Age Adjusted Effective Modulus (AAEM) Method

Age adjusted effective modulus method is implemented to keep track of the time-dependent material effects of concrete members [2, 3]. This method converts complex creep and shrinkage behavior to a linear elastic problem and hence, it provides an approximate estimate to time-dependent material effects. The AAEM model produces reasonable results for service-stress levels but it may not be recommended for structures with high creep sensitivity.

The second analysis for each stage is carried out to account for time-dependent material effects. If stiffness changes of concrete members is considered in this analysis, the program updates stiffness of concrete members in such a way that an age-adjusted effective modulus is substituted for them. The age-adjusted modulus calculated at time

\hat{t}

for a member loaded at

t_{o}

is expressed as follows:

{\bar{E}}_{c} (\hat{t}, t_{o}) = \frac{E_{c} (t_{o})}{1 + χ (\hat{t}, t_{0}) φ (\hat{t}, t_{o})}

where

$E_{c} (t_{o})$	=	concrete elastic modulus at time $t_{o}$
$φ (\hat{t}, t_{o})$	=	creep coefficient at time $\hat{t}$ for a member loaded at $t_{o}$
$χ (\hat{t}, t_{0})$	=	aging coefficient at time $\hat{t}$ for a member loaded at $t_{o}$

The aging factor $χ (\hat{t}, t_{0})$ is a dimensionless multiplier (smaller than 1) applied to $φ (\hat{t}, t_{o})$ . It is intended to describe the effects of stress changes in creep-related deformations during the period of $(\hat{t}, t_{o})$ .

It should be noted that age-adjusted stiffness modulus for concrete members is included only if stiffness changes are considered in analysis. Otherwise, the program uses nominal elastic modulus for concrete members.