What is the area of 0.6 diameter prestressing strands?

The following is a list of basic formulas for 270 ksi, 7-wire Prestressing steel strand (per ASTM-A416) used in Post-Tensioned concrete.
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Assume 0.5″ diameter strand has cross-sectional area of 0.153 sq.in. and weight of 0.525 lbs/ft.

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Assume 0.6″ diameter strand has cross-sectional area of 0.217 sq.in. and weight of 0.740 lbs/ft.
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Minimum Ultimate Tensile Strength (MUTS) = (Grade of Steel) x (Cross-Sectional Area)

0.5″ inch diameter = (270 ksi) x (0.153 sq.in.) = 41.3 kips

0.6″ inch diameter = (270 ksi) x (0.217 sq.in.) = 58.6 kips
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Minimum Yield Strength = 90% of MUTS = MUTS x 0.90 (per ASTM-A416)

0.5″ inch diameter = (41.3 kips) x (0.90) = 37.2 kips

0.6″ inch diameter = (58.6 kips) x (0.90) = 52.7 kips
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Jacking Force = 80% of MUTS = MUTS x 0.80 (per ACI Code)

0.5″ inch diameter = (41.3 kips) x (0.80) = 33.0 kips

0.6″ inch diameter = (58.6 kips) x (0.80) = 46.9 kips

“Jacking Force” is the force that tendons are stressed to.
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Allowable Initial Force = (Jacking Force) minus (Short-Term Losses) = 70% of MUTS = MUTS x 0.70 (per ACI-318)

Short-Term Losses include:

1. Angular Profile of Tendon
2. Horizontal sweeps in Tendon
3. Wedge-Seating (typically 0.25 inch)
4. Wobble due to installation (CLICK HERE to view the video on how to calculate Angular and Wobble Coefficients in unbonded post-tensioning tendons.)

0.5″ inch diameter = (41.3 kips) x (0.70) = 28.9 kips

0.6″ inch diameter = (58.6 kips) x (0.70) = 41.0 kips

“Initial Force” is the force at the anchorage after the wedges are seated and stressing jack is removed.  The calculated values above are approximate since the actual short-term losses may differ from the theoretical values.
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Final Force = (Initial Force) minus (Long-Term Losses)

Long-Term Losses include:

1. Creep of concrete (permanent deflection due application of constant load)
2. Elastic Shortening of concrete
3. Relaxation of steel prestressing strand
4. Shrinkage of concrete during curing

0.5″ inch diameter = approx 26.9 kips

0.6″ inch diameter = approx. 38.1 kips

“Final Force” is the force at the anchorage after the long-term losses are accounted for.  The calculated values above are approximate since the actual long-term losses may differ from the theoretical values.
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Average Tendon Elongation (approx.) = (P x L) / (A x E)

P = Prestress jacking force (70% of MUTS)

L = Length of steel (inches)

A = Cross-Sectional Area of steel (sq.in.) on mill certificates

E = Modulus of Elasticity of steel (ksi) on mill certificates

For example, using a 100-foot tendon (L = 100 x 12 inches) with Modulus of Elasticity of 28,500 ksi.

0.5″ inch diameter = (28.9 kips x 1,200 inches) / (0.153 sq.in. x 28,500 ksi) = 7.95 inches

0.6″ inch diameter = (41.0 kips x 1,200 inches) / (0.217 sq.in. x 28,500 ksi) = 7.95 inches

***Notice that the 0.5″ and 0.6″ have the same Avg. Elongation***
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Post-Tensioning Institute recommends an allowable elongation range of plus/minus 7% of the Average Tendon Elongation for unbonded post-tensioning tendons.

Min. Allowable Elongation = 93% of Avg. Elongation = 0.93 x (Avg.El.)

Max. Allowable Elongation = 107% of Avg. Elongation = 1.07 x (Avg.El.)

If we use the same 100-foot tendon with average elongation of 7.95 inches, then Min.El. = 0.93 x 7.95 inches = 7.40 inches and Max.El. = 1.07 x 7.95 inches = 8.51 inches.

– Rattan Khosa, Vice President, AMSYSCO

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Copyright © 2010 by AMSYSCO, Inc. All rights reserved.

by Susan Lane and Rekenthaler Jr.

