Analysis of Short-Term Prestress Losses in Post-tensioned Structures Using Smart Strands

International Journal of Concrete Structures and Materials

Table 7 Comparison of the modulus of elasticity of concrete.

Provision	Formula^a	Modulus of elasticity (MPa)
Provision	Formula^a	Full-scale specimen [ratio (%)]	Bridge A [ratio (%)]	Bridge B [ratio (%)]
KCI (2012)	\(\begin{gathered} E_{c} = 0.077m_{c}^{1.5} \sqrt[3]{{f_{cu} }} \hfill \\ \quad \, = 8500\sqrt[3]{{f_{cu} }} \hfill \\ \end{gathered}\) \(f_{cu} = f_{ck} + \Lambda f\)	27,537 [100]	34,351 [100]	37,519 [100]
ACI 318 (2019)	\(\begin{gathered} E_{c} = w_{c}^{1.5} 0.043\sqrt {f_{c}^{\prime } } \hfill \\ \quad \, = 4700\sqrt {f_{c}^{\prime } } \hfill \\ \end{gathered}\)	25,743 [93.5]	36,406 [106.0]	42,038 [112.0]
Eurocode 2 (CEN, 2004)	\(E_{c} = 22,000\left( {f_{cm} /10} \right)^{0.3}\) \(f_{cm} = f_{ck} + 8\)	32,837 [119.2]	39,100 [113.8]	42,244 [112.6]

^a\(E_{c}\) in MPa, \(m_{c}\) and \(w_{c}\): unit weight of concrete with 23 kN/m³ for normal-weight concrete, \(f_{cu}\) and \(f_{cm}\): mean value of compressive strength, \(f_{ck}\) and \(f_{c}^{\prime }\): specified compressive strength, \(\Delta f\) = 4 and 6 MPa for \(f_{ck}\) ≤ 40 MPa and \(f_{ck}\) ≥ 60 MPa, respectively, and linear interpolation for 40 < \(f_{ck}\) < 60 MPa.