In this paper, we demonstrate that with a set of bases weakly satisfying the governing equation of an engineering problem on fictitious subdomains, known here as equilibrated basis functions (EqBFs), a variety of structural problems may be solved with ease of domain decomposition/discretization. Such a feature enables us to select the sub-domains freely (in contrast to the finite element method for instance). The EqBFs are constructed using Chebyshev polynomials and through a weighted residual integration over fictitious rectangular subdomains. Through some numerical examples, it is shown that the method performs very well even in comparison with efficient existing methods.