Filling with wood provides virtually no stiffness. With the same deformation, almost all the load will be absorbed by the steel beam, which, in terms of material, has about 40 times greater stiffness than wood. As a thought experiment: place a rubber band on a steel ruler and subject the sandwich to tensile stress. Which material takes the majority of the load?
If you are to receive any help from the wooden studs at all, they must interact with the steel beam, i.e., be "connected" to each other and not just "wedged in". There is a significant difference in strength between steel and wood, so any contribution here is likely negligible.
Well, one can imagine that it becomes stiffer BUT when the beam breaks, the force is such that it doesn't matter what the dimension is or the number of pieces of wood in between. However, this is now speculating the worst-case scenario that it just snaps all at once ^^
but my theory in my little pink world is that one must calculate the load-bearing capacity separately for the beam (HEA from the size) and wood (C16 C24 C30) and then span and load that want to play are also considered... so one can be meticulous with the fastening of the woodwork... the use of a bolt gun and how much the holes in the beam affect it, etc.
there's a lot
but my theory in my little pink world is that one must calculate the load-bearing capacity separately for the beam (HEA from the size) and wood (C16 C24 C30) and then span and load that want to play are also considered... so one can be meticulous with the fastening of the woodwork... the use of a bolt gun and how much the holes in the beam affect it, etc.
there's a lot
No. You are thinking incorrectly. The fastening of the materials into each other has negligible significance in this case. If it were a sandwich construction, it would be important, but that is not the case.
The deflection for a given geometry is directly proportional to the material's modulus of elasticity (E-modulus). The E-modulus is a material constant for a material's stiffness. Steel has about 210 GPa, and wood somewhere around 5 GPa. That's a difference by a factor of 40. Now, the different materials do indeed have different geometries, but that has little significance for the reasoning. If we combine wood with steel according to the first sketch, the load will cause the exact same deformation, won't it? After all, they are joined together. The stress in a loaded construction with a given deformation is directly dependent on the E-modulus. This is called Hooke's Law. This leads to the stress in the steel being so much higher that it takes almost the entire load, and the wood carries almost no load at all. With such low stress in the wood, the stiffness of the total construction is barely affected at all by adding wood.
The deflection for a given geometry is directly proportional to the material's modulus of elasticity (E-modulus). The E-modulus is a material constant for a material's stiffness. Steel has about 210 GPa, and wood somewhere around 5 GPa. That's a difference by a factor of 40. Now, the different materials do indeed have different geometries, but that has little significance for the reasoning. If we combine wood with steel according to the first sketch, the load will cause the exact same deformation, won't it? After all, they are joined together. The stress in a loaded construction with a given deformation is directly dependent on the E-modulus. This is called Hooke's Law. This leads to the stress in the steel being so much higher that it takes almost the entire load, and the wood carries almost no load at all. With such low stress in the wood, the stiffness of the total construction is barely affected at all by adding wood.
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