When post-tensioning (PT) tendons are stressed, force in the tendons is reduced due to slippage at the anchors (called seating losses), friction between the tendon and the sheathing (called friction losses), and other long-term losses due to concrete shrinkage, concrete creep, and steel relaxation. Shrinkage is caused by the curing and drying of the concrete after it is placed.
Today’s design software can easily calculate the seating and friction losses. However, in the real world, friction calculations provided by system suppliers are seldom considered when detailing the number and location of tendons. Structural engineers should consider these losses during design and not force detailers to make assumptions that can increase the cost and complexity of post-tensioned structures.
History: How We Got Here
In the 1970s and early 1980s, post-tensioning suppliers often performed unbonded post-tensioned concrete design as value engineering or as a deferred submittal. They calculated moment redistribution on a slide rule and, later, handheld calculators. Systems and materials were proprietary, with different sheathing, anchorage, and stressing equipment. Some used “stress-relieved” strand and some used “low-lax” strand.
All this complicated design made many structural engineers uncomfortable specifying a particular system. Instead, they designed a mild-steel reinforced system with a value engineering option or used a deferred submittal process. But by the mid-1980s, virtually all suppliers had moved to extruded tendon sheathing, making friction and loss coefficient assumptions uniform across the industry. Better design software was developed. Crunching the numbers became less laborious and designs more efficient because engineers could easily analyze alternate profiles and tendon quantities.
It became common practice to specify post-tensioning by showing the average force over the length of the tendon. This was perfectly reasonable as long as certain parameters were met – especially considering everyone was assuming a “lump sum” loss that included seating loss, friction, and long-term losses instead of doing the tedious friction calculations.
However, the American Concrete Institute (ACI) 318-11 commentary (R18.6.1) states that “lump sum values of prestress losses for pre-tensioned and post-tensioned members that were indicated before the 1983 commentary are considered obsolete.” ACI 318 has recommended against using lump sum losses since the 1985 edition, and the current edition provides references to techniques for calculating friction and long-term losses.
I believe Committee 318 expects engineers to take advantage of today’s powerful design software, but most are not. Herein lies the problem. Even though suppliers typically provide friction/loss calculations, most engineers still use the lump-sum method and a final effective force in the tendon of 175 ksi is assumed all along the tendon.
Why These Practices are Problematic
This long-winded introduction brings me to my primary concern: Post-tensioning design software is so sophisticated today that seating loss and friction calculations can easily be considered – and should be. Why they aren’t is a pet peeve of mine for the following reasons.
Forces in Post-Tensioned Tendons
Jacking stress is 80% of the tendon’s ultimate strength (Fpu) = 216 ksi
Seating and friction losses bring stress in the tendon down to70% Fpu = 189 ksi
Long-term losses in the tendon are assumed to be 14 ksi
Therefore, the final effective force in the tendon is 189 minus 14 = 175 ksi
The cross-sectional area of a ½-inch diameter tendon is 0.153 in2. Therefore, the force in each tendon is 175 ksi times 0.153 in2 = 26.8 kips per tendon. This value is used throughout the post-tensioning industry when calculating actual number of tendons required during shop drawing creation.
Tendon elongation during stressing (D) is typically considered to be 0.081 inches per foot of concrete. This value comes from D = sL/AE where s = 189 ksi, L = 12 inches, A = 0.153 in2, and E = 28,000 ksi.
Point 1: Tendon elongations are calculated based on the assumed value of tendon stress of 189 ksi. This is an industrywide non-secret because it’s always on the first sheet of shop drawings.
Point 2: Shop drawing tendon quantities are based on the magic number of 26.8 kips per tendon of post-tensioning stress. The PT supplier’s friction calculations are rarely used to calculate tendon quantities. This is another industrywide non-secret.
Point 3: Force specifications introduce ambiguities. Where along the tendon is this magic force supposed to be taken? Or is it the average force, the value that’s historically been used?
If the specification requires force to be 26.8 at any point along the tendon, additional tendons must be added if just one point falls below that. This may well overstress/overbalance spans closer to the stressing end. ACI’s commentary section states “overestimation of prestress losses can be almost as detrimental as underestimation, since the former can result in excessive camber and horizontal movement.” In one case I know of, the tendon was 2% low in only one span; adding tendons to meet the required force increased the effective force in the span adjacent to the stressing end to 18% above the specified force.
This is why friction losses should be considered during design.
Today’s design software is so sophisticated there’s no excuse for structural engineers to still be using force specifications instead of considering seating and friction losses when determining required number of tendons.
Point 4: Another problem with force specifications is the actual number of tendons is not explicit. What is the magic number for force? We used 26.8 kips during my years as head of a detailing department, but the problem is the round-off. Slight changes in the force requirement can increase the number of tendons. In this fiercely competitive industry, that can mean the difference between winning or losing a bid. When you have multiple banded tendons on multiple floors or distributed tendons where the force is highly variable, round-off can result in a significant increase in the quantity of tendons.
In this fiercely competitive industry, that can mean the difference between winning or losing a bid. When you have multiple banded tendons on multiple floors or distributed tendons where the force is highly variable, round-off can significantly increase the number of tendons. Expecting the PT estimator to figure all of this out during take-off is unreasonable.
Point 5: These calculations should be done by the structural engineer and the required number of tendons specified on structural plans. The actual effective force has a direct effect on the nominal flexural capacity and tensile stresses in the concrete. Due to friction losses, this force varies along the tendon. It also affects balance loading, which in turn reflects in the deflections of the member.
In my opinion, the engineer hasn’t completed the design unless these calculations are done. Shop drawing detailers are excellent interpreters of structural drawings, but they’re not engineers; they don’t know anything about loads, member deflections, or member stresses. They only know the codes that directly affect their drawings.
Why are they being asked to do part of the structural engineer’s job?
Point 6: The other issue with shop drawings is the requirement for a professional engineer (P.E.) stamp. This is also directly related to force specifications.
The definition of engineering is met when the forces are used to calculate the number of tendons required. Design software lays out the tendons during modeling. If these quantities are transferred to the design drawings, engineering isn’t required during shop drawing creation and therefore the stamp shouldn’t be required. However, I believe all jurisdictions require shop drawings to be stamped even when tendon quantities are specified.
In a perfect world, engineers would specify tendon quantities. Designs would be easier to take off for bidding, easier for the supplier to detail, easier for the engineer to check the shop drawings, and this would eliminate the need for suppliers to have their shop drawings stamped.
