BMD of portal frame

[dccd]

Is it possible to solve this using the free body diagram? Or anyone can show how to solve this ? The moment at joint D due to 8F is 16FL, due to 4F is 4FL. Any other simple way to solve this without using the moment distribution method with considering the relative stiffness?

 

[phamENG]

You may be able to come up with a very approximate solution using superposition and some other assumptions, but moment distribution or slope/deflection would be the best way to approach it for anything like accuracy.

Approximate:
Solve two frames, one with the 8F load using the basis of symmetry to evenly distribute the loading (or you can get fancy and consider the axial stiffness of the beam) and one from the 4F load on a beam with fixed ends. Again, you can get more accurate by assuming they're rotational springs based on the stiffness of the columns. Then superimpose the load effects (BMD, SFD, etc.) and sum them to get peak load effects.

Another approximation method would be to use the K factor nomographs in the steel manual appendix which takes relative stiffness of frame members into account.

 

[1503-44]

No need to get too fancy, if you can accept a conservative answer.
It would be good to know the moments of inertia for each element.