Design of an I Beam used in a Crane
We assume that the I beam can be modeled as a cantilever beam fixed at the left end with a concentrated load at the end.  
Using the 7th edition of Roark's Formulas for Stress and Strain we will make use of two tables:
The I beam cross section can be located in Appendix 1, Table A.1.
Table 8.1, case 1a provides the shear, stress, and deflection formulas for our load and support condition.
Both cases get loaded into TK Solver using the on-line menuing system.
We then enter the data for the cross section and the beam. After solving we get the following results.

Here is the cross section plot.  
Here are the deflection and stress plots.  
We find that the stress is too high for the type of material we have in mind and the deflection is too great. One way to reduce the stress is to change the cross section. In this case let us assume that we are prepared to change the depth of the beam cross section (variable t1d).  
At this point we will change the value of stress (variable sty) from the calculated value of -107166 psi to a new value of –50000 psi by entering it in the input column. We then go to the status column for variable t1d (beam cross section depth) and type a G to assign a guess to that variable. When we solve, new results are immediately available.  
Here is the updated Variable Sheet.  
Here is the new cross-section plot.  

Here are the new stress and deflection plots.