It sounds like what you're looking for is a program like Sketchup where you can build a 3D model of your structure and then press an Analyze! button and have it give you feedback about the general structural integrity. There is no such program.
First of all, any software package capable of doing anything more sophisticated than a single beam or so is probably going to be too complicated to use without training or experience.
But more importantly, you need to know the kinds of analysis you want to do for the program to be useful and for you to get the answers your looking for out of it. E.g.: Do you want to check for lateral torsional buckling? Euler buckling? Block shear failure? Have you modeled the bracing points accurately? What kind of loads have you applied and in what direction? What assumptions did you make when modeling contact points with the environment? Is it important that you model the stress in the fasteners?
You can certainly find tools that will do a specific set of calculations, as @Ecnerwal has linked to. But those are very narrowly focused and require that you already know the type of calculation you're interested in. Also they probably require you to simplify the problem to focus on the aspect you're interested in.
Side Note About This Project
I think this King-sized loft bed is an interesting idea and I've been enjoying following your progress, but I am concerned that this may be too big a project to bit off for a new DIYer. A king-sized bed with a mattress + people could be very heavy (I would plan on at least 1000 lbs of weight... preferably more). Plus raising it off the ground adds a host of additional technical challenges and safety risks.
If you do want to see this project through, let me offer these general stability suggestions:
- Plan for a lot of weight. More than you think is reasonable. Some day your teenage kids are going to climb up there with all their friends and their 20 lb. book bags and your 2 golden retrievers.
- In addition to the gravity weight, think about how the structure can collapse in a trapezoid shape. For a cube-shaped structure like this, there are 3 possible trapezoid collapses. (Diagonal bracing in all three directions is probably the easiest way.)
- I would not rely too much (or at all) on the walls for support unless you know what's back there. A standard 2x4 framed wall is not going to be remotely strong enough, even for bracing against sideways collapse.
- After you've finished, check the joints regularly for several months until you're sure that the piece isn't pulling itself apart.
