Recently, a concrete contractor called me to find out the volume of our unbonded post-tensioning system within an elevated concrete deck.  He wanted to find out how much concrete was NOT used due to the volume-displacement from the post-tensioning tendons.

For the sake of simplicity, the following calculation shows the volume of 0.5″ Unbonded PT within a flat-plate concrete structure.

Known Values:

1. Diameter of Unbonded PT = D = 0.5 inches
2. Weight of PT Strand = w = 0.52 pounds per foot
3. Length of PT Anchor = L = 2.50 inches
4. Height of PT Anchor = H = 5.25 inches
5. Width of PT Anchor = W = approx. 1.25 inch

Assumptions:

1. Area of Concrete = A = 100,000 square feet (or 11,111 sq.yd.)
2. Thickness of Concrete = t = 8.0 inches (or 0.222 yd.)
3. PT Quantity = 0.8 pounds of PT per square foot of concrete
4. PT Anchor per Foot of Strand= 1 anchor per 50 feet
5. Thickness of PT Sheathing = T = 50 ml (0r 0.05 inch)

Calculations:

Concrete…

• Volume = A x t = (11,111 sq.yd.) x (0.222 yd.) =  2,469 cubic yards

Post-Tensioning Strand…

• Diameter of 1 Coated Strand = 0.50″ + 0.05″ + 0.05″ = 0.60 inches (or 0.01667 yards)
• Area of 1 Strand = (pi) x (radius x radius) = (3.14159) x (0.01667 /2) x (0.01667 /2) = 0.0002 cubic yards
• Total Length of all Strand = (100,000 sq.ft. x 0.80 lbs/sq.ft) / 0.52 lb/ft = 163,462 feet (or 54,487 yards)
• Volume of all Strand = (0.0002) x (54,487 yards) = 11.89 cubic yards

Post-Tensioning Anchors…

• Volume of 1 Anchor = 2.5″ x 5.25″ x 1.25″ = 16.41 cu.inches (or 0.00035 cubic yards)
• Number of Anchors = (163,462 feet) x (1 anchor per 50 feet) = 3,269 anchors
• Volume of all Anchors = (0.00035 cu.yds) x 3,269 = 1.15 cubic yard

Other items that displace concrete (but not factored in the analysis)…

• PT Support Chairs
• PT Support Rebar
• PT Pocket Former (eventually filled with grouted)
• Rebar (mild steel)
• Other Embeds

Assuming concrete costs $100 per cubic yard, the concrete contractor could potentially reduce his bid by 13 cubic yard of concrete (or $1,300) for this 100,000 sq.ft. concrete deck.

– Neel Khosa, Vice President, AMSYSCO

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