-72, 41 MPa with cost premium.
Figure 15. Optimum cost curves for a FL BT-72, 83 MPa with cost premium.
Consequently, it may be concluded that even if a 69-MPa (10,000&#;psi) concrete has an in-place cost that is 25 percent greater than a 28-MPa (4,000-psi) concrete, the overall unit cost of the superstructure will only increase in the range of 5&#;10 percent.
The analyses performed in task 1 considered only the initial costs. They did not take into account that high-strength concrete in the deck is also high-performance concrete and will have improved durability compared to a deck produced with a lower strength concrete. This should result in less maintenance costs and reduced life cycle costs. A life cycle cost study is beyond the scope of work of this report.
Based on analyses made in task 1, the following conclusions are made:
Waterjet has been the favorite cutting process in a wide range of sectors in the manufacturing world, over alternatives like laser cutting.
However, certain professionals are still new to the technology and in the early stages of adoption for their industry. One common question that comes up frequently from these professionals is, &#;what is the correct water jet cutting pressure?&#;
This article discusses all the details regarding waterjet cutting pressure. You will also learn what influences the pump you require and the difference between a hyperpressure and a normal pressure pump.
What is the Average Pressure of a Water Jet Cutter?
Understanding the average waterjet cutting pressure means knowing the typical range within which it can vary. There is no single value for pressure because of the variations that can occur based on several variables.
Water pressure for waterjet cutting starts at 30,000 psi (210 MPa) and goes up to 90,000 psi (620 MPa).
Since abrasive waterjet cutting machines use high-pressure water for piercing the materials, many people wrongly believe that using higher pressure will cut greater thicknesses of material. However, that is an incorrect assumption.
A 30,000 psi machine can cut the same material thickness as a 90,000 psi machine. However, higher pressures provide a significantly faster cutting speed, increasing productivity exponentially. Additionally, increasing the water pressure of the jet stream increases the accuracy of this cold-cutting process.
Factors That Influence Water Jet Cutter Pressure
Here are the factors that influence the water pressure of a waterjet cutter:
When buying a pump, most people focus on the water stream pressure. However, the horsepower of the pump is also a critical factor one should consider. The horsepower determines the pressure required at a given flow rate, and is derived from the formulae:
Horsepower = Pressure x Flow Rate
Therefore, for a given pump horsepower, increased water pressure results in decreased flow rate. To compensate, the water jet will need a smaller nozzle orifice.
As mentioned earlier, an increase in the nozzle pressure will increase the cutting speed. The suggestion is that increasing productivity is easy by using higher pressures. That is true, but only up to 50,000 psi to 60,000 psi.
Beyond that, with hyper-pressure pumps. The waterjet cutting speed increases with pressure, but so does the equipment wear and tear, leading to frequent breakdowns of the waterjet system, resulting in downtime &#; which can lower operational productivity.
In abrasive waterjet cutting, the choice of abrasive grains can also dictate the most effective water pressure. Finer mesh abrasives allow using narrower nozzle orifices without clogging them, increasing the output pressure at the nozzle.
80 mesh abrasive is usually suitable for most requirements. In high-precision cutting, 120 mesh abrasive is the recommended choice. A 120 mesh abrasive material also provides a better quality cut when cutting thin materials.
Appropriate abrasive hardness leads to creating high efficiency without increasing pressure. For instance, using super-hard materials like aluminum oxide as an abrasive means an increased cutting speed for hard materials. However, it also leads to faster wear of the mixing tube and other components.
Super-hard abrasives are not required to cut soft materials like aluminum and gold. Normal abrasives such as garnets are adequate for cutting soft materials.
The waterjet cutting process occurs due to the high velocity of the jet stream. Many people use water velocity and pressure interchangeably, but that shouldn&#;t be the case. The velocity of the water jets varies depending on the pressure and the nozzle orifice. Increasing water velocity at a fixed pressure is possible by decreasing the orifice size. However, the size of the garnet abrasive used subsequently limits the diameter of the orifice.
Therefore, the easier way to extract high-speed water is by increasing the water pressure. It is important to note that increased water velocity will only increase the cutting speed but not the thickness of the materials it can cut. Additionally, water jet speeds govern the speed of the garnet since it travels in the stream.
Professionals often use multiple cutting heads to increase productivity without increasing water pressure in hyperpressure operations. However, while production speed increases, a high horsepower pump is also required to provide adequate pressurizing for the individual cutting head.
Additionally, parts of the individual cutting heads, such as the waterjet nozzle, will deteriorate at their own rate, leading to inaccuracy when cutting materials since the wear and tear on each cutting head will be at different levels.
Two popular types of pumps available for waterjet cutting are an intensifier pump and a direct drive pump. An intensifier pump works on a hydraulic mechanism, while direct drive pumps employ a crankshaft mechanism.
These two pump technologies vary in terms of many factors, such as the maximum pressure they can provide. Direct drive pumps can go up to 60,000 psi, while intensifier systems can provide up to 100,000 psi. It is vital to note that the higher maximum pressures of intensifiers come with disadvantages such as high failure rates, coolant requirements, and a high noise level.
Hyperpressure vs. Normal Pressure
In waterjet cutting, normal pressure refers to a water pressure of up to 60,000 psi. Of course, this value is not &#;normal&#; compared to the water pressure in non-cutting applications. However, compared with a hyperpressure pump which goes from 60,000 psi to 90,000 psi, or higher &#; it is &#;normal&#;.
Using hyperpressure pumps means a faster cutting process, so it might seem the obvious choice to use all the time. However, hyperpressure pumps have greater component wear and tear due to the extreme force of the water. These components include not only the internal parts of the pump but also parts of the delivery system, like the tube and nozzles.
Hyperpressure pumps undoubtedly produce significantly more efficient cutting &#; leading to high production rates in abrasive waterjet cutting. However, the costs saved by higher efficiency may be less than the higher consumables cost incurred due to shorter life, higher maintenance costs, and higher failure rates for parts such as the orifice, valve, and tubing.
Conclusion
Choosing the ideal pressure is one of the big questions for users of waterjet cutting technology. In short, there is no one-size-fits-all solution. It varies based on the requirement of the situation, so machine shops need to adjust the water pressure they use based on their experience with the machine for their applications.
For best results, use a good quality machine that can provide the full benefits of a high-pressure pump without the high failure rates and replacement costs. Techni Waterjet cutting equipment is a winner in this regard, renowned for its good build quality and rugged design to suit the requirement of cutting virtually any material.
Frequently Asked Questions
Here are the answers to some common questions that people ask regarding waterjet cutting:
The optimal pressure for waterjet cutting varies based on the project requirements. In general, 50,000 psi to 60,000 psi provides the best results for most applications of waterjet technology.
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