  In 2005, Liu et al. calculated the dimensionality of the intersection of
Sierpinski carpet and a straight line with rational slope in the sense of
Lebesgue measure.Sierpinski carpet is a self-similar set in two-dimensional
planes obtained by an iterative function system, so each layer has the same
structure. While the Sierpinski carpet set with Moran structure is the limit
set obtained by the action of two iterative function systems in the
two-dimensional plane, which we denote as ~$F_{\sigma}$~. And the structure of
each layer may be different, controlled by 0,1 sequence ~$\sigma$~ and
controlled by the set. In this paper, the upper and lower box dimensions of the
set ~$F_{\sigma}$~ and the straight line ~$L_{a}$~ with rational slope are
calculated, where ~$a$~ is the intercept of the straight line. In addition, we
consider some related problem. The main difficulty in the research is that the
structure of each layer of the set ~$F_{\sigma}$~ may be different, so the
structure of each layer needs to be considered with the help of the sequence
~$\sigma$~ in the calculation process.
