Prestressed Concrete Calculator
Calculate prestress losses and tendon force for prestressed concrete beam design. Enter values for instant results with step-by-step formulas.
Formula
Total Loss = ES + CR + SH + RE
Where ES is elastic shortening loss, CR is creep loss, SH is shrinkage loss, and RE is steel relaxation loss, all in ksi. The effective prestress fpe equals the initial prestress fpi minus the total loss. Each loss component is calculated based on material properties, section geometry, and environmental conditions.
Worked Examples
Example 1: Bridge Girder Prestress Loss Calculation
Problem: A pretensioned bridge girder has 20 x 0.5-in strands (Aps=3.06 sq in) stressed to 189 ksi. Concrete section: Ac=560 sq in, I=125,000 in4, eccentricity=12 in, fc=6000 psi.
Solution: Initial Force Pi = 189 x 3.06 = 578.3 kips\n\nElastic Shortening:\nEci = 57 x sqrt(4800) = 3,950 ksi\nnp = 28,500 / 3,950 = 7.22\nfcgp = 578.3/560 + 578.3 x 12 x 12/125,000 = 1.033 + 0.667 = 1.700 ksi\nES loss = 7.22 x 1.700 / (1 + 7.22 x 3.06 x (1/560 + 144/125,000)) = 11.3 ksi\n\nCreep loss = ~22.3 ksi | Shrinkage = 14.25 ksi | Relaxation = 4.7 ksi
Result: Total losses: 52.6 ksi (27.8%) | Effective prestress: 136.4 ksi | Effective force: 417.4 kips
Example 2: Parking Garage Double-Tee Beam
Problem: A double-tee beam with 12 x 0.5-in strands (Aps=1.836 sq in) at fpi=189 ksi. Section: Ac=400 sq in, I=45,000 in4, e=8 in, fc=5000 psi.
Solution: Pi = 189 x 1.836 = 346.9 kips\n\nElastic Shortening:\nEci = 57 x sqrt(4000) = 3,604 ksi, np = 7.91\nfcgp = 346.9/400 + 346.9 x 64/45,000 = 0.867 + 0.493 = 1.360 ksi\nES loss = 9.7 ksi\n\nCreep = 18.9 ksi | Shrinkage = 14.25 ksi | Relaxation = 4.7 ksi
Result: Total losses: 47.6 ksi (25.2%) | Effective prestress: 141.4 ksi | Effective force: 259.6 kips
Frequently Asked Questions
What is prestressed concrete and how does it differ from reinforced concrete?
Prestressed concrete is a structural technique where high-strength steel tendons are tensioned before or after the concrete is cast, introducing compressive stresses into the concrete that counteract the tensile stresses from applied loads. Unlike conventional reinforced concrete which allows cracking under service loads and relies on steel reinforcement to carry tension, prestressed concrete keeps the entire cross-section in compression under normal loading conditions. This means prestressed members can span longer distances, use smaller cross-sections, carry heavier loads, and remain crack-free under service conditions. The two main methods are pre-tensioning (tendons stressed before concrete is poured) and post-tensioning (tendons stressed after concrete has hardened).
What causes elastic shortening loss in prestressed concrete?
Elastic shortening occurs immediately when the prestressing force is transferred to the concrete member. As the tendons compress the concrete, the concrete shortens elastically, and the bonded tendons shorten by the same amount, reducing the tendon stress. The magnitude of elastic shortening loss depends on the ratio of the steel modulus to the concrete modulus (modular ratio), the initial concrete stress at the centroid of the tendons, and the tendon eccentricity. For pretensioned members with multiple tendons released sequentially, the average elastic shortening loss equals half the loss calculated for simultaneous release. For post-tensioned members, elastic shortening loss can be partially compensated by overstressing the tendons during jacking.
What are the allowable stress limits for prestressed concrete at transfer and service?
The ACI 318 building code specifies allowable stress limits at two critical stages: at transfer (when prestress is applied to the young concrete) and at service (under full dead and live loads on the hardened concrete). At transfer, the maximum compressive stress is limited to 0.60 times the concrete strength at transfer (typically 0.8 times the 28-day strength), and the maximum tensile stress is limited to 3 times the square root of the transfer strength in psi units, or 6 times the square root if the tensile zone has bonded reinforcement. At service under sustained loads, the compressive stress limit is 0.45 times the 28-day concrete strength, and under total loads it is 0.60 times the 28-day strength.
How do I calculate the amount of concrete needed for a project?
Calculate volume in cubic feet (length x width x depth), then divide by 27 to convert to cubic yards. Add 5-10% for waste and spillage. One cubic yard of concrete covers 81 square feet at 4 inches thick.
What are the standard concrete mix ratios?
Common ratios by volume are 1:2:3 (cement:sand:gravel) for general purpose, 1:1.5:3 for structural work, and 1:2:4 for foundations. The water-to-cement ratio should be 0.45-0.55 for optimal strength. Lower water content produces stronger concrete.
What is the correct rebar spacing for concrete slabs?
Standard residential slabs use #3 or #4 rebar on 18-inch centers both ways, placed at mid-depth. Driveways and heavy-load areas use #4 rebar on 12-inch centers. Rebar should have 2-3 inches of concrete cover on the bottom. Wire mesh (6x6 W1.4xW1.4) is an alternative for light-duty slabs.