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Each year, ribbon-cutting ceremonies are held throughout the United States and abroad to dedicate majestic new bridges and highways designed to move millions of people from one place to another as efficiently and comfortably as possible. Speeches are made; photographs are taken; and much attention is paid to the latest link in the highway system serving the public.

Nevertheless, designers and engineers know that just inches beneath the veneer of shiny new steel and pristine concrete lie the structural skeleton and sinewy muscle that are the preeminent parts of the bridge. Little is ever made of these fundamental pieces of the construction puzzle - the delicate balance of concrete and steel with which the bridge is built and the sophisticated mathematical formulas through which these disparate compounds are bound.

 But upon their backs rides the safety of the people who cross the bridge, the commerce of the nation, and the justification for billions of dollars of taxpayer-supported construction funds. Therefore, the design processes behind these projects are time-worn and true, subject to change only when a specific improvement is sought.

So, when manufacturers almost a decade ago proposed increasing by one-tenth of one inch (2.54 millimeters) the size of the steel strands that form the structural backbone in the nation's prestressed concrete bridges, the immense regulatory machinery of the engineering community kicked into gear, and a battle was on to rewrite the rules.

What's One-Tenth of an Inch?

The story begins almost a decade ago with the structural engineering community actively seeking new methodologies for improving the strength and longevity of the nation's increasingly overburdened roads and bridges.

In 1988, much was happening in the U.S. engineering community. Specifically, strand manufacturers were interested in bumping the 0.5-inch- (12.7-mm-) diameter threshold to 0.6 inches (15.24 mm) to increase structural durability and strength.

 Prestressed strands represent an important contribution to the nation's roads, bridges, and skyscrapers because, as opposed to the solid steel rebars employed in early construction techniques, strands (a group of seven tightly wrapped, thin steel wires) have more "give" when being stressed. This is a critical consideration when it comes to the process of prestressing because the inherent tension resulting from that operation can, in effect, be used to further energize the concrete with which it is bonding. When the stressed steel is cut, the tension is transferred to the concrete beam, which ultimately cambers upward, providing it with additional strength. As a result, the composite steel and concrete "member" is made stronger and more durable.

Although the prestressed strands have proven to be a boon to structural engineers, the growing prominence of improved construction materials - such as high-performance concrete, which requires an equally powerful strand - forced manufacturers to consider even stronger strands. Consequently, they surmised that a larger strand would adequately complement the improved concrete. Thus, in 1988, strand manufacturers announced they intended to increase the size of prestressed strands - a move that was welcomed by many engineers who were searching for stronger construction materials.

In conjunction with their 0.6-inch strand proposal, manufacturers also wanted to maintain the minimum spacing between the strands at 2.0 inches (60.96 mm), the same spacing as allowed for a 0.5-inch strand. This represented a significant increase in the load transferred to the concrete part of the beam.

The minimum spacing requirement is necessary to guarantee adequate bonding between the strands and concrete. Too little spacing and the additional tension from the prestressed strands will crack the concrete. Such a move would be in keeping with the conventional "4x standard," which is known as the bond length-development length equation, which states that the amount of spacing must be equal to four times the strand diameter. By that rule, an increase to 0.6-inch-diameter strand should add an additional 0.4 inches (10.16 mm) to the spacing requirement.

 This equation represents a fundamental safety issue, and one that a lot of people have focused on for many years.

A problem with this proposal quickly became evident. Manufacturers would have been forced to completely retool their prestressing operations to accommodate the new spacing requirements, and this is a prohibitively expensive prerequisite. As a result, the strand manufacturers opted to remain with the 2-inch spacing requirement even though it ran counter to the reigning convention that the spacing must be equal to four times the diameter of the strand.

But a more serious problem was about to befall the proponents of 0.6-inch-diameter strands. A study team at North Carolina State University was poised to render a verdict that the existing bond length-development length equation was inadequate. The FHWA Bridge Division researchers recommended that structural engineers incorporate a safety factor into the equation to guard against potential bonding deficiencies. This new safety factor, which would require engineers to add a 1.6 multiplier to the bond-length equation, would thwart not only the advocates of the 0.6-inch-diameter strands, but all of the engineers who previously had been playing by the existing rules.

