20.1.1 Development of Strength with Time

The compressive strength of concrete f_cm at an age of t days depends on the type of cement, temperature and curing conditions. It could be estimated as

$$\beta_{{\mathrm{cc}}}^{}$$ (20.1)

in which f_cm28 is the mean compressive strength at the age of twenty-eight days and $\beta_{{\mathrm{cc}}}^{}$ is a time dependent coefficient whose expression is

$$\beta_{{\mathrm{cc}}}^{} \left(\vphantom{ s \left( 1 - \sqrt{ \frac{ 28 }{ t_{\mathrm{eq}} } } \; \right) }\right. \left(\vphantom{ 1 - \sqrt{ \frac{ 28 }{ t_{\mathrm{eq}} } } \; }\right. \sqrt{{ \frac{ 28 }{ t_{\mathrm{eq}} } }} \left.\vphantom{ 1 - \sqrt{ \frac{ 28 }{ t_{\mathrm{eq}} } } \; }\right) \left.\vphantom{ s \left( 1 - \sqrt{ \frac{ 28 }{ t_{\mathrm{eq}} } } \; \right) }\right)$$ (20.2)

Coefficient s depends on the type of cement [Table 20.1].
Parameter t_eq is the equivalent age of concrete, defined as

$$\int_{{0}}^{{t}} \left(\vphantom{ \frac{ 1 }{ T_{\mathrm{ref}} } - \frac{ 1 }{ T(\tau) } }\right. {\frac{{ 1 }}{{ T_{\mathrm{ref}} }}} {\frac{{ 1 }}{{ T(\tau) }}} \left.\vphantom{ \frac{ 1 }{ T_{\mathrm{ref}} } - \frac{ 1 }{ T(\tau) } }\right)$$ (20.3)

in which T($\tau$) is the temperature of concrete at an age of $\tau$ days, T_ref is the reference temperature equals to 293 K, c_A is the Arrhenius constant equals to 4000 K^-1 . The characteristic value of the tensile strength f_tk at an age of t days may be estimated from

$$\left(\vphantom{ \frac{ f_{\mathrm{ck}}(t) }{ f_{\mathrm{cko}} } }\right. {\frac{{ f_{\mathrm{ck}}(t) }}{{ f_{\mathrm{cko}} }}} \left.\vphantom{ \frac{ f_{\mathrm{ck}}(t) }{ f_{\mathrm{cko}} } }\right)^{{\!\!\frac{2}{3}}}_{}$$ (20.4)

with f_{tko, m} = 1.4 MPa, f_cko = 10 MPa and where f_ck is the characteristic concrete compressive strength defined as

$$\Delta$$ (20.5)

where $\Delta$f = 8 MPa and f_cm is the mean compressive strength of concrete in (20.1).