Material Properties of Post-Tension Strands

Below is a comprehensive overview of essential calculations related to the 270 ksi, 7-wire Prestressing steel strand as per ASTM-A416. This type of strand commonly finds use in Post-Tensioned concrete applications.
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For instance, a strand with a diameter of 0.5 inches possesses a cross-sectional area of 0.153 sq.in. and a weight of 0.525 lbs/ft.

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Continuing, for a strand measuring 0.6 inches in diameter, we find a cross-sectional area of 0.217 sq.in. and a weight of 0.740 lbs/ft.
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Minimum Ultimate Tensile Strength (MUTS) is calculated as follows: (Steel Grade) x (Cross-Sectional Area)

For a diameter of 0.5 inches: (270 ksi) x (0.153 sq.in.) = 41.3 kips

For a diameter of 0.6 inches: (270 ksi) x (0.217 sq.in.) = 58.6 kips
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The Minimum Yield Strength can be derived using the equation: 90% of MUTS = MUTS x 0.90 (as specified in ASTM-A416)

For a diameter of 0.5 inches: (41.3 kips) x (0.90) = 37.2 kips

For a diameter of 0.6 inches: (58.6 kips) x (0.90) = 52.7 kips
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Jacking Force is determined at 80% of MUTS = MUTS x 0.80 (as per ACI Code)

For a diameter of 0.5 inches: (41.3 kips) x (0.80) = 33.0 kips

For a diameter of 0.6 inches: (58.6 kips) x (0.80) = 46.9 kips

The 'Jacking Force' refers to the stress under which the tendons are tensioned.
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Allowable Initial Force is defined as: (Jacking Force) minus (Short-Term Losses) = 70% of MUTS = MUTS x 0.70 (according to ACI-318)

Short-Term Losses encompass:

1. Angular Profile of Tendon
2. Horizontal curvature within the Tendon
3. Wedge-Seating (typically 0.25 inch)
4. Installation-induced Wobble (CLICK HERE to access a video detailing how to calculate Angular and Wobble Coefficients in unbonded post-tensioning tendons.)

For a diameter of 0.5 inches: (41.3 kips) x (0.70) = 28.9 kips

For a diameter of 0.6 inches: (58.6 kips) x (0.70) = 41.0 kips

'Initial Force' defines the force at the anchorage once the wedges have been seated, and the stressing jack has been removed. It is important to note that the estimated values may vary from the actual short-term losses.
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Final Force is determined as: (Initial Force) minus (Long-Term Losses)

Long-Term Losses comprise:

1. Concrete Creep (permanent deformation due to constant load)
2. Elastic Shortening of Concrete
3. Stress Relaxation in Prestressing Steel
4. Concrete Shrinkage during the curing process

For a diameter of 0.5 inches: approximately 26.9 kips

For a diameter of 0.6 inches: approximately 38.1 kips

'Final Force' represents the force at the anchorage subsequent to accounting for long-term losses. Similar to before, the calculated values may not align precisely with actual long-term losses.
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Average Tendon Elongation (approx.) can be computed as follows: (P x L) / (A x E)

Where:

P = Prestress jacking force (70% of MUTS)

L = Length of steel (inches)

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

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

By way of an example, consider a tendon measuring 100 feet (L = 100 x 12 inches) with a Modulus of Elasticity at 28,500 ksi.

For a diameter of 0.5 inches: (28.9 kips x 1,200 inches) / (0.153 sq.in. x 28,500 ksi) = 7.95 inches

For a diameter of 0.6 inches: (41.0 kips x 1,200 inches) / (0.217 sq.in. x 28,500 ksi) = 7.95 inches

***Notably, both the 0.5 and 0.6 diameters exhibit the same Average Elongation.***
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The Post-Tensioning Institute recommends maintaining an acceptable elongation range of plus/minus 7% of the Average Tendon Elongation for unbonded post-tensioning tendons.

Minimum Acceptable Elongation = 93% of Avg. Elongation = 0.93 x (Avg.El.)

Maximum Acceptable Elongation = 107% of Avg. Elongation = 1.07 x (Avg.El.)