When determining the stress and displacement of a coupled linear support, in which concrete as a linear highly elastic material with the property of aging and several types of steel, which are linear elastic materials, are combined, the functions $K^*_h(t,\tau)$ and $R^*_h(t,\tau)$ $(h=1,2)$, the so-called dimensionless functions of the transformation of the coupled section, which refer to an arbitrary section of the support. The paper examined the properties of these functions, on the basis of which it was concluded that a homogeneous material can be joined to a connected cross-section, whose properties depend on the properties of all the materials participating in the cross-section and on the geometric characteristics-risks of that cross-section. This material has, like concrete, a variable modulus of elasticity and viscoelasticity and aging properties, but all these properties are less pronounced compared to the corresponding properties of concrete, which is a consequence of the presence of steel cross-sections. In the general case, the dimensionless transformation functions of the coupled section lie in the regions bounded by the functions $K^*$ and $R^*$, which describe the properties of concrete, and the function $1^*$, which describes the properties of steel. In the special case of the section, where the presence of steel parts is pronounced, these functions are located immediately next to the function $1^*$, which represents Hooke's law; in sections where the presence of a concrete part is pronounced, they are located immediately next to the functions $K^*$ and $R^*$, which describe the properties of concrete.