The `join` method is unable to create beams with discontinuous values of elastic modulus.

[mvg2002]

The join method in the Beam module joins two beams that can have different Elastic modulus (E) and second moments (I). In the docstring it says: "This method can be used to form beams having Discontinuous values of Elastic modulus or Second moment."

This is not the case. The method can not be used for beams with different Elastic modulus. This is visible in the code:

    def join(self, beam, via="fixed"):
        """
        This method joins two beams to make a new composite beam system.
        Passed Beam class instance is attached to the right end of calling
        object. This method can be used to form beams having Discontinuous
        values of Elastic modulus or Second moment.

        Parameters
        ==========
        beam : Beam class object
            The Beam object which would be connected to the right of calling
            object.
        via : String
            States the way two Beam object would get connected
            - For axially fixed Beams, via="fixed"
            - For Beams connected via rotaion hinge, via="hinge"

        Examples
        ========
        There is a cantilever beam of length 4 meters. For first 2 meters
        its moment of inertia is `1.5*I` and `I` for the other end.
        A pointload of magnitude 4 N is applied from the top at its free end.

        >>> from sympy.physics.continuum_mechanics.beam import Beam
        >>> from sympy import symbols
        >>> E, I = symbols('E, I')
        >>> R1, R2 = symbols('R1, R2')
        >>> b1 = Beam(2, E, 1.5*I)
        >>> b2 = Beam(2, E, I)
        >>> b = b1.join(b2, "fixed")
        >>> b.apply_load(20, 4, -1)
        >>> b.apply_load(R1, 0, -1)
        >>> b.apply_load(R2, 0, -2)
        >>> b.bc_slope = [(0, 0)]
        >>> b.bc_deflection = [(0, 0)]
        >>> b.solve_for_reaction_loads(R1, R2)
        >>> b.load
        80*SingularityFunction(x, 0, -2) - 20*SingularityFunction(x, 0, -1) + 20*SingularityFunction(x, 4, -1)
        >>> b.slope()
        (-((-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))/I + 120/I)/E + 80.0/(E*I))*SingularityFunction(x, 2, 0)
        - 0.666666666666667*(-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))*SingularityFunction(x, 0, 0)/(E*I)
        + 0.666666666666667*(-80*SingularityFunction(x, 0, 1) + 10*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 4, 2))*SingularityFunction(x, 2, 0)/(E*I)
        """
        x = self.variable
        E = self.elastic_modulus
        new_length = self.length + beam.length
        if self.second_moment != beam.second_moment:
            new_second_moment = Piecewise((self.second_moment, x<=self.length),
                                    (beam.second_moment, x<=new_length))
        else:
            new_second_moment = self.second_moment

        if via == "fixed":
            new_beam = Beam(new_length, E, new_second_moment, x)
            new_beam._joined_beam = True
            return new_beam

        if via == "hinge":
            new_beam = Beam(new_length, E, new_second_moment, x)
            new_beam._joined_beam = True
            new_beam.apply_rotation_hinge(self.length)
            return new_beam

In the second line it says E = self.elastic_modulus. This E is equal to the elastic modulus of only one of the joined beams and it is placed as the Elastic modulus for the whole new beam.