The aim of this article is to analyze the two-phase peridynamic Euler-Bernoulli beams for two general cases, i.e., statically determinate and indeterminate beams, under different loading types, utilizing the Green’s function method. To achieve this goal, three different types of Green’s functions are extracted according to the beams’ determinacy and loading type. The first kind of Green’s function is introduced for static analysis of determinate beams under distributed loading in absence of concentrated load. In this case, the moment function of the beam is known, and the first derivative of the curvature is continuous. Based on these two facts, the Green’s function is straightforwardly obtained by solving the second-order differential equation together with two boundary conditions. However, the second kind of Green’s function which attained for indeterminate beams (with unknown moment function) under distributed loading (still in absence of concentrated external load which guarantees the continuity of the first derivative of the curvature) depends on the sixth-order differential equation together with six boundary conditions. It should be noted that the analysis of indeterminate two-phase peridynamic Euler-Bernoulli beams is performed for the first time in this article. The third and the last kind of Green’s function which could be used for the both determinate and indeterminate beams, is obtained for the case of presence of concentrated load. In this case, the Green’s function is obtained by solving the two sixth-order differential equations together with twelve boundary conditions. The above-mentioned three kinds of Green’s functions are thoroughly illustrated in the article for two determinate beams (clamped-free and simple-simple), and two indeterminate beams (simple-clamped and clamped-clamped). In all beams, the closed-form expressions are obtained for the curvature and the deflection functions. Moreover, the series solution is numerically performed for simple-simple beam under both distributed and concentrated loading for verification purposes. Additionally, for further verification of the analytical results obtained by the Green’s functions, all four beams examined in the paper, i.e., SS, CS, CC and CF beams, are also numerically analyzed using the finite difference method (FDM). The experimental order of convergence for proposed FDM is also obtained equal to almost 2, for all four beams. Besides, Compared to the classical Euler-Bernoulli beam model, the peridynamic theory models the beam with more softening effect, although the amount of this softening can be calibrated with two parameters defined in the article.

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