You have to define contact between those beams, otherwise their collision won’t be detected. Ansys, like other advanced FEA programs, has contact elements that can be used to model contact of beams.

Thank you for your response! I have tried to search for this but still do not know how I would do this. Do you have any idea how I could define the contact?
I am using SpaceClaim and then importing into Ansys Mechanical
Thanks!

You would need to manually define the contact by selecting the contact/target surfaces, and applying the contact behavior etc. You may need to refine the load time steeping to detect the contact. With that being said something may be incorrect with the model or design. The model may be improperly constrained allowing for excess deformation. How do your deflections compare to hand calculations? Are your reactions consistent with what you would expect to see? If your results are meeting the expectation of your hand calculations there may be issues with the design itself. The image looks like some sort of truss structure deflection in the members should be low enough that the beam should not intersect or rub. If they do you no longer have a truss. I would look to add additional gap between members to avoid this behavior altogether.