For a pre-tensioned prestressed concrete beam, the prestress loss due to elastic shortening Delta f_ pES where n = E_p / E_c and f_ cgp is the concrete stress at the centroid of prestressing steel at transfer is:

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Architecture Engineering QUESTION #2339

Question 1

For a pre-tensioned prestressed concrete beam, the prestress loss due to elastic shortening \(\Delta f_{pES}\) where \(n = E_p / E_c\) and \(f_{cgp}\) is the concrete stress at the centroid of prestressing steel at transfer is:

\(\Delta f_{pES} = \dfrac{E_c}{E_p} \cdot f_{cgp}\)
\(\Delta f_{pES} = n \cdot f_{cgp}\)✔️
\(\Delta f_{pES} = \dfrac{f_{cgp}}{n}\)
\(\Delta f_{pES} = \dfrac{n \cdot f_{cgp}}{2}\)

Correct Answer Explanation

Elastic shortening loss: \(\Delta f_{pES} = n \cdot f_{cgp}\) where \(n = \dfrac{E_p}{E_c}\). At transfer, the concrete compresses elastically by strain \(\varepsilon_c = f_{cgp}/E_c\). The bonded prestressing steel undergoes the same strain, losing stress \(\Delta f_{pES} = E_p \cdot \varepsilon_c = \dfrac{E_p}{E_c} \cdot f_{cgp} = n \cdot f_{cgp}\).

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