 peteroznewman
Subscriber
When you say a pair of beams, do you mean they will be parallel with 6 feet between them? Is there a hydraulic cylinder on each beam? Is there a lifting cable on each beam? It would be worth sketching out a 3D concept to discuss further.
To get an idea of the size of a single beam needed to lift 1 ton (2000 lb), you can do a hand calculation, which you can also do with an online calculator such as this one: https://skyciv.com/free-beam-calculator/
Here is the output data for Reaction Forces, Shear Forces and Bending Moments.   Here is another website that gives you to formula to calculate the stress in a beam if you know the Bending Moment M. https://mechanicalc.com/reference/beam-analysis
Maximum Bending Stress = Mc/I where c half the depth of the beam cross-section and I is the beam area moment of inertia about the axis used to bend the beam, which would be X-X if you stand the beam upright as shown below.
Here is a website that has Standard Steel I-Beam Sizes: https://amesweb.info/Profiles/Standard-Steel-I-Beam-Sizes-Chart.aspx  For example, if you choose the row highlighted, the value of I is 24.7 in^4 and the value of c is 5 inch, which is half the depth. Therefore you can calculate the bending stress is 22000*5/24.7 = 4,453 psi For a long beam, the shear stress is going to be smaller than the bending stress.
Next you need to know the strength of the material. You can look that up on this site: http://www.matweb.com/
A common structural steel material is ASTM A36 that has a tensile yield strength of 36,300 psi. Now you don't want your beam to reach that value of stress. You apply a Factor of Safety (FS) to divide that down to a smaller number. Let's use FS = 5. For a beam made out of A36 steel, the maximum stress must be less than 36,300/5 = 7,260 psi. The beam selected above with the load and supports specified meets this requirement.
There is a lot more to do before you can know that a design can safely lift a load. There are regulatory requirements on equipment to lift loads in the workplace. If you are in the USA, see for example https://www.osha.gov/cranes-derricks/ 