FHWA Says, "Not So Fast; Safety First"

Shortly after the 0.6-inch proposal was publicized, FHWA put the brakes on any changes to prestressing strands until a number of questions could be answered:

• How safe are 0.6-inch-diameter strands?
• Can the 2-inch spacing requirement safely accommodate 0.6-inch-diameter strands?
• Is the bonding equation still valid?

In October 1988, the FHWA Bridge Division issued a memorandum that forbade the use of 0.6-inch strands until additional studies were carried out to determine its safety. In addition, the agency said the requirement that strand spacing be equal to four times the strand diameter must remain in place, again pending further study. And most importantly, FHWA ruled that the 1.6 multiplier must be added to the bonding equation as a safety factor.

The memorandum created quite an uproar across the country, and it started a race to solve these problems. In addition to research by FHWA, a dozen studies immediately were launched at a variety of colleges and institutes in the United States and Canada.

Highway and bridge designers were particularly incensed at the new bonding equation multiplier rule that forced them to reengineer their designs to incorporate the 1.6 safety factor. In some cases, it meant designers had to create larger or thicker members to carry out their projects.

As might be expected, the industry questioned the N.C. State University figures, arguing that surely the study's authors made an error in their calculations. Clearly, the race was on to disprove the school's findings. Over the next several years, findings from various studies began trickling in. FHWA's own study took five years just to gather the necessary data. Analysis of that data continues to this day.

FHWA broke down the "job" into three separate issues and opted to tackle the development length issue separately. The agency contracted with Prof. Dale Buckner from Virginia Military Institute (VMI) to gather data from as many of the ongoing studies as possible and to try to make sense of them.

By December 1994, Buckner had at least some of the answers.

Paving the Way for High-Performance Concrete

Buckner concluded that the 0.6-inch strands were "behaving fine" but that additional testing was required to answer the myriad of questions regarding spacing. Specifically, he suggested that the entire question of the bond development equation be reassessed. So, FHWA added a new phase to the study to make a comprehensive decision about spacing. Clearly, the answer to the question of spacing would have to wait.

In May 1996, advocates of 0.6-inch-diameter strands got the news they had been awaiting when FHWA released a memorandum announcing that 0.6-inch-diameter strands were acceptable. The agency also stated that 2-inch spacing for 0.6-inch-diameter strands was acceptable. FHWA went one step further and said designers could use 0.5-inch-diameter strands at 1.75-inch (44.45-mm) spacing if they wanted. In effect, FHWA not only accepted the argument for 0.6-inch-diameter strands but also allowed designers to reverse-engineer 0.5-inch-diameter spacing equations if they were so inclined.

One year later, members of the American Association of State Highway and Transportation Officials (AASHTO) passed by voice vote the allowance for 0.6-inch strands at 2-inch spacing and for 0.5-inch strands at 1.75-inch spacing. This was an important milestone in the crusade for 0.6-inch strands because AASHTO guidelines are the "Bible" of highway and bridge engineering principles. AASHTO design specifications were promptly changed to reflect the new strand and spacing allowances.

This change has ramifications beyond the United States. These rules eventually are adopted by many foreign governments for their own construction processes.

For highway and bridge engineers, the new strand and spacing specifications will give a badly needed boost to high-performance concrete (HPC), which FHWA has been urging state departments of transportation to adopt for their construction projects. The 0.6-inch strand can be a perfect match with HPC, making stronger, longer lasting bridges. HPC and the larger strands have a real synergy, and before this ruling, that was missing. Now, the argument against the larger strand can no longer be used against HPC.

Indeed, by literally paving the way for high-performance concrete, the new 0.6-inch strands will fundamentally alter the way highways and bridges are built and will end up saving this country a lot of money.

And the ribbon-cutters will carry on, unaware of the critical importance of the material just inches below their feet and of the decade-long battle to put it there.

Susan Lane is a research structural engineer in FHWA's Structures Division, Office of Engineering Research and Development, at the Turner-Fairbank Highway Research Center in McLean, Va.

Doug Rekenthaler Jr. is a freelance writer and editor. His experiences as a writer and editor include cub reporter covering Capitol Hill and Pentagon news beats; managing editor responsible for 12 newsletters covering a wide array of communications technologies; founder of the multimedia industry's first daily fax news service; and corporate communications manager for America Online Inc., the largest commercial on-line service in the world.

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