The correct answer is: D. (1 – C) mf + eE
Creep is the time-dependent deformation of a material under sustained load. Shrinkage is the decrease in volume of a material due to drying. The combined effect of creep and shrinkage is the deformation of a material due to both creep and shrinkage.
The creep coefficient, $C$, is a dimensionless number that represents the amount of creep that a material will experience. The original pre-stress in concrete, $f$, is the stress that is applied to the concrete before it starts to creep. The modular ratio, $m$, is the ratio of the Young’s modulus of steel to the Young’s modulus of concrete. The Young’s modulus of steel, $E$, is the elastic modulus of steel. The shrinkage strain, $e$, is the strain that is caused by shrinkage.
The combined effect of creep and shrinkage is given by the following equation:
$$\epsilon_{c + s} = (1 – C) mf + eE$$
where:
- $\epsilon_{c + s}$ is the combined effect of creep and shrinkage
- $C$ is the creep coefficient
- $f$ is the original pre-stress in concrete
- $m$ is the modular ratio
- $E$ is the Young’s modulus of steel
- $e$ is the shrinkage strain
Option A is incorrect because it does not include the creep coefficient, $C$. Option B is incorrect because it does not include the shrinkage strain, $e$. Option C is incorrect because it has the wrong sign in front of the shrinkage strain, $e$.