I'm an amateur at engineering, working more on musical instruments, and I'm often in confusion regarding what exactly constitutes stiffness of a beam for a load applied on it so it could resist deformation, for example on googling for a rectangular beam I get the basic definition that it is proportional to breadth × square of height. But the moment of inertia is proportional to breadth × cube of height/12.
And for a triangular beam there's even less information (think the general shape of a guitar brace with the base of the triangle taking the load and the point hanging freely downwards).
Please give me some simple formulas to calculate both if possible, the load will not be uniformly distributed on the beam but for the present consideration, the load may be applied either downward at the middle of the beam (like a violin) or pulling the beam upwards (like an acoustic guitar). If possible please provide both scenarios.
I'd like to add pictures of the forces acting on the bracing (or beam if you will) so you could get a better picture of what stiffness I'm seeking. The red colour defines the beam and the blue is the location where the load will be applied on the beam, the arrow pointing towards or away from the blue marker shows the direction of the force being applied to the beam