Elastic Shortening Loss in Pretensioning
Mediumlosseselastic shortening
Use the pretensioning elastic-shortening approximation Δfp = (Ep/Eci)·fcgp. Prestressing steel modulus Ep = 195 GPa; concrete modulus at transfer Eci = 30 GPa; concrete compression at the tendon centroid fcgp = 6 MPa. What is the stress loss Δfp?
- A33.4 MPa
- B0.92 MPa
- C6.5 MPa
- D39 MPa
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Answer: D. 39 MPa
Δfp = (Ep/Eci)·fcgp. Ep/Eci = 195/30 = 6.5 (GPa cancel). Δfp = 6.5(6) = 39 MPa. Check: concrete strain 6/30,000 = 0.0002 times Ep = 195,000 MPa gives 39 MPa. 33.4 MPa uses a later-age modulus (35 GPa) instead of the transfer modulus Eci. 0.92 MPa inverts the ratio (30/195). 6.5 MPa is just the modulus ratio, forgetting to multiply by fcgp.
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